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Those vacuum fluctuations are generally deemed an elusive phenomenon that manifests itself only indirectly. Here, we report direct detection of the vacuum fluctuations of electromagnetic radiation in free space. The ground-state electric field variance is found to be inversely proportional to the four-dimensional space-time volume sampled electro-optically with tightly focused few-femtosecond laser pulses. Sub-cycle temporal readout and nonlinear coupling far from resonance provide signals from purely virtual photons without amplification. Our findings enable an extreme time-domain approach to quantum physics with nondestructive access to the quantum state of light. 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By performing high-resolution emission spectroscopy for individual colloidal quantum dots at cryogenic temperatures, we prove the causal link between the quantum-confined Stark effect and SD. Statistically analyzing the wavelength of emitted photons, we show that increasing the sensitivity of the transition energy to an applied electric field results in amplified spectral fluctuations. This relation is quantitatively fit to a straightforward model, indicating the presence of a stochastic electric field on a microscopic scale, whose standard deviation is 9 kV/cm, on average. The current method will enable the study of SD in multiple types of quantum emitters such as solid-state defects or organic lead halide perovskite quantum dots, for which spectral instability is a critical barrier for applications in quantum sensing.","abstract_source_suggest":{"input":"ACS"}},{"source":"arXiv","value":"Spectral diffusion (SD) represents a substantial obstacle towards implementation of solid-state quantum emitters as a source of indistinguishable photons. By performing high-resolution emission spectroscopy for individual colloidal quantum dots at cryogenic temperatures, we prove the causal link between the quantum-confined Stark effect and SD. Statistically analyzing the wavelength of emitted photons, we show that increasing the sensitivity of the transition energy to an applied electric field results in amplified spectral fluctuations. This relation is quantitatively fit to a straightforward model, indicating the presence of a stochastic electric field on a microscopic scale whose standard deviation is 9 kV/cm, on average. Compensating the commonly observed intrinsic electric bias with an external one, we find that SD can be suppressed by up to a factor of three in CdSe/CdS core/shell nanorods. The current method will enable the study of SD in multiple types of quantum emitters, such as solid-state defects or organic lead-halide perovskite quantum dots, for which spectral instability is a critical barrier for applications in quantum sensing.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["cond-mat.mes-hall"],"titles":[{"source":"ACS","title":"Electric-Field Fluctuations as the Cause of Spectral Instabilities in Colloidal Quantum Dots"},{"source":"arXiv","title":"Electric-field fluctuations as the cause of spectral instabilities in colloidal quantum dots"}],"imprints":[{"date":"2023-10-23"}],"curated":false},"created":"2023-10-17T06:31:36.543703+00:00","id":"2711435","updated":"2025-06-11T14:38:10.901696+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/2711435?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/2711435?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/2711435?format=latex-us","json":"https://inspirehep.net/api/literature/2711435?format=json","json-expanded":"https://inspirehep.net/api/literature/2711435?format=json-expanded","cv":"https://inspirehep.net/api/literature/2711435?