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Tiny changes in the weight of the vacuum contained in high-temperature superconductors can be measured using a high-precision balance. These structures can absorb or expel vacuum energy depending on their normal or superconductive status. In the measurement, the state of the sample is modulated into two states, normal and superconducting, with a reversible transition achieved by periodically varying the temperature of the thermal bath. The paper provides the current status of the experiment, highlighting the study and construction of the balance with its thermal modulation and cryogenic systems, and the investigation of high-temperature superconductor candidates.","abstract_source_suggest":{"input":"WSP"}},{"value":"Exploring the complex connection between vacuum fluctuations and gravitational field is the goal of Archimedes experiment. Tiny changes in the weight of the vacuum contained in high-temperature superconductors can be measured using a high-precision balance. These structures can absorb or expel vacuum energy depending on their normal or superconductive status. In the measurement, the state of the sample is modulated into two states, normal and superconducting, with a reversible transition achieved by periodically varying the temperature of the thermal bath. The paper provides the current status of the experiment, highlighting the study and construction of the balance with its thermal modulation and cryogenic systems, and the investigation of high-temperature superconductor candidates."}],"titles":[{"source":"WSP","title":"Weighing the vacuum with the Archimedes experiment"},{"source":"submitter","title":"Weighing the vacuum with the Archimedes Experiment"}],"imprints":[{"date":"2025-02-03"}],"curated":true},"links":{"bibtex":"https://inspirehep.net/api/literature/2875125?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/2875125?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/2875125?format=latex-us","json":"https://inspirehep.net/api/literature/2875125?format=json","json-expanded":"https://inspirehep.net/api/literature/2875125?format=json-expanded","cv":"https://inspirehep.net/api/literature/2875125?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A2875125"},"id":"2875125"},{"created":"2018-10-25T00:00:00+00:00","updated":"2025-03-14T17:18:48.393618+00:00","metadata":{"documents":[{"filename":"PoS(GRASS2018)020.pdf","attachment":{"content":"P\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nArchimedes experiment: weighing the vacuum\n\nS. Avinoa,b, A. Bastic,E. Callonid,b, S. Caprarae, f ,M. De Laurentis∗d,b,R. De Rosad,b,L.\nErricod,b, G. Espositob, F. Frasconic, G. Gagliardia,b, M. Grillie, f , E. Majorana f , G. P.\nPeped,b, S. Petrarcae, f , P. Puppo f , P. Rapagnanie, f , F. Riccie, f , L. Rosad,b, C.\nRovellig,h, P. Ruggii, N. L. Sainie, f , C. Stornaiolob, D. Stornaiuolod,b, F. Tafurid,b\n\nAuthor affiliation\na INO-CNR, Comprensorio Olivetti, Via Campi Flegrei 34-80078 Pozzuoli (NA), Italy\nb INFN Sezione di Napoli, Via Cintia Edificio 6, I-80126 Naples, Italy\nc INFN sezione Pisa, Largo Pontecorvo 1, I-56127 Pisa, Italy\nd Università Federico II Napoli, via Cinthia, I-80126, Naples, Italy\ne Università di Roma La Sapienza, Piazzale A. Moro, I-00185 Roma, Italy\nf INFN Sezione di Roma, Piazzale A. Moro, I-00185 Roma, Italy\ng Aix Marseille Université CNRS, CPT, UMR 7332, 13288 Marseille, France\nh Universitè de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France\ni European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy E-mail:\nmartina.delaurentis@na.infn.it\n\nArchimedes is an experiment devoted to measure the weight of zero point energy by weighing\na cascade of rigid Casimir cavities constituted by a layered type II superconductor, when the\nreflectivity of the cavities is modulated and thus the energy inside. In this paper the working\nprinciple of the experiment is presented and the results of the existing prototype are presented,\nshowing the torque sensitivity of about 10−11 Nm/\n\n√\nHz in the region of frequency from about\n\n50 mHz up two 150 mHz. Moreover the major upgrades needed to reach the desired final sensi-\ntivity are discussed.\n\nGRAvitational-waves Science&technology Symposium - GRASS2018\n1-2 March 2018\nPalazzo Moroni, Padova (Italy)\n\n∗Speaker.\n\nc© Copyright owned by the author(s) under the terms of the Creative Commons\nAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/\n\nmailto:martina.delaurentis@na.infn.it\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\n1. Introduction\n\nDoes the vacuum fluctuations gravitate or not? This is one of the oldest, unsolved question\nraised since the dawn of quantum mechanics [1]. Despite of the many theoretical investigations to\nexplore the motivations and consequences of assuming of discarding such hypothesis [2, 3], never a\ndirect experimental measurement has been carried out to investigate the weight of the vacuum. Few\nyears ago we proposed an experiment to test the interaction of vacuum fluctuations with gravity\nby weighing a suitable rigid Casimir cavity, being nowadays the Casimir effects recognized by the\nscientific community as a macroscopic manifestation of vacuum fluctuations [4, 5].\nThe name of the experiment, Archimedes, derives from the partial analogy that we found with the\nArchimedes force in the fluid when we studied the interaction of such type of cavity with the\ngravitational field on the earth under the hypothesis that the vacuum fluctuations interact with this\nfield and follows the strong equivalence principle: in fact it is found that the gravitational field\nexerts a force on the cavity equal to the weight of the vacuum modes expelled by the cavity. The\nanalogy is partial because the cavity follows the equivalence principle and falls with the gravita-\ntional acceleration [6].\n\nThe proposed experimental scheme to measure the Archimedes force of the vacuum was pro-\nvided considering the present small force detectors and the available superconductors materials of\ntype II, like YBCO or BSCOO. This kind of materials can be considered as natural cascade of\nCasimir cavities, being structured as multilayer of superconducting planes separated by dielectric\nplanes [7, 8]. By measuring the weight of the condensation energy of the layered-superconductor,\nwe will able to measure the weigh of the vacuum fluctuations. The order of magnitude of this force\nis expected of about 10−16 N. It can be measured by lock-in technique at modulation frequency of\nseveral mHz by inducing a periodic transitions from normal to superconducting state in the material\nby temperature modulation [6]. Being a very tiny force, an extremely sensitive balance, working\nat the temperature of about 100 K, is required. The Casimir cavities, i.e. two almost equivalent\nblocks of superconductor material which undergo modulate transition in thermal equilibrium with\nsurrounding temperature modulated vessel, will be suspended to the balance like in fig 1.\n\nTo point up eventual hindrances, a prototype of such a balance, working at room temperature,\nhas been realized. We describe it, illustrate the main results reached with it and discuss them with\nrespect to the final measurement.\n\n2. Experiment working principle\n\nAssuming that the pressure of the vacuum fluctuation follows the equivalence principle, the\nforce exerted by the gravitational field on a rigid Casimir cavity at rest on earth is directed upward\nand has been calculated to be [6, 9, 10]:\n\nF =\nEc\n\nc2~g (2.1)\n\nwhere Ec is the vacuum energy stored in the cavity, c is the speed of light and ~g is the earth\ngravitation acceleration.\n\n1\n\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\nFigure 1: Scheme of the final balance. Each disc is suspended to one end-arm and surrounded by a metallic\nenclosure for thermal actuation (shown in the inset). The optical read-out is a Mack-Zender interferometer\nand the signal is taken with respect to a reference arm.\n\nBeing this force extremely tiny, the measurement must be performed by modulating the effect,\ni.e., by modulating the Casimir energy in the rigid cavity.\nThis can be performed modulating the reflectivity of the cavity, since when the reflectivity of the\ntwo planes is higher, all the vacuum modes that are not resonant in the cavity are better expelled\nfrom the cavity, resulting in a lowered weight [12, 13, 14, 15]. When the cavity plates are consti-\ntuted by layers of superconductive material, the reflectivity modulation can be performed inducing\n\nFigure 2: Noise budget compared with expected signal (blue line) and final sensitivity (black curve).\n\n2\n\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\na transition of the material from the superconductor to not superconductor state, being the material\nreflectivity higher in the superconductive state. The transition from superconductor to not super-\nconductor can be actuated by means of temperature modulation around the transition temperature.\n\nIn our experiment type II like YBCO or BiSCCO superconductors will be used. This kind\nof superconductors are layer structured: layers that perform the transition to superconductivity\nalternate to layers that remain dielectric. They provide a natural cascade of rigid Casimir cavities,\nwhose condensation energy is expected to be influenced by vacuum fluctuation [6, 7, 8]. The\npercentage of condensation energy that is due to Casimir energy is still under evaluation and in the\noptimistic case is almost the totality [7].\n\nAccuracy of the order of percent of weight measurement is expected, so it will be possible\nto uncertain the interaction of gravitational field with vacuum fluctuations even if the contribution\nwill prove to be of this order of magnitude.\n\nIn figure 1 the proposed scheme of the measurement is reported: two discs of layered super-\nconductor are suspended to the arm of the balance. The balance arm is aluminum made to maintain\nlower the weight and the momentum of inertia, that, with an arm length of 1.40 m and a mass of\n1.7 kg, will be 0.72 kg m2.\n\nBoth the discs suspended to the balance are made of the same material but with different dop-\ning. This allow the superconductive transition only for one of them when the same temperature\nmodulation is applied, leading to the common phonon energy variation cancelation. The discs\nhave a 300 mm diameter and 1 mm thick. The modulated heating is performed by heat two metal-\nlic enclosures around the superconductive discs (radiating heating). To achieve the temperature\nequilibrium, the modulation frequency has been estimated to be several mHz.\n\nThe read-out of the balance is optically performed by means of a Mach-Zender interferometer\nilluminated with 5 mW laser power. A vacuum chamber at the transition temperature of the samples\n(about 100 K) contains the whole system.