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A2711435"}},{"metadata":{"citation_count":29,"citation_count_without_self_citations":17,"authors":[{"raw_affiliations":[{"value":"Department of Physics U. and Center for Applied Photonics - 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unewald.1","C.S.Unnikrishnan.1","V.Huang.1","Alan.J.Weinstein.1","Chang.Hwan.Lee.1","D.Jones.4","D.V.Seletskiy.1","E.Coccia.1","Keith.Alan.Thorne.1","Kip.S.Thorne.1","R.Romano.2","Rana.Adhikari.1","Raul.Murillo.Garcia.1","M.Evans.1","Romain.Bonnand.1","N.Beveridge.1","S.A.Usman.5","Margaret.Millhouse.1","V.Loriette.41","A.D.Silva.1","Andrew.R.Williamson.1","H.Vocca.4","H.Cho.4","W.Z.Korth.11","P.Veitch.1","Elena.Cuoco.1","G.Hammond.18","C.Bogan.6","A.Freise.1","L.Wallace.29","N.J.Cerf.2","E.E.Schmidt.1","V.Mangano.6","Abhirup.Ghosh.1","Eric.Thrane.1","Hong.Yu.1","N.Gordon.4","C.O.Kim.1","J.Li.30","C.Adams.1","K.E.Dorfman.1","Xin.Chen.2","B.Moe.10","M.I.Kolobov.1","S.W.Ballmer.1","K.A.Hodge.3","Mark.A.Barton.1","D.Feldbaum.3","F.Seifert.1","A.Cumming.4","G.Ballardin.1","P.D.Lasky.1","R.W.OShaughnessy.1","M.C.Tringali.1","C.Robinson.11","Paul.B.Corkum.1","C.M.Reed.11","W.Kells.6","R.Nawrodt.6","L.T.London.6","Farit.Khalili.1","A.PalSingh.2","Christelle.Buy.1","J.Aasi.1","G.Davies.49","M.S.Shahriar.4","Marica.Branchesi.1","R.Conte.1","G.Bergmann.3","G.Wu.6","A.Melatos.1","L.Sancho.de.la.Jordana.9","M.G.van.Beuzekom.1","T.Hardwick.3","S.Vass.5","B.C.Stephens.2","S.Cortese.2","Maxime.Fays.1","F.Travasso.1","M.J.Szczepanczyk.10","F.Bruckner.2","W.Katzman.2","M.Thomas.2","R.Passaquieti.1","Brett.Shapiro.1","J.B.Kanner.1","Huan.Yang.1","E.D.Harstad.9","S.Drasco.1","E.Quintero.2","O.V.Tikhonova.1","M.Vardaro.1","I.Maksimovic.1","Xing.Jiang.Zhu.1","Alessandra.Corsi.1","K.J.Blow.1","Irene.Di.Palma.1","A.Libson.9","K.S.Lee.1","L.Gondan.1","Gregory.M.Harry.1","S.E.Whitcomb.1","N.M.Brown.2","A.Buonanno.1","N.A.Lockerbie.15","D.B.Kelley.2","Maximiliano.Isi.1","J.H.Chow.3","H.Gabbard.1","R.Dannenberg.1","Lin.Qing.Wen.1","M.C.Kinsey.1","M.Cabero.1","Duncan.A.Brown.1","S.Hild.3","A.Grant.43","Laura.K.Nuttall.1","E.J.King.2","Rajeev.Kumar.1","T.L.Sidery.2","S.E.Gossan.1","L.Gammaitoni.1","C.Biwer.2","P.Patel.2","E.L.Robinson.11","J.R.Gleason.1","R.Poggiani.2","H.Wittel.1","V.Herrera.1","D.F.Menendez.1","P.B.Graff.2","S.Mirshekari.2","M.Gosselin.1","S.Foley.5","H.Ward.27","C.Ramet.2","Romain.Gouaty.1","M.Jacobson.2","M.Thomas.5","I.SantiagoPrieto.6","D.Nolting.1","B.Sorazu.19","O.D.Aguiar.1","Rainer.Weiss.1","J.Worden.4","M.Boer.2","A.Di.Virgilio.1","B.Krishnan.1","R.Stone.1","B.Kim.6","T.Briant.2","Karen.Haughian.1","S.Frasca.1","E.Genin.2","Z.L.Zhou.1","K.Grover.2","J.Warner.7","M.S.Shahriar.2","V.Tiwari.1","Alberto.Vecchio.1","G.L.Mansell.7","C.Graef.1","R.Wooley.17","Bala.R.Iyer.1","Kenneth.A.Strain.1","P.Puppo.1","D.DeBra.1","P.Murray.1","W.Winkler.1","Grant.D.Meadors.1","D.Abrams.1","F.Donovan.2","H.Y.Shih.2","D.Keitel.1","Joseph.Betzwieser.1","M.P.Thirugnanasambandam.5","V.Predoi.1","Stefan.Gossler.1","Andrew.G.Ivanov.1","K.A.Hodge.9","J.Gleason.2","F.Sorrentino.1","R.Kurdyumov.1","M.V.Chekhova.1","X.Amador.1","A.Stochino.10","J.Berakdar.1","G.Hammond.4","J.R.Taylor.1","S.Steplewski.1","Young.Min.Kim.2","S.Penn.50","B.K.Kim.1","G.Manca.2","M.Montani.3","Kipp.C.Cannon.1","K.Nedkova.1","I.Kamaretsos.2","M.Yvert.2","C.Casentini.1","M.Wang.21","M.H.Lee.2","G.M.Guidi.6","R.J.E.Smith.7","G.Moreno.1","L.Matone.1","R.VincentFinley.2","A.Marandi.1","Joris.Van.Heijningen.1","L.Milano.1","M.A.Broome.1","K.V.Tokmakov.1"],"figures":[{"filename":"Fig0.png","material":"preprint","caption":"\\textbf{Scheme of the generation and detection setup and the corresponding evolution of the mid-infrared quantum field $\\hat{\\varepsilon}(z,t)$ inside the nonlinear crystal for a half-cycle mid-infrared driving field with effective squeezing strength $r=5$. a}, A strong mid-infrared coherent field $\\mathcal{E}(z,t)$ is sent into the nonlinear generating crystal (GX) of length $l$ where it squeezes the co-propagating vacuum field $\\hat{\\varepsilon}(z,t)$. The squeezed quantum field is then detected using electro-optic sampling: a probe pulse with intensity envelope $I_\\mathrm{p}$ plays the role of a temporal gating applied at various time points $t_\\mathrm{d}$. Statistical readout allows to obtain the time-resolved variance of $\\hat{\\varepsilon}(z,t)$. Subcycle resolution is achieved for sufficiently short probe pulse durations $t_\\mathrm{p}$. \\textbf{b}, Horizontal plane: Grey lines depict the world lines for $\\hat{\\varepsilon}(z,t)$ [determined by $\\tau(z,t)=\\mathrm{const}$, characteristic curves of Eq.~\\eqref{PDE}], shown for the case of a half-cycle driving field \\eqref{HCP} with duration $\\Gamma_0^{-1}$. The equidistant spacing of the lines at the entrance gets distorted as the quantum light propagates through the crystal. Vertical plane: Field enhancement at the crystal exit is shown together with the final spacing between the world lines. In the simplified picture, red (blue) lines correspond to anti-squeezing (squeezing).","label":"Fig0","source":"arxiv","key":"52c5758c9e51bf4adeeb5f222090989d","url":"https://inspirehep.net/files/52c5758c9e51bf4adeeb5f222090989d"},{"filename":"Fig1.png","material":"preprint","caption":"{\\bf Behaviour of the conformal time with respect to the lab time illustrated for the half-cycle pulse [cf. Eq.~\\eqref{HCP}] with $r=5$ and $\\Gamma_0/(2\\pi)=26$ THz. a}, Conformal time $\\tau'(z',t')$ as a function of the lab time $t'$ and the propagation length inside the crystal $z'=z$. The retarded reference frame is used. $\\tau'(z',t')$ coincides with $t'$ at the entrance of the crystal $z'=-l/2$ and starts to deviate from it for $z'>-l/2$. The graph is coloured according to the values of the inverse conformal factor $\\frac{\\partial\\tau'(z',t')}{\\partial t'}$. In the simplified picture, which does not yet incorporate the detection process influenced also by the change in the local density of the world lines, departure from green towards blue (red) leads to squeezing (anti-squeezing) of the vacuum fluctuations. The black lines help the visualization of the surface. \\textbf{b}, Red line: final conformal time $\\tau_{\\mathrm{out}}(t)=\\tau(z=l/2,t)$ at the exit of the crystal as a function of the lab time $t$, shown in the original reference frame. Dashed black line: same without the driving field --- delayed by $nl/c_0$ with respect to $t$. Full black line: the run of the lab time $t$ is shown for comparison. Values of $\\tau_{\\mathrm{out}}(t)$ must stay below the red area defined by the delay time $t_{\\mathrm{d,0}}=l/c_0$ in order not to violate causality (cf. Supplementary Information).","label":"Fig1","source":"arxiv","key":"dc93e2f14bd59a1f9970701f0f013351","url":"https://inspirehep.net/files/dc93e2f14bd59a1f9970701f0f013351"},{"filename":"Fig2.png","material":"preprint","caption":"{\\bf Relative detected variance (RDV) in dependence on the strength of the half-cycle driving field and probe pulse duration. a}, Temporal profiles of the driving field $\\mathcal{E}'$ with two opposite polarities and probe pulse intensity envelope $I_\\mathrm{p}$ with duration $t_\\mathrm{p}=0.49$ fs (blue). \\textbf{b}, Dynamics of the normalized RDV for a fixed probe pulse duration $t_\\mathrm{p}=0.49$~fs and different squeezing strengths $r$=0.1 (red), 0.5 (green) and 2 (blue), proportional to the driving field amplitude. The normalization by $r$ is chosen to keep the signal magnitude in the same range. For comparison, the exact analytical result within the first-order perturbation theory (PT) in $r$ and limit of vanishing $t_\\mathrm{p}$ is shown (black dashed line). The light blue dotted line shows the RDV for the half-cycle pulse with $\\mathcal{E}'\\!