\n\nIn Figure 2 the expected signal and sensitivity are reported for 1 months integration time. It is\ncalculated for a seismic noise equal to the measured in the Sardinia site of SOS-Enattos [16] where\nthe final experiment will be hosted (see discussion in last section) and thermal noise is calculated\nin the hypothesis of resonance frequency of 5 mHz and loss angle φ = 10−5. These two noises are\nexpexted to be the main limitation to the final sensitivity, while other fundamental sources of noise,\nlike radiation pressure noise, shot noise, internal thermal noise, are negligible.\n\n3. Prototype description\n\nIn Figure 3 is shown a picture of the prototype. The Aluminum arm has a length of 0.56 m\n(shorter than the arm of the final balance) and a moment of inertia is 0.042 kg∗m2. It is coupled to\nthe ground by means of soft joints designed to have a restoring force with a resonance frequency of\nfew mHz when the center of mass of the arm is lying on the rotation axis. The technical design of\nthe joints is reported in the inset of the figure. The peculiar semi-ribbon shape, with two separated\n\n3\n\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\nFigure 3: Picture of the Archimeds balance prototype. Inset: techinical design of the semi-ribbon joints of\nthe balance.\n\nbending points that remain in a couple of attenuation distance, warrant the desired recovering stiff-\nness [18]. The ribbon length is 6 mm, the width is 10 mm and thickness is 50 µm. This design is\noptimized for the final balance, which will have the length of 1.4 m and the total moment of inertia\n(included the suspended superconducting samples) of 0.72 kg ∗m2, but have been tested on the\nbalance prototype to prove robustness and performances. The joint are made of berillium-copper.\nThe resonance frequency can be suitable tuned by acting on some screws on the balance arm (see\nnext subsection). During the tests it has been tuned to 3 mHz.\n\n3.1 Center of mass positioning\n\nAs detailed described in [18], a crucial condition to not reintroduce seismic noise is to mini-\nmize the coupling among ground acceleration along arm direction and arm tilt. As it is known [17]\na ground acceleration z̈ generates a torque τ on the arm equal to:\n\nτ = mδ z̈. (3.1)\n\nbeing m the balance arm mass and δ the distance from center of mass to rotation axis. In our\nprototype is m = 1.75 kg and this noise is minimized when δ is of the order of few microns.\nIn our estimations of the final Archimedes noise reported in Figure 2, we choose a conservative\ndistance δ = 10µm. This distance can be tuned by regulating a set of screws placed on the upper\nsurface of the arm, having a vertical range of 20 mm and 10 mm with a sensitivity of about 1 µm\nfor the finest screw rotation. The tuning is performed in air, then the system is evacuated and the\n\n4\n\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\ndistance measured by measuring the resonance frequency. The performed simulations show that the\nstiffness of the joint contributes to the frequency for about fk = 3.2 mHz. The gravitational stiffness\ncontribution is given by: fg =\n\n√\nmgδ I, where g is the gravitational acceleration and I = 0.042 kg∗\n\nm2 is the moment of inertia of the arm. The resonance frequency is thus fR =\n√\n\nf 2\nk + f 2\n\ng = 10.4 mHz\nfor δ = 10 µm.\nSetting of working point within few microns are possible with high robustness and repeatability. In\ntests of several days it has been observed that working within the tens of microns of distances the\nsystem is more stable.\n\n3.2 Balance sensing and control\n\nThe sensing of the balance prototype oscillation, i.e. the sensing of the torque exerted on the\nbalance arm, is performed by a very sensitive optical lever: the light of a SLED (Superluminescent\nLight-Emitting Diode) is sent to a mirror lying at the center of the upper surface of arm and then\nreflected toward a quadrant photodiode with a gap of 100 µm. The distance between the mirror and\nthe photodiode is d = 0.32 m. The angle of incidence of the beam on the mirror is 0.05 rad. To\nhave a suitably high sensitivity, the SLED beam is collimates to a 400 µm spot diameter.\nA feed-back controls the balance position: the signal of quadrant photodiode is acquired at sam-\npling rate of 1 kHz and low pass filtered; then electrostatic actuation is performed by means of\naluminum plates placed on the sides of the arm. To properly rotate the phase, a couples of (real)\nzeroes are set before the resonance, while real poles after the resonance to recover the slope and\nfurther complex zeroes and poles to compensate for high frequency resonances are set. The open-\nloop unity gain is at 0.2 Hz.\n\nThe whole system, balance, read-out and actuators is under vacuum, with residual pressure of\nabout 2∗10−5 mbar.\n\n4. Results, next steps and conclusion\n\nThe test performed on the balance prototype have showed that there are not hindrances to re-\nalize the final apparatus for the measurement of the Archimedes force of vacuum. Several tests\non the balance joints and on the robustness against thermal drifts and long term stability of the\ncontrol system have been performed. They do not provide evidence of show-stopper problems. All\nmechanical parts, particularly the joints, do not show significant aging effects on the time-scale of\nthe year, even when exposed in air. Feed-back stability of the orders of weeks of data taking is ob-\nserved. The transfer function and working point are not significantly affected by lab-environment\nvariations of temperature or humidity.\n\nThe torque sensitivity reached is shown in Figure 4. In intermediate frequency region from\n0.1 to about 21 Hz, the sensitivity represents – at our knowledge – the best torque sensitivity in\nthe world. Nevertheless in the region of particular interest for the final experiment, the lower fre-\nquency range from tens of mHz and lower, the sensitivity is limited by the high seismic noise of\nour laboratory. Figure 5 shows the latest measured with a Trillium accelerometer for a quiet night.\n\n5\n\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\nFigure 4: Prototype sensitivity.\n\nFigure 5: Seismic noise in our lab during day (cyan) and night (red), in a concrete plinth near our lab (green,\nblue), and in the Sos-Enattos mine (violet), compared with High and Low Peterson model\n\n6\n\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\nFigure 6: Cad view of the final balance with interferometric read-out.\n\nIn the same figure is reported also the seismic noise as measured in SOS-Enattos mine (Sardinia,\nItaly). The noise in the Naples laboratory is more than four order of magnitude (in power spectral\ndensity) with respect to quiet site in almost all frequencies from few mHz to few Hz. This condi-\ntions is important because it is yet not proved that there no noise down-converted in our system.\nSOS-Enattos mine is one of the lowest seismic noise site in Europe and has a low anthropic noise.\nAn underground laboratory, named SAR−GRAV , is at present under construction there. We will\nmove the prototype in this quieter place as soon as the laboratory will be ready to perform all the\nfinal test on the prototype sensitivity to help designing the last details of final experiment.\n\nIn meantime the next step is to switch from the optical level read-out to the interferometer one\nin order to increase the read-out sensitivity (we expect a gain of about two orders of magnitude).\nTo do this a robust and rigid monolithic holder for the the interferometer has been designed and\nbuild (see Figure 6 and Figure 7). It will mounted on the same balance platform inside the vacuum\nchamber and will host two of the mirrors of the interferomiter. Tests will be soon performed.\n\nReferences\n\n[1] For an historical review see for example: H. S. Kragh, J. Overduin, “The Weight of the Vacuum: A\nScientific History of Dark Energy” . Springer Heidelberg New York Dontrect London (2014)\n\n[2] S. Weinberg, \"The cosmological constant problem\", Rev. Mod. Phys. 61, 1 (1989).\n\n[3] T. Padmanabhan, \"Why Does Gravity Ignore the Vacuum Energy?\", Int. J. Mod. Phys. D 15, 2029\n(2006)\n\n[4] G. Bressi, G. Carugno, R. Onofrio, G. Ruoso: \"Measurement of the Casimir force between parallel\nmetallic surfaces\", Phys.Rev.Lett. 88 (2002) 041804\n\n[5] For a recent review: G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, \"‘The Casimir force\nbetween real materials: Experiment and theory\"’, Rev.Mod.Phys. 81 (2009) 1827-1885\n\n7\n\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\n[6] E. Calloni, M. De Laurentis, R. De Rosa, L. Di Fiore, G. Esposito, F. Garufi, L. Rosa, C. Rovelli, P.\nRuggi, F. Tafuri: \"Towards weighing the condensation energy to ascertain the Archimedes force of\nvacuum\" Phys. Rev. D 90, 022002 (2014)\n\n[7] A. Kempf \" On the Casimir effect in the high-Tc cuprates\" Journal of Physics A: Mathematical and\nTheoretical, Volume 41, Number 16\n\n[8] L. Rosa, S. Avino, E. Calloni, S. Caprara, M. De Laurentis, R. De Rosa, Giampiero Esposito, M.\nGrilli, E. Majorana, G. P. Pepe, S. Petrarca, P. Puppo, P. Rapagnani, F. Ricci, C. Rovelli,P. Ruggi, N.\nL. Saini, C. Stornaiolo, F. Tafuri: \" Casimir energy for two and three superconducting coupled\ncavities: numerical calculations \" Submitted to\n\n[9] E. Calloni, L. Di Fiore, G. Esposito, L. Milano, and L. Rosa, \"Vacuum fluctuation force on a rigid\nCasimir cavity in a gravitational field\" Phys. Lett. A 297, 328 (2002).\n\n[10] S. A. Fulling, K. A. Milton, P. Parashar, A. Romeo, K. V. Shajesh, and J. Wagner, \" How Does\nCasimir Energy Fall? \"Phys. Rev. D 76, 025004 (2007)\n\n[11] G. Bimonte, E. Calloni, G. Esposito, and L. Rosa, \"Energy-momentum tensor for a Casimir apparatus\nin a weak gravitational field\" Phys. Rev. D 74, 085011 (2006); erratum Phys. Rev. D 75, 049904\n(2007); erratum Phys. Rev. D 75, 089901 (2007), erratum Phys. Rev. D 77, 109903 (2008).\n\n[12] G. Bimonte, E. Calloni, G. Esposito, L. Milano, and L. Rosa: \"Towards measuring variations of\nCasimir energy by a superconducting cavity\" Phys. Rev. Lett. 94, 180402 (2005).\n\n[13] G. Bimonte, E. Calloni, G. Esposito, and L. Rosa: \"Variations of Casimir energy from a\nsuperconducting transition\" Nucl. Phys. B 726, 441 (2005). Articolo come il precedente con tutti i\ndettagli di calcolo e dipendenza dai parametri fisici.\n\nFigure 7: Aluminum monolithic holder for the iterferometric read-out.\n\n8\n\n\n\nP\no\nS\n(\nG\nR\nA\nS\nS\n2\n0\n1\n8\n)\n0\n2\n0\n\nweighing the vacuum M. De Laurentis\n\n[14] G. Bimonte, D. Born, E. Calloni, G. Esposito, U. Huebner, E. Il’ichev, L. Rosa, F. Tafuri, and R.\nVaglio: \"Low noise cryogenic system for the measurement of the Casimir energy in rigid cavities \" J.\nPhys. A 41, 164023 (2008).\n\n[15] A. Allocca, G. Bimonte, D. Born, E. Calloni, G. Esposito, U. Huebner, E. Il’ichev, L. Rosa, and F.\nTafuri: \"Results of measuring the influence of Casimir energy on superconducting phase transitions\"\nJour. Super. and Novel Mag. 25, 2557 (2012).