<\\!0$ for $r=2$. \\textbf{c}, Temporal profiles of the driving field $\\mathcal{E}'$ (black, normalized by its amplitude $\\mathcal{E}_0$) and probe pulse intensity envelope $I_\\mathrm{p}$ for different probe pulse durations $t_\\mathrm{p}=0.49$~fs (blue), $5.9$ fs (magenta) and $14.7$ fs (cyan) are shown on the same time scale as the RDV. \\textbf{d}, Dynamics of the RDV for a fixed $r=2$ and the same probe pulse durations as in the upper panel.","label":"Fig2","source":"arxiv","key":"604358ba139775aadcdfd5f6a9aa82cc","url":"https://inspirehep.net/files/604358ba139775aadcdfd5f6a9aa82cc"},{"filename":"Fig3.png","material":"preprint","caption":"{\\bf Pulsed squeezing for single-cycle driving. a}, Temporal profiles of the driving field $\\mathcal{E}'(t')=\\mathcal{E}_0\\left[\\exp\\left(-\\Gamma_0^2 t'^2\\right)-1\\right]/(\\Gamma_0t')$ with $\\Gamma_0/(2\\pi)= 26$ THz (black) and probe pulse intensity envelope $I_\\mathrm{p}$ with $t_\\mathrm{p}=5.9$~fs (blue). \\textbf{b}, Corresponding dynamics of the RDV for $r=0.5$ (black line). Dark grey (light grey) areas denote anti-squeezing (squeezing). The red line depicts the noise trace obtained within the simplified picture, where the degree of squeezing (right axis) can be extracted directly from the ratio between the variances of the outgoing and incoming quantum field at each $t_\\mathrm{d}=t$. Negative values for the degree of squeezing correspond to anti-squeezing. \\textbf{c}, Values of the RDV at $t_\\mathrm{d}=0$~fs plotted against $r$ for two different polarities of the driving field. Depending on the polarity, it is the maximum (anti-squeezing, dark grey line, upper inset) or the minimum (squeezing, light grey line, lower inset) value of the RDV. The degree of squeezing (dashed red lines) results from an exponential fit (cf. Supplementary Information). The RDV in \\textbf{b} is then rescaled according to this fit to obtain the degree of squeezing at arbitrary times. The red lines in \\textbf{c} show the degree of squeezing calculated within the simplified picture. For a vanishing probe pulse duration $t_\\mathrm{p}\\rightarrow 0$, the squeezing and anti-squeezing curves obtained from the RDV converge towards this result.","label":"Fig3","source":"arxiv","key":"7f508218e19644f0579dabe96f8df937","url":"https://inspirehep.net/files/7f508218e19644f0579dabe96f8df937"},{"filename":"S2.png","material":"preprint","caption":"Function $g(r)$ for the half-cycle (blue line) and single-cycle (red line) driving. For $r\\ll 1$, $g(r)$ approximately equals $r$ ($0.64r$) in the case of half-cycle (single-cycle) driving. For higher squeezing strengths, $g(r)$ grows more slowly with $r$.","label":"S2","source":"arxiv","key":"08c7fe21801c2ceada3993c2aa17c85a","url":"https://inspirehep.net/files/08c7fe21801c2ceada3993c2aa17c85a"},{"filename":"S1.png","material":"preprint","caption":"Comparison between the half-cycle pulse (black) used for the calculations depicted in Fig. \\ref{Fig2} and the more realistic propagating pulse (red) that it approximates. The two side wings of the red curve compensate the big maximum in the center but are still small compared to the maximum.","label":"S1","source":"arxiv","key":"6f6e01e0e75bb3ca1c3cf770e4154343","url":"https://inspirehep.net/files/6f6e01e0e75bb3ca1c3cf770e4154343"},{"filename":"S3.png","material":"preprint","caption":"Comparison of the RDV for the single-cycle pulse, sampled with a probe pulse with $t_\\mathrm{p}=0.49$ fs, for different squeezing