\n\n[16] ET collaboration, “Einstein Gravitational wave Telescope Conceptual Design”, European\nCommission FP7 Grant Agreement 211743\n\n[17] K. Venkateswara, C. A. Hagedorn, M. D. Turner, T. Arp, J. H. Gundlach. Jan 16, 2014 “A\nhigh-precision mechanical absolute-rotation sensor” Rev.Sci.Instrum. 85 (2014) 015005\n\n[18] S. 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Grilli","1423873_Martina De Laurentis","1424033_Paola Puppo","2502495_Franco Frasconi"],"core":true,"license":[{"license":"CC-BY-NC-ND-4.0","imposing":"SISSA"}],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:1700313","updated":"2025-03-14T17:18:48.393618"},"journal_title_variants":["PoS"],"referenced_authors_bais":["E.Calloni.1","Giampiero.Esposito.1","K.A.Milton.1","Carlo.Rovelli.1","J.A.Wagner.1","L.Milano.1","S.Avino.2","S.Caprara.1","T.Padmanabhan.1","F.Frasconi.1","J.H.Gundlach.1","L.Rosa.1","Stephen.A.Fulling.1","U.Mohideen.1","F.Ricci.20","A.Allocca.2","P.Puppo.1","E.Majorana.1","L.K.Saini.1","G.Pepe.1","L.Di.Fiore.1","Matthew.D.Turner.1","A.Basti.1","K.Venkateswara.11","Rosario.De.Rosa.1","D.Born.2","F.Ricci.6","U.Huebner.2","P.Ruggi.17","Mariafelicia.De.Laurentis.1","T.B.Arp.1","C.A.Hagedorn.1","M.Grilli.1","G.Bimonte.1","P.Rapagnani.1","C.Stornaiolo.1","Steven.Weinberg.1","G.Carugno.1","E.Ilichev.2","G.Gagliardi.2","A.Kempf.1","R.Vaglio.2","F.Tafuri.1","A.Romeo.3","D.Stornaiuolo.1","F.Garufi.1","S.Petrarca.1","P.Parashar.3","K.V.Shajesh.1","Martina.De.laurentis.1","V.M.Mostepanenko.1","G.Ruoso.1","R.Onofrio.1","G.L.Klimchitskaya.2","G.Bressi.4"],"legacy_version":"20190726042845.0","inspire_categories":[{"term":"Instrumentation"}],"accelerator_experiments":[{"legacy_name":"Archimedes","curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/experiments/2655535"}}],"urls":[{"description":"PoS server","value":"https://pos.sissa.it/325/020/pdf"}],"first_author":{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/015kcdd40"}],"full_name":"Avino, Saverio","last_name":"Avino","first_name":"Saverio","recid":1954251},"control_number":1700313,"dois":[{"source":"SISSA","value":"10.22323/1.325.0020"}],"document_type":["conference paper"],"texkeys":["Archimedes:2018rkh","Avino:2018pkp","DeLaurentis:2018tyz"],"abstracts":[{"source":"SISSA","value":"Archimedes is an experiment devoted to measure the weight of zero point energy by weighing acascade of rigid Casimir cavitities costituted by a layered type II superconductor, when the reflec-tivity of the cavities is modulated and thus the energy inside. In this paper the working principleof the experiment is presented and the results of the existing prototype are presented, showingthe torque sensitivity of about 10−11 Nm/sqrtHz in the region of frequency from about 50 mHzup two 150 mHz. Moreover the major upgrades needed to reach the desired final sensitivity arediscussed.","abstract_source_suggest":{"input":"SISSA"}}],"titles":[{"source":"SISSA","title":"Archimedes experiment: weighing the vacuum"}],"imprints":[{"date":"2018-09-14","publisher":"SISSA"}],"curated":true},"links":{"bibtex":"https://inspirehep.net/api/literature/1700313?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1700313?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1700313?format=latex-us","json":"https://inspirehep.net/api/literature/1700313?format=json","json-expanded":"https://inspirehep.net/api/literature/1700313?format=json-expanded","cv":"https://inspirehep.net/api/literature/1700313?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1700313"},"id":"1700313"},{"created":"2018-06-07T00:00:00+00:00","updated":"2023-05-01T15:50:41.662548+00:00","metadata":{"documents":[{"filename":"PoS(MULTIF2017)084.pdf","attachment":{"content":"P\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum with the Archimedes\nexperiment\n\nS. Avinoa,b, A. Bastic, E. Callonid,b, S. Caprarae, f , M. De Laurentis∗d,b, R. De Rosad,b,\nG. Espositob, F. Frasconic, G. Gagliardia,2, M. Grillie, f , E. Majorana f , G. P. Peped,b, S.\nPetrarcae, f , P. Puppo f , P. Rapagnanie, f , F. Riccie, f , L. Rosad,b, C. Rovellig,h, P. Ruggii,\nN. L. Sainie, f , C. Stornaiolob, D. Stornaiuolod,b, F. Tafurid,b\n\na INO-CNR, Comprensorio Olivetti, Via Campi Flegrei 34-80078 Pozzuoli (NA), Italy\nb INFN Sezione di Napoli, Via Cintia Edificio 6, I-80126 Naples, Italy\nc INFN sezione Pisa, Largo Pontecorvo 1, I-56127 Pisa, Italy\nd Università Federico II Napoli, via Cinthia, I-80126, Naples, Italy\ne Università di Roma La Sapienza, Piazzale A. Moro, I-00185 Roma, Italy\nf INFN Sezione di Roma, Piazzale A. Moro, I-00185 Roma, Italy\ng Aix Marseille Université CNRS, CPT, UMR 7332, 13288 Marseille, France\nh Universitè de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France\ni European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n\nE-mail: saverio.avino@ino.it, andrea.basti@pi.infn.it,\nenrico.calloni@na.infn.it,sergio.caprara@roma1.infn.it,\nmartina.delaurentis@na.infn.it,rosario.derosa@na.infn.it,\ngesposit@na.infn.it,franco.frasconi@pi.infn.it,\ngianluca.gagliardi@ino.it,marco.grilli@roma1.infn.it,\nettore.majorana@roma1.infn.it,gpepe@na.infn.it,\nsilvano.petrarca@roma1.infn.it,paola.puppo@roma1.infn.it,\npiero.rapagnani@roma1.infn.it,fulvio.ricci@roma1.infn.it,\nluigi.rosa@na.infn.it,rovelli@cpt.univ-mrs.fr,\npaolo.ruggi@ego-gw.it,naurang.saini@roma1.infn.it,\ncosimo.stornaiolo@na.infn.it,daniela.stornaiuolo@na.infn.it,\nfrancesco.tafuri@na.infn.it\n\nWe present the status of the art of the Archimedes experiment, devoted to measure the weight of\nzero point energy by weighing the condensation energy of a layered type II superconductor. The\nexperimental scheme of the Archimedes experiment is presented and the sensitivity needed for\nthe final measurement illustrated. The results of the balance prototype are presented showing the\ntorque sensitivity of about 10−11 Nm/\n\n√\nHz in the region of frequency from about 50 mHz up two\n\n150 mHz. The major upgrades needed to reach the desired final sensitivity are discussed.\n\nXII Multifrequency Behaviour of High Energy Cosmic Sources Workshop\n12-17 June, 2017\nPalermo, Italy\n\n∗Speaker.\n\nc© Copyright owned by the author(s) under the terms of the Creative Commons\nAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/\n\nmailto:saverio.avino@ino.it\nmailto:andrea.basti@pi.infn.it\nmailto:enrico.calloni@na.infn.it\nmailto:sergio.caprara@roma1.infn.it\nmailto:martina.delaurentis@na.infn.it\nmailto:rosario.derosa@na.infn.it\nmailto:gesposit@na.infn.it\nmailto:franco.frasconi@pi.infn.it\nmailto:gianluca.gagliardi@ino.it\nmailto:marco.grilli@roma1.infn.it\nmailto:ettore.majorana@roma1.infn.it\nmailto:gpepe@na.infn.it\nmailto:silvano.petrarca@roma1.infn.it\nmailto:paola.puppo@roma1.infn.it\nmailto:piero.rapagnani@roma1.infn.it\nmailto:fulvio.ricci@roma1.infn.it\nmailto:luigi.rosa@na.infn.it\nmailto:rovelli@cpt.univ-mrs.fr\nmailto:paolo.ruggi@ego-gw.it\nmailto:naurang.saini@roma1.infn.it\nmailto:cosimo.stornaiolo@na.infn.it\nmailto:daniela.stornaiuolo@na.infn.it\nmailto:francesco.tafuri@na.infn.it\n\n\nP\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum M. De Laurentis\n\n1. Introduction\n\nOne of the oldest questions concerning quantum mechanics and gravitation is whether vacuum\nfluctuations do gravitate. The question of the weight of vacuum was raised soon after the birth of\nquantum mechanics [1] and many theoretical attempts were performed to explore the motivations\nand consequences of assuming or discarging such hyphothesis [2, 3]. From an experimental point\nof view it is remarkable that up to now not a direct experimental measurement has been carried\nout. Considering that nowadays the scientific community regards the Casimir effect as a macro-\nscopic manifestation of vacuum fluctuations [4, 5], we recently proposed an experiment, named\nArchimedes, to test the interaction of vacuum fluctuations with gravity by weighing a suitable rigid\nCasimir cavity.\nIn various papers we have estimated the effect of the gravitation field on such a cavity on the earth\n(the cavity is intended as rigid)under the hypothesis that vacuum energy does interact with gravita-\ntional field and follows the strong equivalence principle: it is found that the gravitation field exerts\na force on the cavity equal to the weight of the vacuum modes expelled by the cavity, in partial\nanalogy with the Archimedes force in the fluid. The analogy is partial because the cavity follows\nthe equivalence principle and falls with the gravitational acceleration [7].\nFurther, considering the present small force detectors we also provided an experimental scheme\nto measure the Archimedes force of vacuum: the cavity is actually a multi-layer cavity obtained\nusing a layered superconductor of type II, like YBCO or BSCOO. In these kind of superconductors\nthe superconducting planes are separated by dielectric planes, thus forming a natural multi-layer\nCasimir cavity [8, 9]. Thus the actual measure will be the weight of the condensation energy of\na layered-superconductor. The order of magnitude of the expected force to be measured is about\n10−16 N at a modulation frequency of several mHz, obtained by inducing a transition from normal\nto superconducting state by temperature modulation [7]. The measurement of such a tiny force\nrequires an extremely sensitive balance, working at the temperature of about 100 K, suspending\ntwo almost equivalent blocks of superconductor material which undergo modulate transition in\nthermal equilibrium with surrounding temperature modulated vessel, like in fig 1. A prototype\nof such a balance, working at room temperature, has been realized to test eventual show-stopper\nor major problems. In this paper we set the main experimental parameters, we show the relevant\nexperimental prototype results and discuss them with respect to the final measurement.\n\n2. Measurement principles\n\nIn varius papers [7, 10, 11] it has been calculated the force exerted by the gravitational field\non a rigid Casimir cavity at rest on earth: it is directed upward and it is equal:\n\nF =\nEc\n\nc2~g (2.1)\n\nwhere c is the speed of light and ~g is the earth gravitation acceleration. In the calculation of this\nforce it is assumed that also the pressure of the vacuum fluctuation does follow the equivalence\nprinciple and thus the measurement is actually also a zero measurement of the read-shifting of vac-\nuum pressure in gravitational field [12, 7]. The force is extremely tiny and thus measurement must\nbe performed by modulating the effect.\n\n1\n\n\n\nP\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum M. De Laurentis\n\nThe method proposed to modulate the Casimir energy in a rigid cavity is by modulating the reflec-\ntivity of the plates by a superconducting transition: when the plates are superconducting they are\nmore reflective and the vacuum is better expelled from the cavity, resulting in a lowering of the\nweight [13, 14, 15, 16]. The superconductor will be actually a layered type II superconductor, like\nYBCO or BiSCCO: indeed a type II superconductor is formed by planes that perform the transition\nto superconductivity alternate to layers that remain dielectric. Thus a layered superconductor is\na natural stack of partially-reflecting, coupled Casimir cavities, whose condensation energy is ex-\npected to be influenced by vacuum fluctuation [7, 8, 9]. The percentage of condensation energy that\nis due to Casimir energy is still under evaluation and in the optimistic case is almost the totality [8].