strengths.","label":"S3","source":"arxiv","key":"691ef4a3ddb7683a56a847c3a6225f92","url":"https://inspirehep.net/files/691ef4a3ddb7683a56a847c3a6225f92"}],"legacy_version":"20191003225546.0","inspire_categories":[{"term":"General Physics","source":"arxiv"},{"term":"Gravitation and Cosmology","source":"arxiv"},{"term":"Quantum Physics","source":"arxiv"}],"first_author":{"affiliations_identifiers":[{"schema":"GRID","value":"grid.9811.1"}],"full_name":"Kizmann, Matthias","last_name":"Kizmann","ids":[{"schema":"ORCID","value":"0000-0001-6014-9622"},{"schema":"INSPIRE BAI","value":"M.Kizmann.1"}],"first_name":"Matthias","recid":1869214},"control_number":1684219,"dois":[{"source":"bibmatch","value":"10.1038/s41567-019-0560-2"},{"material":"publication","source":"arXiv","value":"10.1038/s41567-019-0560-2"}],"document_type":["article"],"texkeys":["Kizmann:2018mlc"],"abstracts":[{"source":"Springer","value":"Light as a carrier of information and energy plays a fundamental role in both general relativity and quantum physics, linking these areas that are still not fully compliant with each other. Usually the quantum nature of light is described in the frequency domain. Even for broadband quantum states with a well-defined carrier frequency, a quasi-continuous-wave picture is still applicable. However, recent access to subcycle quantum features of electromagnetic radiation promises a new class of time-dependent quantum states of light. Paralleled with the developments in attosecond science, these advances motivate an urgent need for a theoretical framework that treats arbitrary wavepackets of quantum light intrinsically in the time domain. Here, we formulate a consistent time-domain theory of the generation and sampling of few-cycle and subcycle pulsed squeezed states, leading to a relativistic interpretation in terms of induced changes in the local flow of time. Our theory enables the use of such states as a resource for novel ultrafast applications in quantum optics and quantum information.","abstract_source_suggest":{"input":"Springer"}},{"source":"arXiv","value":"Light as a carrier of information and energy plays a fundamental role in both general relativity and quantum physics, linking these areas that are still not fully compliant with each other. Its quantum nature and spatio-temporal structure are exploited in many intriguing applications ranging from novel spectroscopy methods of complex many-body phenomena to quantum information processing and subwavelength lithography. Recent access to subcycle quantum features of electromagnetic radiation promises a new class of time-dependent quantum states of light. Paralleled with the developments in attosecond science, these advances motivate an urgent need for a theoretical framework that treats arbitrary wave packets of quantum light intrinsically in the time domain. Here, we formulate a consistent time domain theory of the generation and sampling of few-cycle and subcycle pulsed squeezed states, allowing for a relativistic interpretation in terms of induced changes in the local flow of time. Our theory enables the use of such states as a resource for novel ultrafast applications in quantum optics and quantum information.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Subcycle squeezing of light from a time flow perspective"}],"imprints":[{"date":"2019-07-01"}],"curated":false},"created":"2018-07-30T00:00:00+00:00","id":"1684219","updated":"2025-11-17T08:22:36.158759+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/1684219?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1684219?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1684219?format=latex-us","json":"https://inspirehep.net/api/literature/1684219?format=json","json-expanded":"https://inspirehep.net/api/literature/1684219?format=json-expanded","cv":"https://inspirehep.net/api/literature/1684219?