\nThe actual weight measurement will have the accuracy of the order of percent, so it will be possible\nto uncertain the interaction of gravitational field with vacuum fluctuations even if the contribution\nwill prove to be of this order of magnitude.\nThe proposed scheme of the measurement is reported in fig 1: two discs of layered superconductor\nare suspended to the arm of the balance. The two discs are made of the same material but with\ndifferent doping. The arm is in aluminum to maintain low weight and momentum of inertia. The\ntemperature modulation is the same in the two discs but only one performs the superconductive\ntransition: in this way the common phonon energy variation cancels (does not give a signal on the\nbalance).\n\nThe discs are 300 mm diameter and 1 mm thick. They are enclosed in two metallic enclosures\nthat are modulated in temperature and the discs temperature modulation is about 1 K. The arm-\nlength is 1.40 m, the mass 1.7 kg, the total momentum of inertia is 0.72 kg m2. The modulation\nfrequency is several mHz, in agreement with the time needed to the samples to reach the tempera-\nture of equilibrium. The read-out optical system is a Mach-Zender interferometer illuminated with\n5 mW laser power. The whole system is enclosed in vacuum at the transition temperature of the\nsamples, about 100 K.\nThe expected signal and sensitivity are reported in fig 4, for 1 months integration time. The sen-\nsitivity is calculated for a seismic noise equal to the measured in the Sardinia site of SOS-Enattos\n[17] (see discussion in last section) and the thermal noise is calculated in the hypothesis of res-\nonance frequency of 5 mHz and loss angle φ = 10−5. Seismic and suspension thermal noise are\nexpected to limit the sensitivity. Other fundamental sources of noise, like radiation pressure noise,\nshot noise, internal thermal noise, are negligible.\n\n3. The prototype\n\nThe main aim of the prototype has been the test of the feasibility of a balance with low moment\nof inertia yet maintaining a low resonance frequency, a good sensitivity and capability of control in\nthe short and long term. A picture of he prototype is reported in fig 2. The first important test has\nregarded the suspension joint. The balance arm is coupled to ground by soft joints whose restoring\nforce is tuned to have a resonance frequency of about 3 mHz when the center of mass of the arm is\nlying on the rotation axis. The use of joints is similar to the solution proposed in ref [18] for the\nrealization of an absolute rotation sensor. The main difference among the balance and the rotation\n\n2\n\n\n\nP\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum M. De Laurentis\n\nFigure 1: Scheme of the final balance. Each disc is suspended to one end-arm and surrounded by a metallic\nenclosure for thermal actuation (not shown). The optical read-out is a Mack-Zender interferometer and the\nsignal is taken with respect to a reference arm.\n\nsensor is given by optimal moment of inertia of the arm. Differently from the rotation sensor in the\nbalance the arm should be as light as possible, compatible with the other constructive requirements,\nto furnish a detectable signal even when driven by the tiny vacuum force.\nTo recover a low resonance frequency the joints should in principle made thinner but this choice\nwould require thickness only of a few micron, extremely difficult to machine and to work with.\n\nThis problem has been solved by designing joints, named semi-ribbon, in which the bending\npoints separates but remain in a couple of attenuation distance, so to warrant the desired recovering\nstiffness.\nThe joint used, reported in fig 3 are made of berillium-copper. The length of the ribbon is 6 mm, the\nwidth is 10 mm and the thickness is 50 µm. This design is optimized for the final balance, which\nwill have the length of 1.4 m and the total moment of inertia (included the suspended supercon-\nducting samples) of 0.72 kg m2, but have been tested on the balance prototype to prove robustness\nand performances.\n\nThe balance prototype has arm-length of 0.56 m, the arm is made of Aluminum, the moment\nof inertia is 0.042 kg m2. The read out is a very sensitive optical lever: the light of a SLED\n(Superluminescent Light-Emitting Diode) is sent to a mirror lying at the center of the upper surface\n\n3\n\n\n\nP\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum M. De Laurentis\n\nFigure 2: Picture of the prototype.\n\n1\n\n1\n\n2\n\n2\n\n3\n\n3\n\n4\n\n4\n\n5\n\n5\n\n6\n\n6\n\nA A\n\nB B\n\nC C\n\nD D\n\nlamella type_1_2_6mm\n\n1  di 1 \n\nA3\n\nISTITUTO NAZIONALE DI FISICA NUCLEARE\nSezione di Pisa\n\nLega di rame\n\nAssy:\n\nSize:\n\nSheet N°:Scale:\n\nEmission Date:\n\nDrawing N°:\n\nTitle:\n\nProgram/Order:\n\nAuthor:\n\nChecked by:\n\nApproved by:\n\nAuthorized by:\n\nDate:\n\nDate:\n\nDate:\n\nDate:\n\nAngles\n\nx0,1\n\nX, xx0,05\n\nRev. N°:\n\n28/08/2015\n\nbasti\n\nX0,5\n\nDimensions and general\n\ntolerances are in [mm] unless\n\notherwise specified\n\nUnless otherwise specified\n\nthe following stds apply:\n\nFirst Angle Projection\n\n0,1°\n\nMaterial:\n\nX,\n\n28/08/2015\n\nNote:\n\n20,00\n\n3\n0\n,\n0\n0\n\n8\n,\n5\n0\n\n8\n,\n5\n0\n\n0,05\n\nR\n\n3\n\n,\n\n5\n\n0\n\n6\n,\n0\n0\n\n10,00\n\n5,00\n\n5,00\n\n4\n\n,\n\n0\n\n0\n\n2\n0\n,\n0\n0\n\n10,00\n\nLamella type_1_2_6mm\n\n6,48\n\n3\n,\n5\n0\n\nMateriale Rame-Berillio\n\n5\n,\n0\n0\n\nFigure 3: Design of the semi-ribbon. This configuration of joints is designed to maintain a low resonance\nfrequency for low momentum of inertia.\n\n4\n\n\n\nP\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum M. De Laurentis\n\nof arm. The reflected light is read by a quadrant photodiode fixed on the ground: the distance d\nform the mirror to the photodiode is d = 0.32 m. The angle of the incident beam on the mirror is\n0.05 rad. The gap among the quadrants of the photodiode is 100 µm and the width SLED beam is\ncollimated to 400 µm, to have a suitably high sensitivity.\nThe system is under vacuum, with residual pressure of about 2×10−5 mbar. The balance position\nis controlled in feed-back.\n\n3.1 Center of mass positioning\n\nOne of the key conditions to not reintroduce seismic noise is minimizing the coupling among\nground acceleration along arm direction and arm’s tilt. As it is known [18] a ground acceleration z̈\ngenerates a torque τ on the arm equal to:\n\nτ = mδ z̈ (3.1)\n\nwhere m = 1.75 kg is the arm’s mass and δ is the distance from center of mass to rotation\naxis. To minimize this noise it is necessary to set δ within few microns: in our estimations of the\nfinal Archimedes noise of fig. 4 we choose a conservative distance δ = 10 µm. Several tests have\nbeen performed to uncertain the difficulties of setting this distance within this limit. The tuning\nis made by regulating a set of screws placed on the upper surface of the arm, having a vertical\ncourse of 20 mm and 10 mm. The sensitivity is about 1 micron for the finest screw rotation. The\ntuning is performed in air, then the system is evacuated and the distance measured by measuring\nthe resonance frequency. As estimated by simulation the stiffness of the joint contributes to the\nfrequency for about fk = 3.2 mHz. The contribution of the gravitational stiffness is given by:\nfg =\n\n√\nmgδ I where g is the gravitational acceleration and I = 0.042 kg m2 is the moment of inertia\n\nof the arm. The resonance frequency is thus fR =\n√\n\nf 2\nk + f 2\n\ng and for δ = 10 µm the frequency\nfR = 10.4 mHz.\nThe setting of the working point described above is indeed quite robust and reproducible. Settings\nwithin few microns are possible. It was in any case decided to work within the tens of microns of\ndistances because the system shows better stability for measurements lasting several days.\n\n3.2 The control system\n\nThe photodiode signal is acquired with sampling rate of 1 kHz. The filter is a usual low pass\nfilter with couples of (real) zeroes before the resonance to properly rotate the phase, real poles after\nthe resonance to recover the slope and further complex zeroes and poles to compensate for high\nfrequency resonances. The actuation is made by electrostatic actuators composed by aluminum\nplates placed on the sides of the arm. The open-loop unity gain is at 0.2 Hz.\n\n4. Results\n\nThe main results are reported in fig. 4. The experimental sensitivity is compared with the\nexpected signal and the expected sensitivity of the final Archimedes experiment. For frequencies\nabove 0.1 Hz the sensitivity is limited by the sensing noise. For lower frequency the sensitivity\nis limited by the seismic noise. Indeed the ground noise present in the laboratory is quite high,\n\n5\n\n\n\nP\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum M. De Laurentis\n\ndetermined both by seismic noise and anthropic noise. Good sensitivities are reached only during\nthe night, particularly within the hours from 2 am to 4 am.\n\nFigure 4: Prototype sensitivity (upper curve) compared with expected signal (blue line) and final sensitivity\n(lower curve).\n\nFigure 5: Seismic noise in our lab during day (cyan) and night (red), in a concrete plinth near our lab (green,\nblue), and in the Sos-Enattos mine (violet), compared with High and Low Peterson model [6].\n\nThe present results, in the region of 0.1 to about 2 Hz, represents at our knowledge the best\ntorque sensitivity in the world. The long term stability has been checked and no effects have been\nappreciated. The feed-back remains stable over weeks of data taking, the transfer function and\noperating point don’t get significantly affected by lab-environment variations of temperature or\nhumidity. All mechanical parts, particularly the joints, don’t show significant aging effects on the\n\n6\n\n\n\nP\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum M. De Laurentis\n\ntime-scale of the year, even when exposed in air. In the region of lower frequencies, of tens of mHz\nand lower, the seismic noise is clearly dominating. This region is of particular interest for the final\nexperiment and it is deserving a strong attention. At the present a low seismic and low anthropic\nnoise underground laboratory, named SAR−GRAV , is under construction in the SOS-Enattos mine\n(Sardinia, Italy).\nThe laboratory seismic noise has been measured with a Trillium accelerometer and reported, for a\nquiet night, in fig. 5. In the figure is reported also the seismic noise as measured in SOS-Enattos\nsite. The noise in the lab is more than four order of magnitude (in power spectral density) with\nrespect to quiet site in almost all frequencies from few mHz to few Hz. This conditions is important\nbecause it is yet not proved that there no noise down-converted in our system. SOS-Enattos mine\nis one of the lowest seismic noise site in Europe and indeed the prototype balance is expected to\nmove in this quieter place as soon as the laboratory will be ready.\n\n5. Conclusion\n\nThe balance prototype has shown that there no show-stopper in realizing the final apparatus\nfor the measurement of the Archimedes force of vacuum. Tests on joints and balance behavior have\ndriven the final design toward long arm and soft joints and the final project can now start. Other\ncontrol tests, like robustness against thermal drifts and long term stability haven’t shown show-\nstopper problems as well. The torque sensitivity reached is the best in the intermediate frequency\nregion and is limited in lower frequency by the high seismic noise of our laboratory. Moving in\nthe quiet site of SOS-Enattos mine is the next step to ultimate prototype sensitivity tests and help\ndesigning the last details of final experiment.\n\nReferences\n\n[1] For an historical review see for example: H. S. Kragh, J. Overduin, âĂIJThe Weight of the Vacuum:\nA Scientific History of Dark EnergyâĂİ . Springer Heidelberg New York Dontrect London (2014)\n\n[2] S. Weinberg, \"The cosmological constant problem\", Rev. Mod. Phys. 61, 1 (1989).\n\n[3] T. Padmanabhan, \"Why Does Gravity Ignore the Vacuum Energy?\", Int. J. Mod. Phys. D 15, 2029\n(2006)\n\n[4] G. Bressi, G. Carugno, R. Onofrio, G. Ruoso: \"Measurement of the Casimir force between parallel\nmetallic surfaces\", Phys.Rev.Lett. 88 (2002) 041804\n\n[5] For a recent review: G.L. Klimchitskaya, U. Mohideen, V.M. Mostepanenko, \"‘The Casimir force\nbetween real materials: Experiment and theory\"’, Rev.Mod.Phys. 81 (2009) 1827-1885\n\n[6] Peterson, J., 1993. “ Observations and modelling of background seismic noise.” Open-file report\n93-322, U. S. Geological Survey, Albuquerque, New Mexico.\n\n[7] E. Calloni, M. De Laurentis, R. De Rosa, L. Di Fiore, G. Esposito, F. Garufi, L. Rosa, C. Rovelli, P.\nRuggi, F. Tafuri: \"Towards weighing the condensation energy to ascertain the Archimedes force of\nvacuum\" Phys. Rev. D 90, 022002 (2014)\n\n[8] A. Kempf \" On the Casimir effect in the high-Tc cuprates\" Journal of Physics A: Mathematical and\nTheoretical, Volume 41, Number 16\n\n7\n\n\n\nP\no\nS\n(\nM\nU\nL\nT\nI\nF\n2\n0\n1\n7\n)\n0\n8\n4\n\nWeighing the vacuum M. De Laurentis\n\n[9] L. Rosa, S. Avino, E. Calloni, S. Caprara, M. De Laurentis, R. De Rosa, Giampiero Esposito, M.\nGrilli, E. Majorana, G. P. Pepe, S. Petrarca, P. Puppo, P. Rapagnani, F. Ricci, C. Rovelli,P. Ruggi, N.\nL. Saini, C. Stornaiolo, F. Tafuri: \" Casimir energy for two and three superconducting coupled\ncavities: numerical calculations \" Submitted to\n\n[10] E. Calloni, L. Di Fiore, G. Esposito, L. Milano, and L. Rosa, \"Vacuum fluctuation force on a rigid\nCasimir cavity in a gravitational field\" Phys. Lett. A 297, 328 (2002).\n\n[11] S. A. Fulling, K. A. Milton, P. Parashar, A. Romeo, K. V. Shajesh, and J. Wagner, \" How Does\nCasimir Energy Fall? \"Phys. Rev. D 76, 025004 (2007)\n\n[12] G. Bimonte, E. Calloni, G. Esposito, and L. Rosa, \"Energy-momentum tensor for a Casimir apparatus\nin a weak gravitational field\" Phys. Rev. D 74, 085011 (2006); erratum Phys. Rev. D 75, 049904\n(2007); erratum Phys. Rev. D 75, 089901 (2007), erratum Phys. Rev. D 77, 109903 (2008).\n\n[13] G. Bimonte, E. Calloni, G. Esposito, L. Milano, and L. Rosa: \"Towards measuring variations of\nCasimir energy by a superconducting cavity\" Phys. Rev. Lett. 94, 180402 (2005).\n\n[14] G. Bimonte, E. Calloni, G. Esposito, and L. Rosa: \"Variations of Casimir energy from a\nsuperconducting transition\" Nucl. Phys. B 726, 441 (2005). Articolo come il precedente con tutti i\ndettagli di calcolo e dipendenza dai parametri fisici.\n\n[15] G. Bimonte, D. Born, E. Calloni, G. Esposito, U. Huebner, E. Il’ichev, L. Rosa, F. Tafuri, and R.\nVaglio: \"Low noise cryogenic system for the measurement of the Casimir energy in rigid cavities \" J.\nPhys. A 41, 164023 (2008).\n\n[16] A. Allocca, G. Bimonte, D. Born, E. Calloni, G. Esposito, U. Huebner, E. Il’ichev, L. Rosa, and F.\nTafuri: \"Results of measuring the influence of Casimir energy on superconducting phase transitions\"\nJour. Super. and Novel Mag. 25, 2557 (2012).\n\n[17] ET collaboration, âĂIJEinstein Gravitational wave Telescope Conceptual DesignâĂİ, European\nCommission FP7 Grant Agreement 211743\n\n[18] K. Venkateswara, C. A. Hagedorn, M. D. Turner, T. Arp, J. H. Gundlach. 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cavity: a thin superconducting film of thickness $d$ is placed between two thick metallic slabs, which constitute the plates of the cavity. The gaps of width $a$ that separate the film from the plates are filled with insulating material.","source":"arxiv","key":"8961ec73874a9b7424367151f3aef0a0","url":"https://inspirehep.net/files/8961ec73874a9b7424367151f3aef0a0"},{"filename":"disegnoArchimedes.png","caption":"Sketch of the optical link. The cavity acting as an optical spring is composed by the Archimedes Cavity input mirror, $\\rm{AC_{IM}}$, by the steering mirror $\\rm{AC_{S1}}$, by the back surface of the Gravitational wave detector test mass, AD-Virgo EM, by a second steering mirror $\\rm{AC_{IM}}$ and closed by the Archimedes Cavity end mirror $\\rm{AC_{IM}}$. Also a top view of the apparatus and the Gravitational wave detectors is sketched in the top-left box, not in scale, to show a complete view. The cavity is illuminated by a laser reflecting on the upper stage that suspends the input mirror, as shown in figure.","source":"arxiv","key":"363b751257fbf5cf544e576d2296e67b","url":"https://inspirehep.net/files/363b751257fbf5cf544e576d2296e67b"},{"filename":"ADVexpectedSignal.png","caption":"Expected signal for the YBCO actuator described in the previous Section.","source":"arxiv","key":"17dd728a876928905d85b135f8659d20","url":"https://inspirehep.net/files/17dd728a876928905d85b135f8659d20"},{"filename":"ETexpectedSignal.png","caption":"Expected signal when using ET optimized for low frequency.","source":"arxiv","key":"c662f09547d3dbaed90123b245303ac4","url":"https://inspirehep.net/files/c662f09547d3dbaed90123b245303ac4"},{"filename":"disegnoBilancia.png","caption":"Sketch of the balance with the optical lever detection read-out. The seismic attenuation chain is composed by the three-legs inverted pendulum and by the blades-attenuation element. The read-out is composed by a laser beam that reflects on the bottom of the bar and impinges on a quadrant photodiode.","source":"arxiv","key":"238f2715c0cbb9e7a7008dcaabcfe4a8","url":"https://inspirehep.net/files/238f2715c0cbb9e7a7008dcaabcfe4a8"},{"filename":"TFzt.png","caption":"Transfer function from displacement suspension point to balance's tilt for 1mHz and 5 mHz resonance frequency. The coupling depends on the resonant frequency.","source":"arxiv","key":"1de9d6695ac49c4b9c1a6ed3b7038eb9","url":"https://inspirehep.net/files/1de9d6695ac49c4b9c1a6ed3b7038eb9"},{"filename":"sensitivityAndNoises.png","caption":"Expected signal and noises for the balance. In the region of frequencies $5 &lt; f &lt; 100$ mHz the signal is about two orders of magnitude above the noise.","source":"arxiv","key":"d6508f6636d55daa904d14f0d7ea2cb1","url":"https://inspirehep.net/files/d6508f6636d55daa904d14f0d7ea2cb1"},{"filename":"sensitivityForce.png","caption":"Force signal and noises. The dashed line describes the noise of an optical lever detection system.","source":"arxiv","key":"74b3083bbc8f285ca953540af0668413","url":"https://inspirehep.net/files/74b3083bbc8f285ca953540af0668413"}],"legacy_version":"20171124003732.0","inspire_categories":[{"term":"Gravitation and Cosmology"}],"accelerator_experiments":[{"legacy_name":"Archimedes","curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/experiments/2655535"}}],"first_author":{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/015kcdd40"}],"full_name":"Calloni, Enrico","last_name":"Calloni","first_name":"Enrico","recid":1014715},"control_number":1278851,"dois":[{"value":"10.1103/PhysRevD.90.022002"}],"document_type":["article"],"texkeys":["Archimedes:2014fid","Calloni:2014pua"],"abstracts":[{"source":"APS","value":"<p>The force exerted by the gravitational field on a Casimir cavity in terms of Archimedes force of vacuum is discussed, the force that can be tested against observation is identified, and it is shown that the present technology makes it possible to perform the first experimental tests. The use of suitable high-<inline-formula><mml:math display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> superconductors as modulators of Archimedes force is motivated. The possibility is analyzed of using gravitational wave interferometers as detectors of the force, transported through an optical spring from the Archimedes vacuum force apparatus to the gravitational interferometer test masses to maintain the two systems well separated. The use of balances to actuate and detect the force is also analyzed, the different solutions are compared, and the most important experimental issues are discussed.</p>","abstract_source_suggest":{"input":"APS"}},{"source":"arXiv","value":"The force exerted by the gravitational field on a Casimir cavity in terms of Archimedes force of vacuum is discussed, the force that can be tested against observation is identified, and it is shown that the present technology makes it possible to perform the first experimental tests. The use of suitable high-Tc superconductors as modulators of Archimedes force is motivated. The possibility is analyzed of using gravitational wave interferometers as detectors of the force, transported through an optical spring from the Archimedes vacuum force apparatus to the gravitational interferometer test masses to maintain the two systems well separated. The use of balances to actuate and detect the force is also analyzed, the different solutions are compared, and the most important experimental issues are discussed.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["gr-qc"],"titles":[{"source":"arXiv","title":"Towards weighing the condensation energy to ascertain the Archimedes force of vacuum"},{"source":"arXiv","title":"Towards measuring the Archimedes force of vacuum"}],"imprints":[{"date":"2014-07-10"}],"curated":true},"links":{"bibtex":"https://inspirehep.net/api/literature/1278851?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1278851?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1278851?format=latex-us","json":"https://inspirehep.net/api/literature/1278851?format=json","json-expanded":"https://inspirehep.net/api/literature/1278851?format=json-expanded","cv":"https://inspirehep.net/api/literature/1278851?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1278851"},"id":"1278851"},{"created":"2024-03-12T17:14:03.746419+00:00","updated":"2025-03-14T17:17:19.237443+00:00","metadata":{"authors":[{"raw_affiliations":[{"value":"Naples U."