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1684219"}},{"metadata":{"citation_count":249,"citation_count_without_self_citations":218,"authors":[{"raw_affiliations":[{"value":"Department of Physics and Center for Applied Photonics, University of Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany"}],"full_name_unicode_normalized":"günter, g.","full_name":"Günter, G.","record":{"$ref":"https://inspirehep.net/api/authors/2793402"},"ids":[{"schema":"INSPIRE BAI","value":"G.Gunter.1"}],"last_name":"Günter","first_name":"G.","uuid":"4deda5df-ee56-4ae5-874a-b0ee847beb1b","recid":2793402},{"raw_affiliations":[{"value":"Department of Physics and Center for Applied Photonics, University of Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany"},{"value":"Laboratorio NEST, CNR-INFM and Scuola Normale Superiore, Piazza San Silvestro 12, I-56127 Pisa, Italy,"}],"full_name_unicode_normalized":"anappara, a.a.","full_name":"Anappara, A.A.","record":{"$ref":"https://inspirehep.net/api/authors/2793403"},"ids":[{"schema":"INSPIRE BAI","value":"A.A.Anappara.1"}],"last_name":"Anappara","first_name":"A.A.","uuid":"326a6b88-9dbc-4485-87b2-d9a085094f7d","recid":2793403},{"raw_affiliations":[{"value":"Department of Physics and Center for Applied Photonics, University of Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany"}],"full_name_unicode_normalized":"hees, j.","full_name":"Hees, J.","record":{"$ref":"https://inspirehep.net/api/authors/2793404"},"ids":[{"schema":"INSPIRE BAI","value":"J.Hees.1"}],"last_name":"Hees","first_name":"J.","uuid":"9db693bb-33f8-4e94-8303-cda374282591","recid":2793404},{"raw_affiliations":[{"value":"Department of Physics and Center for Applied Photonics, University of Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany"}],"full_name_unicode_normalized":"sell, a.","full_name":"Sell, A.","record":{"$ref":"https://inspirehep.net/api/authors/2178255"},"ids":[{"schema":"INSPIRE BAI","value":"A.Sell.1"}],"last_name":"Sell","first_name":"A.","uuid":"cf851892-6a70-46b4-8cc2-adc59bfaa64e","recid":2178255},{"raw_affiliations":[{"value":"Laboratorio Nazionale TASC CNR-INFM, Area Science Park, I-34012 Trieste, Italy,"}],"full_name_unicode_normalized":"biasiol, g.","full_name":"Biasiol, G.","record":{"$ref":"https://inspirehep.net/api/authors/2100136"},"ids":[{"schema":"INSPIRE BAI","value":"G.Biasiol.1"}],"last_name":"Biasiol","first_name":"G.","uuid":"1dddfff7-9197-4b97-b985-6d2258645d7d","recid":2100136},{"raw_affiliations":[{"value":"Laboratorio NEST, CNR-INFM and Scuola Normale Superiore, Piazza San Silvestro 12, I-56127 Pisa, Italy,"},{"value":"Laboratorio Nazionale TASC CNR-INFM, Area Science Park, I-34012 Trieste, Italy,"}],"full_name_unicode_normalized":"sorba, l.","full_name":"Sorba, L.","record":{"$ref":"https://inspirehep.net/api/authors/1933184"},"ids":[{"schema":"INSPIRE BAI","value":"L.Sorba.1"}],"last_name":"Sorba","first_name":"L.","uuid":"3d4a73c2-4c9c-409f-920c-1094ba167938","recid":1933184},{"raw_affiliations":[{"value":"Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot-Paris 7, Case 7021, Bâtiment Condorcet, 75205 Paris, France,"},{"value":"Laboratoire Pierre Aigrain, Ecole Normale Supérieure, UMR 8551, 75005 Paris, France,"}],"full_name_unicode_normalized":"de liberato, s.","full_name":"De Liberato, S.","record":{"$ref":"https://inspirehep.net/api/authors/2122599"},"ids":[{"schema":"INSPIRE BAI","value":"S.De.Liberato.1"}],"last_name":"De Liberato","first_name":"S.","uuid":"7a2b4a76-11fc-4679-8a6c-1542ac3794b6","recid":2122599},{"raw_affiliations":[{"value":"Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot-Paris 7, Case 7021, Bâtiment Condorcet, 75205 