}],"full_name_unicode_normalized":"errico, luciano","full_name":"Errico, Luciano","curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/authors/1874613"},"ids":[{"schema":"INSPIRE BAI","value":"Luciano.Errico.1"}],"last_name":"Errico","affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/903043"},"value":"Naples U."}],"uuid":"212f9f1c-035d-4ba8-bd49-9e3c870a005a","first_name":"Luciano","recid":1874613}],"citation_count":0,"publication_info":[{"year":2022}],"citation_count_without_self_citations":0,"$schema":"https://inspirehep.net/schemas/records/hep.json","keywords":[{"schema":"INSPIRE","value":"gravitation: coupling"},{"schema":"INSPIRE","value":"cosmological model"},{"schema":"INSPIRE","value":"cosmological constant"},{"schema":"INSPIRE","value":"proposed experiment"},{"schema":"INSPIRE","value":"fluctuation: vacuum"},{"schema":"INSPIRE","value":"fluctuation: quantum"},{"schema":"INSPIRE","value":"quantum mechanics"},{"schema":"INSPIRE","value":"general relativity"},{"schema":"INSPIRE","value":"space-time: warped"},{"schema":"INSPIRE","value":"vacuum state: energy"},{"schema":"INSPIRE","value":"energy: zero-point"},{"schema":"INSPIRE","value":"effect: Casimir"},{"schema":"INSPIRE","value":"energy: Casimir"},{"schema":"INSPIRE","value":"cavity"},{"schema":"INSPIRE","value":"temperature: high"},{"schema":"INSPIRE","value":"superconductivity"},{"schema":"INSPIRE","value":"critical phenomena: temperature"},{"schema":"INSPIRE","value":"modulation"},{"schema":"INSPIRE","value":"time dependence"},{"schema":"INSPIRE","value":"oscillation: frequency"},{"schema":"INSPIRE","value":"detector: design"},{"source":"author","value":"Gravitational Physics"},{"source":"author","value":"Quantum Field Theory"},{"source":"author","value":"Fundamental Physics"},{"source":"author","value":"Low-seismic noise experiment"},{"source":"author","value":"Vacuum fluctuations"},{"source":"author","value":"Casimir effect"}],"references":[{"reference":{"publication_info":{"journal_volume":"116","artid":"241103","year":2016,"journal_title":"Phys.Rev.Lett."},"misc":["(a). 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The experiment should measure the force that the earths gravitational field exerts on a Casimir cavity by using a small force detector. Here we analize the main parameters of the experiment and we present its conceptual scheme, which overcomes in principle the most critical problems.","abstract_source_suggest":{"input":"World Scientific"}},{"source":"arXiv","value":"Archimedes is a feasibility study of a future experiment to ascertain the interaction of vacuum fluctuations with gravity. The experiment should measure the force that the earth's gravitational field exerts on a Casimir cavity by using a small force detector. Here we analyse the main parameters of the experiment and we present its conceptual scheme, which overcomes in principle the most critical problems.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["gr-qc"],"titles":[{"source":"arXiv","title":"Archimedes: a feasibility study of an experiment to weigh the electromagnetic vacuum"}],"imprints":[{"date":"2017"}],"curated":true},"links":{"bibtex":"https://inspirehep.net/api/literature/1404677?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1404677?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1404677?format=latex-us","json":"https://inspirehep.net/api/literature/1404677?format=json","json-expanded":"https://inspirehep.net/api/literature/1404677?format=json-expanded","cv":"https://inspirehep.net/api/literature/1404677?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1404677"},"id":"1404677"},{"created":"2014-09-25T00:00:00+00:00","updated":"2023-11-08T21:35:47.854477+00:00","metadata":{"documents":[{"filename":"PoS(FFP14)187.pdf","attachment":{"content":"P\no\nS\n(\nF\nF\nP\n1\n4\n)\n1\n8\n7\n\nThe Archimedes project: a feasibility study for\nweighing the vacuum energy\n\nE. Calloni∗,a S. Caprarab, M. De Laurentisa, G. Esposito c, M. Grillib, E. Majoranad , G.\nP. Pepee, S. Petrarcab, P. Puppod , F. Riccib, L. Rosaa, C. Rovelli f , P. Ruggig, N. L.\nSainib, C. Stornaioloc, F. Tafurih\n\na Università di Napoli Federico II, Dipartimento di Fisica and INFN Sezione di Napoli\nComplesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Napoli, Italy\n\nb Universitá di Roma \"La Sapienza\" e INFN Sezione di Roma - P.le A. Moro 2, I-00185, Roma,\nItaly\n\ncINFN Sezione di Napoli Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6,\n80126 Napoli, Italy\n\nd INFN Sezione di Roma - P.le A. Moro 2, I-00185, Roma, Italy\ne Università di Napoli Federico II, Dipartimento di Fisica and INFN Sezione di Napoli\nPiazzale Tecchio 80 80126 Napoli, and Complesso Universitario di Monte S. Angelo, Via Cintia\nEdificio 6, 80126 Napoli, Italy\n\nf Aix Marseille Université CNRS, CPT, UMR 7332, 13288 Marseille, and Universitè de Toulon,\nCNRS, CPT, UMR 7332, 83957 La Garde, France\n\ng European Gravitational Observatory (EGO) I-56021 Cascina (Pi), Italy\nh Dipartimento Ingegneria dell’Informazione, Seconda Università di Napoli, I-81031 Aversa (CE)\n\nand INFN Sezione di Napoli\nComplesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Napoli, Italy\nE-mail: enrico.calloni@na.infn.it, sergio.caprara@roma1.infn.it,\nmartina.delaurentis@na.infn.it, giampiero.esposito@na.infn.it,\nmarco.grilli@roma1.infn.it, ettore.majorana@roma1.infn.it,\ngpepe@na.infn.it, silvano.petrarca@roma1.infn.it,\npaola.puppo@roma1.infn.it,fulvio.ricci@roma1.infn.it,\nluigi.rosa@na.infn.it, rovelli@cpt.univ-mrs.fr,\npaolo.ruggi@ego-gw.it, naurang.saini@roma1.infn.it,\ncosimo.stornaiolo@na.infn.it, francesco.tafuri@na.infn.it\n\nArchimedes is a pathfinder experiment aimed at verifying the feasibility of measuring the interac-\ntion of vacuum fluctuations with gravity. The future experiment should measure the force that the\nearth’s gravitational field exerts on a Casimir cavity by using a balance as the small force detec-\ntor. Archimedes analyzes the important parameters of the future experiment and experimentally\nexplores solutions to the most critical problems.\n\nFrontiers of Fundamental Physics 14 - FFP14,\n15-18 July 2014\nAix Marseille University (AMU) Saint-Charles Campus, Marseille\n\n∗Speaker.\n\nc© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/\n\nmailto:enrico.calloni@na.infn.it\nmailto:sergio.caprara@roma1.infn.it\nmailto:martina.delaurentis@na.infn.it\nmailto:giampiero.esposito@na.infn.it\nmailto:marco.grilli@roma1.infn.it\nmailto:ettore.majorana@roma1.infn.it\nmailto:gpepe@na.infn.it\nmailto:silvano.petrarca@roma1.infn.it\nmailto:paola.puppo@roma1.infn.it\nmailto:fulvio.ricci@roma1.infn.it\nmailto:luigi.rosa@na.infn.it\nmailto:rovelli@cpt.univ-mrs.fr\nmailto:paolo.ruggi@ego-gw.it\nmailto:naurang.saini@roma1.infn.it\nmailto:cosimo.stornaiolo@na.infn.it\nmailto:francesco.tafuri@na.infn.it\n\n\nP\no\nS\n(\nF\nF\nP\n1\n4\n)\n1\n8\n7\n\nArchimedes project E. Calloni\n\n1. Scientific motivations\n\nOne of the profound open questions of modern physics is the irreconcilability among the\nquantum mechanical theory of vacuum and General Relativity. The enormous value of the en-\nergy density of vacuum fluctuations as foreseen by quantum mechanics, if inserted naively into the\nenergy-momentum tensor on the right-hand side of the field equations of General Relativity, is not\nat all compatible with the observed radius of the universe, nor with the acceleration of expansion:\na problem known as the cosmological constant problem [1]. At present, in spite of a detailed and\nimportant theoretical work [2], there is no general consensus on the theoretical solutions proposed\nand on the fact that vacuum fluctuations do contribute to gravity [3]. Furthermore, even though the\ncommon belief is that this should be the case [4, 5], no experiment has been performed to finally\nverify or discard this assumption. In a recent paper we have shown that considering the present\ntechnological achievements on small force detectors, on superconductors and on seismic isolation,\nit is possible to foresee an experimental path towards such a measurement [6]. The principle of the\nmeasurement is the weighing of a Casimir cavity. Indeed, it can be shown that if a Casimir cavity is\nplaced in the earth’s gravitational field and the vacuum energy does interact with gravity, it receives\na force directed upwards equal to [6]:\n\n~F = A\nπ2h̄\n\n720a3\ng\nc\n\nẑ =\nEcas\n\nc2 ~g, (1.1)\n\nwhere A is the Casimir cavity proper area, a is the Cavity proper distance among the plates, c is the\nspeed of light,~g is the earth’s gravitational acceleration (g its modulus), the unit vector ẑ is directed\nupwards, Ecas is the Casimir energy and the evaluation is performed to first order with respect to\nthe quantity ga\n\nc2 . This force, directed upwards, can be interpreted as the lack of weight of the modes\nthat have been removed by the cavity, in similarity with the Archimedes buoyancy of fluid. No-\ntice that, as expected (the calculation relying upon the assumption that vacuum energy gravitates),\nthe result is in agreement with the equivalence principle [4] and the force can also be interpreted\nas the effect of the gravitational field on the negative mass associated to the Casimir energy [5].\nFrom an experimental point of view, the critical points are essentially two: 1) the expected force\nbeing quite small, the measurement must be performed modulating the effect; 2) a suitable device\nmust be studied to perform the measurement. As far as the first point is concerned, as has been\nrecently discussed [6], a possible way to modulate the vacuum energy contained in a cavity is by\nperforming a superconducting transition of the plates: when the plates become superconducting\nthe reflectivity changes and so it does the vacuum energy contained between the plates [7]. The\nvariation of Casimir energy could be particularly relevant in case of type II layered superconduc-\ntors, like cuprates. Even though a complete study is still lacking, and it is one of the problems to\nbe faced inside the Archimedes project, order of magnitude expectations suggest that measuring\nthe weight of the transition energy of such materials could be a test of the weighing of vacuum\nenergy [6, 8]. The amplitude Fm of the modulation of weight turns out to be quite small, of the\norder of Fm ≈ 10−16 N. This force is not out of reach of the presently most sensitive macroscopic\ndevices for the measurement of small forces, such as the Gravitational Wave detectors or torsion\npendulums [6]. In this paper we present the main choice exploited by the Archimedes project and\ndiscuss the steps to be done to assess the actual feasibility of an experiment for the final measure\nof such a force.\n\n2\n\n\n\nP\no\nS\n(\nF\nF\nP\n1\n4\n)\n1\n8\n7\n\nArchimedes project E. Calloni\n\nFigure 1: Experiment scheme, expected signal and noises. Left: scheme of the balance suspended to the\ninverted pendulum. Right: expected signal (blue curve) and main noises. The detection bandwidth is within\nthe resonance of the balance, limited by the read-out noise, dashed-line, indicated as Oro Noise.\n\n2. Balance versus suspended masses interferometer\n\nIn a recent paper [6] it has been shown that both the Gravitational Wave Detector and balances\ncould be suitable for detecting the Archimedes force from a sensitivity point of view. In particular,\nthe third generation GW detectors, i.e. the planned Einstein Telescope, could reach a sensitivity of\nabout F̃ = 3 ∗ 10−15N/\n\n√\n(Hz) in the low frequency region, corresponding to the detection of the\n\nArchimedes force in tens of minutes of integration time. In order to choose the detection system\none experimental key point is the modulation of the effect, i.e. the periodical transition from normal\nto superconducting state. In particular, it must be compatible with the bandwidth of the detectors.\nThe possible modulations of the transition are by temperature or external field. Both are favored\nin the low frequency region. This motivation leads us to the choice of the balances as the system\nto be experimentally used for the detection of the force. Indeed, in case of balances, the detection\nbandwidth can be in the region of 1-100 mHz, comparable with torsion pendulums, while in case\nof Gravitational Wave detectors it extends from 10 Hz to few KHz. The possibility to modulate at\nso small frequency is seen as a decisive argument in favour of using balances, even though in the\nlong term the use of third generation GW detectors could be re-considered.\n\n3. Seismic isolation and expected sensitivity\n\nOne of the main problems to be addressed in realizing a balance capable of measuring forces\nof the order of few 10−16 N is the lack of an attenuation system in the very low frequency regime\nof 1-100 mHz. The realization of such a system would allow the balance to reach a vertical force\nsensitivity compatible with the torsion pendulums horizontal one, which can be as well of the order\nof few 10−15 N/\n\n√\n(Hz) [9]. One possible strategy is to hang the balance to a seismic isolation\n\ncascade formed by an inverted pendulum and blade-spring attenuator similar to the ones used in\nthe Virgo gravitational wave detector, and actively reduce the residual motion by sensing with\n\n3\n\n\n\nP\no\nS\n(\nF\nF\nP\n1\n4\n)\n1\n8\n7\n\nArchimedes project E. Calloni\n\naccelerometers and feed-backing on the top of the cascade [6, 10]. An alternative reduction of\nresidual noise is based on a mechanical resonator, placed on the top of the Inverted-Pendulum as\nsketched in fig. 1; the absorber is coupled to the Inverted-Pendulum so as to have the complex-zero\nof the transfer function tuned at the signal modulation frequency. In this way the seismic energy is\nabsorbed by the resonator at that frequency and the suspension motion at the frequency is reduced\nby the attenuation transfer function of the Inverted-Pendulum and by the quality factor of absorber\nresonance. The major sources of noise in this scheme will be represented by the thermal noise and\nthe seismic noise, as reported in fig. 1. The read-out system, as discussed in [6] and also reported in\nfig. 1, can be an optical lever. As shown in the figure, with these choices the modulation frequency,\nthe seismic-resonant absorber frequency and the balance frequency must be carefully tuned to be\nthe same, and forced to lie in the low-noise seismic region. Furthermore, the experiment must be\nperformed in very low seismic noise sites, like the Sos-Enattos mine (Sardinia Island, Italy) [11].\nThese limitations should be compared with the use of an active seismic noise reduction scheme, that\nin principle does not require such a quiet environment and relaxes the constraints on the bandwidth,\nbut at the price of a remarkably higher complexity [6]. The assessment of the passive reduction and\ncomparison of these two methods will be one of the major tasks of the Archimedes experiment.\n\nReferences\n\n[1] S. Weinberg, Rev. Mod. Phys. 61 (1989) 1; M. Ishak, Found. Phys. 37 (2005) 1470.\n\n[2] C. Rovelli, Quantum Gravity, Cambridge University Press, Cambridge (2004); E. Bianchi and C.\nRovelli, Nature 466 (2010) 321; C. Kiefer, Quantum Gravity, Clarendon Press, Oxford, (2012); B.S.\nDeWitt and G. Esposito, Int. J. Geom Methods Mod. Phys. 5 (2008) 101.\n\n[3] T. Padmanabhan, Int. J. Mod. Phys. D 15 (2006) 2029.\n\n[4] S. A. Fulling et al, Phys. Rev. D 76 (2007) 025004; S. A. Fulling, K. A. Milton et al, J. Phys. A 40\n(2007) 10935; K. A. Milton et al, J. Phys. A 41 (2008) 164052; K. V. Shajesh et al. J. Phys. A 41\n(2008)164058 ; F. Sorge Class. Quant. Grav 26 (2009) 235002; K. A. Milton et al, Phys. Rev. D 89\n(2014) 064027;\n\n[5] E. Calloni et al, Phys. Lett. A 297 (2002) 328 ; G. Bimonte et al, Phys. Rev. D 74 (2006) 085011; G.\nBimonte et al, Phys. Rev. D 76 (2007) 025008.\n\n[6] E. Calloni et al, Phys. Rev. D 90 (2014) 022002.\n\n[7] G. Bimonte et al, Phys. Rev. Lett. 94 (2005) 180402 ; G. Bimonte et al, Nucl. Phys. B 726 (2005) 441;\nG. Bimonte et al, J. Phys. A 41 (2008) 164023; A. Allocca et al, Jour. Super. and Novel Mag. 25\n(2012) 2557.\n\n[8] G. Barton, J. Phys. A 38 (2005) 2997 ; M. Bordag, J. Phys. A 39 (2006) 6173; A. Kempf, J. Phys. A\n41 (2008) 164038.\n\n[9] L. Carbone et. al, Class. Quant. Grav. 22 (2205) S509.\n\n[10] J. Harms et al, Phys. Rev. D 88 (2013) 122003.\n\n[11] L. Naticchioni et al, Class. Quant. Grav. 31 (2014) 105016.\n\n4"},"fulltext":true,"source":"PoS","key":"2feea2b3f8f0fafb49f05b51d4670dc1","url":"https://inspirehep.net/files/2feea2b3f8f0fafb49f05b51d4670dc1"}],"authors":[{"raw_affiliations":[{"value":"Università Federico II - Napoli, Naples, Italy"}],"full_name_unicode_normalized":"calloni, enrico","full_name":"Calloni, Enrico","record":{"$ref":"https://inspirehep.net/api/authors/1014715"},"last_name":"Calloni","ids":[{"schema":"INSPIRE BAI","value":"E.Calloni.1"}],"affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/903043"},"value":"Naples U."},{"record":{"$ref":"https://inspirehep.net/api/institutions/902883"},"value":"INFN, Naples"}],"signature_block":"CALANe","first_name":"Enrico","uuid":"c6e8f820-4198-4f9f-abdb-64be38f23b74","recid":1014715},{"raw_affiliations":[{"value":"Università di Roma \"La Sapienza\" e INFN  Sezione di Roma - P.le A. 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A 41 (2008) 164038."}],"record":{"$ref":"https://inspirehep.net/api/literature/698920"}},{"reference":{"label":"8","publication_info":{"journal_volume":"41","artid":"164038","year":2008,"journal_title":"J.Phys.A"},"authors":[{"full_name":"Kempf, A."}]},"raw_refs":[{"schema":"text","value":"[8] G. Barton, J. Phys. A 38 (2005) 2997 ; M. Bordag, J. Phys. A 39 (2006) 6173; A. Kempf, J. Phys. A 41 (2008) 164038."}],"record":{"$ref":"https://inspirehep.net/api/literature/1707571"}},{"reference":{"label":"9","misc":["Class. Quant. Grav. 22 (2205) S509"],"authors":[{"full_name":"Carbone, L."}]},"raw_refs":[{"schema":"text","value":"[9] L. Carbone et. al, Class. Quant. Grav. 22 (2205) S509."}]},{"reference":{"label":"10","publication_info":{"journal_volume":"88","artid":"122003","year":2013,"journal_title":"Phys.Rev.D"},"authors":[{"full_name":"Harms, J."}]},"raw_refs":[{"schema":"text","value":"[10] J. Harms et al, Phys. Rev. D 88 (2013) 122003."}],"record":{"$ref":"https://inspirehep.net/api/literature/1247237"}},{"reference":{"label":"11","publication_info":{"journal_volume":"31","artid":"105016","year":2014,"journal_title":"Class.Quant.Grav."},"authors":[{"full_name":"Naticchioni, L."}]},"raw_refs":[{"schema":"text","value":"[11] L. Naticchioni et al, Class. Quant. Grav. 31 (2014) 105016."}],"record":{"$ref":"https://inspirehep.net/api/literature/1294983"}}],"number_of_pages":10,"collaborations":[{"value":"Archimedes"}],"legacy_creation_date":"2014-09-25","preprint_date":"2014-09-24","author_count":16,"public_notes":[{"source":"arXiv","value":"10 pages, 4 figures"}],"earliest_date":"2014-09-24","external_system_identifiers":[{"schema":"HAL","value":"hal-01255195"}],"facet_author_name":["1954252_Sergio Caprara","1954257_Gianpiero Pepe","2062711_Paolo Ruggi","987414_Cosimo Stornaiolo","991095_Carlo Rovelli","991837_Fulvio Ricci","993591_Silvano Petrarca","1010578_Giampiero Esposito","1014715_Enrico Calloni","1031184_Luigi Rosa","1052196_Francesco Tafuri","1054344_Ettore Majorana","1060806_Lovedeep Kaur Saini","1065914_M. Grilli","1423873_Martina De Laurentis","1424033_Paola Puppo"],"core":true,"license":[{"imposing":"arXiv","url":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/"},{"license":"CC-BY-NC-SA","imposing":"SISSA"}],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:1318824","updated":"2023-11-08T21:35:47.854477"},"journal_title_variants":["PoS"],"arxiv_eprints":[{"categories":["gr-qc","hep-th"],"value":"1409.6974"}],"referenced_authors_bais":["L.Milano.1","Mustapha.Ishak.Bourshaki.1","B.S.DeWitt.1","T.Padmanabhan.1","L.Naticchioni.1","L.Rosa.1","Stephen.A.Fulling.1","L.Di.Fiore.1","Fulvio.Ricci.1","H.Muller.16","Rosario.De.Rosa.1","D.Born.2","U.Huebner.2","P.Ruggi.17","G.Loddo.1","G.Bimonte.1","F.Barone.1","Steven.Weinberg.1","E.Ilichev.2","V.Malvezzi.2","J.Harms.1","M.Bordag.1","A.Kempf.1","R.Vaglio.2","M.Perciballi.1","F.Tafuri.1","A.Romeo.3","F.Garufi.1","Yanbei.Chen.1","P.Parashar.3","K.V.Shajesh.1","Matthew.Evans.1","G.Giordano.1","E.Coccia.1","M.Punturo.1","Martina.De.laurentis.1","F.Acernese.1","R.Romano.2","P.Calia.1","M.C.Miller.1","Rana.Adhikari.1","E.Calloni.1","B.J.J.Slagmolen.10","Giampiero.Esposito.1","F.Sorge.1","K.A.Milton.1","Carlo.Rovelli.1","J.A.Wagner.1","Masaki.Ando.1"],"figures":[{"filename":"contributionEntropy.png","caption":"Internal energy variation contributions in the approximation of parabolic critical field dependence from temperature T for a superconductor having $T_c$ = 90 K and thermodinamical critical zero field B0 = 1.16 Tesla  (YBCO typical values): the contribution due to entropy variation (DeltaS), the Gibbs free energy (DeltaG), the total (DeltaU)","source":"arxiv","key":"a4705c32dd6590aef56d74887ffcf614","url":"https://inspirehep.net/files/a4705c32dd6590aef56d74887ffcf614"},{"filename":"SeismicNoiseTF.png","caption":"Transfer function of seismic noise to the balance suspension point. The resonant absorber, continuous line, shows the complex zero-poles behavior that, at the complex zero frequency, reduces further the seismic noise for the zero-anti resonance quality factor","source":"arxiv","key":"aa6daa3d0c48b82ddab37559959e597c","url":"https://inspirehep.net/files/aa6daa3d0c48b82ddab37559959e597c"},{"filename":"2invPend.png","caption":"Schematic picture of the Archimedes force measurement. On the top of the inverted pendulum there is a second inverted pendulum acting as an absorbing stage. The balance is hanged to the intermediate spring-attenuation element. The signal is read by an optical lever system","source":"arxiv","key":"e418d992fe685cdbb81dcbdbab09594c","url":"https://inspirehep.net/files/e418d992fe685cdbb81dcbdbab09594c"},{"filename":"sensitivityForce.png","caption":"Expected signal and noises. The detection bandwidth is within the resonance of the balance, limited by the read-out noise indicated as oroNoise","source":"arxiv","key":"8a9dbccf9731c444b3351b98c68d66f5","url":"https://inspirehep.net/files/8a9dbccf9731c444b3351b98c68d66f5"}],"legacy_version":"20190409110649.0","inspire_categories":[{"term":"Gravitation and Cosmology"},{"term":"Theory-HEP"}],"accelerator_experiments":[{"legacy_name":"Archimedes","curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/experiments/2655535"}}],"urls":[{"value":"http://pos.sissa.it/archive/conferences/224/187/FFP14_187.pdf"},{"description":"PoS server","value":"http://pos.sissa.it/archive/conferences/224/187/FFP14_187.pdf"}],"first_author":{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/015kcdd40"}],"full_name":"Calloni, Enrico","last_name":"Calloni","first_name":"Enrico","recid":1014715},"control_number":1318824,"dois":[{"value":"10.22323/1.224.0187"}],"document_type":["conference paper"],"texkeys":["Archimedes:2014skz","Calloni:2014aya"],"abstracts":[{"source":"arXiv","value":"Archimedes is a feasibility study to a future experiment to ascertain the interaction of vacuum fluctuations with gravity. The future experiment should measure the force that the Earth's gravitational field exerts on a Casimir cavity by using a balance as the small force detector. The Archimedes experiment analyses the important parameters in view of the final measurement and experimentally explores solutions to the most critical problems.