Paris, France,"}],"full_name_unicode_normalized":"ciuti, c.","full_name":"Ciuti, C.","record":{"$ref":"https://inspirehep.net/api/authors/1954865"},"ids":[{"schema":"INSPIRE BAI","value":"C.Ciuti.1"}],"last_name":"Ciuti","first_name":"C.","uuid":"cc9bc7f6-2dc9-40cc-907e-2138b318de66","recid":1954865},{"raw_affiliations":[{"value":"Laboratorio NEST, CNR-INFM and Scuola Normale Superiore, Piazza San Silvestro 12, I-56127 Pisa, Italy,"}],"full_name_unicode_normalized":"tredicucci, a.","full_name":"Tredicucci, 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R.","record":{"$ref":"https://inspirehep.net/api/authors/2114939"},"ids":[{"schema":"INSPIRE BAI","value":"R.Huber.1"}],"last_name":"Huber","first_name":"R.","uuid":"4194fbab-fb28-43ab-b690-24e8a65f4c68","recid":2114939}],"publication_info":[{"journal_volume":"458","page_end":"181","year":2009,"journal_record":{"$ref":"https://inspirehep.net/api/journals/1214565"},"page_start":"178","journal_issue":"7235","journal_title":"Nature"}],"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","references":[{"reference":{"dois":["10.1103/RevModPhys.73.565"],"publication_info":{"journal_volume":"73","page_end":"582","year":2001,"page_start":"565","journal_title":"Rev.Mod.Phys."},"misc":["Colloquium: Manipulating quantum entanglement with atoms and photons in a cavity"],"authors":[{"full_name":"Raimond, J.M."},{"full_name":"Brune, M."},{"full_name":"Haroche, S."}]},"raw_refs":[{"schema":"text","value":"Raimond, J. 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Something that has not been widely studied, however, is how the coupling of light and matter evolves with time. Günter et al. have now developed a time-resolved measurement set-up in which strong light–matter coupling can be switched on in a semiconductor quantum-well structure as rapidly as within one cycle of light. This makes it possible to monitor the conversion of a population of bare photons to polaritons during abrupt switching. The technique lends itself to the study of phenomena such as the generation of quantum vacuum radiation, reminiscent of the dynamical Casimir effect, and Hawking radiation of black holes. This study has developed a time-resolved measurement set-up in which strong light–matter coupling can be switched on in a semiconductor quantum-well structure as fast as within one cycle of light. This makes it possible to monitor directly how a population of bare photons is converted to polaritons, mixed light–matter modes. Controlling the way light interacts with material excitations is at the heart of cavity quantum electrodynamics (QED). In the strong-coupling regime, quantum emitters in a microresonator absorb and spontaneously re-emit a photon many times before dissipation becomes effective, giving rise to mixed light–matter eigenmodes1,2,3,4,5,6,7,8,9,10,11,12. Recent experiments13 in semiconductor microcavities reached a new limit of ultrastrong coupling14, where photon exchange occurs on timescales comparable to the oscillation period of light. In this limit, ultrafast modulation of the coupling strength has been suggested to lead to unconventional QED phenomena14,15. Although sophisticated light–matter coupling has been achieved in all three spatial dimensions, control in the fourth dimension, time, is little developed. Here we use a quantum-well waveguide structure to optically tune light–matter interaction from weak to ultrastrong and turn on maximum coupling within less than one cycle of light. In this regime, a class of extremely non-adiabatic phenomena becomes observable. In particular, we directly monitor how a coherent photon population converts to cavity polaritons during abrupt switching. This system forms a promising laboratory in which to study novel sub-cycle QED effects and represents an efficient room-temperature switching device operating at unprecedented speed.","abstract_source_suggest":{"input":"Springer"}}],"refereed":true,"titles":[{"source":"Springer","title":"Sub-cycle switch-on of ultrastrong light–matter interaction"}],"facet_author_name":["2122599_Simone De Liberato","1892738_Alessandro Tredicucci","1954865_Cristiano Ciuti","1933184_Lucia Sorba","2029388_A. Leitenstorfer","2100136_G. Biasiol","2178255_Alexander Sell","2114939_R. Huber","2793402_G. Günter","2793403_A.A. Anappara","2793404_J. 