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["gr-qc"],"titles":[{"source":"arXiv","title":"The Archimedes project: a feasibility study for weighing the vacuum energy"}],"imprints":[{"date":"2014-12-23","publisher":"SISSA"}],"curated":true},"links":{"bibtex":"https://inspirehep.net/api/literature/1318824?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1318824?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1318824?format=latex-us","json":"https://inspirehep.net/api/literature/1318824?format=json","json-expanded":"https://inspirehep.net/api/literature/1318824?format=json-expanded","cv":"https://inspirehep.net/api/literature/1318824?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1318824"},"id":"1318824"},{"created":"2026-06-24T17:10:48.552625+00:00","updated":"2026-07-16T13:37:34.005551+00:00","metadata":{"documents":[{"filename":"fulltext.pdf","attachment":{"content":"Weighing the Quantum Vacuum: \nLatest Progress and Experimental Status of the\n\nArchimedes experiment\n\nMarina Esposito\nUniversity of Napoli “Federico II” \nINFN - Sezione di Napoli\n\nJun 5, 2026\n\n\n\nOUTLINE \n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nI. Scientific Motivation\nDoes vacuum energy weigh? \n\nII. The Archimedes Modulation Strategy\nCasimir Energy\n\nHigh-𝑇𝐶 Superconductors as a Vacuum Switch\n\nIII. Current Status of the Experiment \n\n2\n\n\n\nGravity and EM field coupling\n\n• Gravity on massive objects also depends on their stress state\n\n• Gravity also applies to non-massive fields\n(like the e.m. field)\n\n• While QED in curved spacetimes is established, its coupling with \ngravity is still topic of debate \n\n→ Cosmological Constant Problem [Weinberg, 1989]\n\n𝐺𝜇𝜈 + Λ𝑒𝑓𝑓𝑔𝜇𝜈 =\n8𝜋𝐺\n\n𝑐4\n𝑇𝜇𝜈\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nDoes the Zero Point Energy (ZPE) satisfy the Equivalence Principle? \n\n3\n\n\n\nHow much does Nothing weigh?\n\n• Macroscopic bulk samples (+ their internal energy) \nsuspended from a highly sensitive interferometric beam-\nbalance;\n\n• The samples host a significant amount of quantum \nvacuum energy;\n\n• The internal quantum vacuum energy is periodically \nmodulated;\n\nIf quantum vacuum couples to gravity, the weight \nchanges and the weight variation is detected in real \ntime with the balance\n\nLes Rencontres de Noirmoutier - June 5, 2026 4\n\n\n\nThe Casimir Effect\nVacuum Energy confined using Casimir Effect (1948), also the most direct proof \nof vacuum fluctuations\n\n𝐸𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑣𝑒 𝑝𝑙𝑎𝑡𝑒𝑠 − 𝐸𝑒𝑚𝑝𝑡𝑦 ≡ ℇ𝐶𝑎𝑠 = −\n𝜋2\n\n720\n\nℏ𝑐\n\n𝑎3\n𝐿2 negative \n\nenergy \n\n1\n\n𝐿2\n𝐹 𝑎 = −\n\n1\n\n𝐿2\n\n𝜕\n\n𝜕𝑎\nℇ𝐶𝑎𝑠 𝑎 = −\n\n𝜋2ℏ𝑐\n\n240𝑎4\nCasimir Force\n\nfor 𝑎 ~ 1 𝜇𝑚,  𝐿 ~ 1 𝑐𝑚 →  ℇ𝐶𝑎𝑠 ~ 40 𝑛𝐽,  𝐹𝐶𝑎𝑠 ~10−7𝑁\n\nFirst experimental observation: Sparnaay, 1958\n2005 Mohideen: force tested with 5‰ accuracy\n\nVacuum energy inside is less when plates are reflective\n\n𝐿\n\n𝑎\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nArchimedes aims to measure the interaction \nbetween gravity and the vacuum energy density \nlocalized in a Casimir cavity.\n\n5\n\n\n\nCasimir Cavity in the Gravitational Field\n\nԦ𝑓 =\nℇCas\n\nc2\ng ොz\n\nԦf is the weight of the cavity in GR \nframework\n\nFor a single Casimir cavity with S ≈ 1 dm2 and a ≈ 1 μm, \n\nthe signal force intensity would be F ~ 4 ∙ 10−28 N\n\n[G.Bimonte,  E. Calloni, G. Esposito, L. Rosa - Phys. Rev D 76:025008 (2007)]\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nToo small for static detection!\n\n6\n\n\n\nModulating Vacuum Energy \nSuperconductivity as a switch\n\nPhase Transition\nTransitioning from the normal to superconducting state \nalters the material’s reflectivity ▻ “amount of vacuum” \nmodulated\n\nHTS are natural multi-layered Casimir cavities. For a disk-\nshaped YBCO with R = 5 cm, thickness 5 mm, the force \nexerted by the gravitational field is:\n\nԦ𝐹  ≈ 5 ×  10−16 𝑁\n\nCasimir on\n\nCasimir off\n\nL. Rosa et al, Eur. Phys. J. Plus 137, 826 (2022)\nA. Allocca et al., Phys. Rev. B 106, 134502 (2022)\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nExpelling electromagnetic modes reduces \nlocal vacuum energy\n\n7\n\n\n\nThe Archimedes Experiment\n\n• Cryogenic double suspended beam balance \n\n• interferometer readout  \n\n• reference arm (upper) insulates the measurement arm (bottom) \nfrom the ground disturbances.\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nkept at cryogenic temperature of ∼90 K thanks to a suitably designed 3-chambers \ncryostat filled with liquid Nitrogen\n\nTwo superconductive samples are \nsuspended to the measurement \narm\n\nSpectral Torque Signal in 2 weeks of \nintegration: \n\n𝜏𝑆 = 3.5 × 10.−13\n𝑁 𝑚\n\n√𝐻𝑧 8\n\n\n\nStatus of the experiment\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\n• Measurement arm very light to lower the moment of inertia\n\n• Suspended with thin flexible joints (Cu-Be, 100 μm x 100 μm)\n\n9\n\n\n\nHTS Sample Requirements\n\n(1) Target mass ~ 200 𝑔\n\n(2) sharp superconducting transition:  ∆𝑇 =  𝑇𝑜𝑛𝑠𝑒𝑡 − 𝑇𝑧𝑒𝑟𝑜 = 1 𝐾 \n\n(3) fast heat exchange for quasi-static approach\n\nThe prime candidate: GdBCO (𝐺𝑑𝐵𝑎2𝐶𝑢3𝑂7−𝑥)\n\n- Critical Temperature 93.5 K \n- proven feasibility for single-domain scaling and ring \nshape -> efficient thermal exchange\n\nGdBCO\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nRoom temperature XRD \n\nverified a highly crystalline \n\nstructure consisting of 77% \n\nactive superconducting Gd-123 \n\nphase \n\nmeasurements performed by R. Fittipaldi, A. Guarino CNR-\n\nSPIN Salerno\n\n10\n\n\n\nStatus of the experiment\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nSystem installation at room temperature fully completed \nsince April 2025.\nFirst data taking in October 2025.  \n\nVacuum level reached 2e-6 mbar \n\nVirgo-like vacuum pump and system\n\nInstalled at the SarGrav surface \nlaboratories in Lula (NU) at Sos Enattos \nmine, one of the candidate sites for third \ngeneration GW interferometer Einstein \nTelescope.\n\n11\n\n\n\nStatus of the experiment\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nSystem installation at room temperature fully completed \nsince April 2025.\nFirst data taking in October 2025.  \n\nLow frequency noise still high for the experiment \npurposes (about 3 orders of magnitude), but we are \n\nfocusing on it in the commissioning\n\nExpected signal\n\n12\n\n\n\nStatus of the experiment\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nSystem installation at room temperature fully completed \nsince April 2025.\nFirst data taking in October 2025.  \n\nBest sensitivity in the world in the 1-10 Hz range\n2e-12 rad/sqrt(Hz) \n\n13\n\n\n\nThank you for your \nattention!\n\nLes Rencontres de Noirmoutier - June 5, 2026 15\n\n\n\nBibliography\n\nLes Rencontres de Noirmoutier - June 5, 2026\n\nE. Calloni. L. Di Fiore, G. Esposito, L. Milano, L. Rosa - Phys. Letters A, 297, 328-333, (2002)\n\nG. Bimonte, E Calloni, Di Fiore, G. Esposito, L. Milano, L. Rosa -  CQG 21 647 (2004)\n\nG. Bimonte, E. Calloni , G. Esposito, L. Rosa -  Phys. Rev D  74, 085011 (2006)\n\nG.Bimonte,  E. Calloni, G. Esposito, L. Rosa - Phys. Rev D 76:025008 (2007)\n\nG. Bimonte, E. Calloni, L. Rosa -  Phys. Rev D 77, 044026 (2008)\n\nA. Allocca G. Bimonte, E. Calloni, G. Esposito, U. Huebner, E. Il’ichev, L. Rosa, F. Tafuri.,  Jour. Of. Supercond. And Novel Magnetism. 25, 2557-\n2565 (2012)\n\nE. Calloni et al., Eur. Phys. J. Plus (2021) 136:335\n\nA. Allocca, E. Calloni, L. Errico et al, Eur. Phys. J. Plus (2021) 136: 1069\n\nL. Rosa et al, Eur. Phys. J. Plus 137, 826 (2022)\n\nA. Allocca et al., Phys. Rev. B 106, 134502 (2022)\n\nCalloni, E. et al. Eur. Phys. J. Plus 139, 158 (2024) - https://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-\nelucidate-the-origins-of-dark-energy\n\nV. Mangano et al. PoS TAUP2023 (2023), 317 doi:10.22323/1.441.0317\n\n16\n\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\nhttps://www.epj.org/epjplus-news/2736-epjplus-highlight-beam-balance-designs-could-elucidate-the-origins-of-dark-energy\n\n\nRoom-Temperature Modulation Prototype\n\nThermal modulation through radiative \nprocess (not to introduce any radiation \npressure effect on the sample) studied \nboth at room temperature and at \ncryogenic temperature\n\nRoom temperature setup (NA) installed at \nEGO-Virgo 1500W test facility\n\nLes Rencontres de Noirmoutier - June 5, 2026 17\n\n\n\nVacuum Energy and \nsuperconductive phase transition\n\n𝑉\n𝐻𝑐\n\n2(𝑇)\n\n8𝜋\n= ℇ𝑐𝑜𝑛𝑑(𝑇)\n\n𝑉\n𝐻𝑐\n\n2(𝑇)\n\n8𝜋\n= ℇ𝑐𝑜𝑛𝑑 𝑇 + Δℇ𝐶𝑎𝑠 (𝑇)\n\nALADIN experiment (2005-2012): test if vacuum fluctuations affects the \nsuperconducting phase transition in type I superconductors. \n\nWhen the film is part of a Casimir cavity, we have to augment the right-\nhand side of the eq. by the difference between the Casimir energy \nin the normal and superconducting phase\n\nSuperconductivity lab of Federico II in Naples (Prof. F. Tafuri)\n\nIndication of a phase transition influenced by vacuum fluctuations.\n\nAl (10 nm)\n\nAu (100 nm)\n\n𝐴𝑙2𝑂3 (10 nm)\n\nLes Rencontres de Noirmoutier - June 5, 2026 18\n\n\n\nCasimir Cavities with type I superconductors\n\nCondensation energy is very small so the variation of \nCasimir Energy can be comparable to the total transition \nenergy\n\nΔℇcas\n\nℇcas\n≃ 10−6\n\nA. Allocca et Al. Jour. Of. Supercond. And Novel MaG. Bimonte et Al.  - J. Phys. A: Math. 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