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(a), setup consisting of a nonlinear electro-optic medium (EOM), a waveplate inducing a phase shift of $\\theta$ along its fast axis, a Wollaston prism (WP) separating the two polarization directions and two photon detectors $D_s$ and $D_z$. An intense $\\vec{e}_z$-polarized coherent near-infrared (NIR) probe pulse (blue) $\\mathcal{E}_{\\mathrm{p},z}$ is applied to the setup to probe a co-propagating quantum THz field $\\hat{E}_{\\mathrm{THz},s}$ polarized in the perpendicular $\\vec{e}_s$-direction. $\\hat{E}_{\\mathrm{p},s}$  denotes the induced $\\vec{e}_s$-polarized NIR quantum field. (b), level scheme for the molecules representing the EOM, comprising 3 levels $i,j=g,g',f$ with transition frequencies $\\omega_{ij}$ and lifetime broadenings $\\gamma_{ij}$.","label":"Fig1","source":"arxiv","key":"41e7a9186d4f2f994a8c7fd3a6bff6eb","url":"https://inspirehep.net/files/41e7a9186d4f2f994a8c7fd3a6bff6eb"},{"filename":"Fig2.png","material":"preprint","caption":"Diagrams showing the leading contributions to the electro-optic sampling of the THz vacuum fluctuations [Eq.~\\eqref{result}] for two molecules $a$ and $b$. Each diagram depicts the time evolution of both the electric field modes and the density matrix of the matter system. The vertical arrows indicate the time evolution of molecules $a$ and $b$ from the past (bottom) to the present (top), respectively. The red wavy lines denote an interaction with the THz vacuum field (either $\\hat{E}_{\\mathrm{THz},s}$ or $\\hat{E}^\\dagger_{\\mathrm{THz},s}$), the blue zigzag arrows pointing to the left (right) represent interactions with the  detected NIR field $\\hat{E}^\\dagger_{\\mathrm{p},s}$ ($\\hat{E}_{\\mathrm{p},s}$) and the straight blue arrows pointing to the left (right) denote interactions with the coherent probe field $\\mathcal{E}^*_{\\mathrm{p},z}$ ($\\mathcal{E}_{\\mathrm{p},z}$), respectively. The $\\pm$ signs next to the horizontal arrows denote the type of superoperator interaction for the corresponding field mode. ($\\mathrm{I}$), a process that can  be described by classical susceptibilities. This diagram is the only one captured by the classical treatment. ($\\mathrm{II}$a)$-$($\\mathrm{II}$c), processes that involve quantum susceptibilities due to two $'-'$-type interactions of molecule $b$ with $\\hat{E}_{\\mathrm{p},s}$ and $\\hat{E}_{\\mathrm{THz},s}$. ($\\mathrm{III}$a) and ($\\mathrm{III}$b), cascading processes that can be described by classical susceptibilities but are not captured by the classical treatment described in the main text. The depicted diagrams survive the rotating wave approximation (RWA). For a detailed calculation and the full set of diagrams see Appendix \\hyperref[AppB]{B}.","label":"Fig2","source":"arxiv","key":"d3c4baa916a6609ad6362408115ba4e2","url":"https://inspirehep.net/files/d3c4baa916a6609ad6362408115ba4e2"},{"filename":"Fig3.png","material":"preprint","caption":"Normally-ordered second moment $\\Gamma$ of the electro-optic signal [calculated according to Eqs.~\\eqref{gammaI}, \\eqref{gammaII} and \\eqref{gammaIII}] evaluated for the vacuum state of the THz field and for different phase shifts $\\theta$. (a), case of the level scheme shown in Fig.~\\ref{Fig1}(b). The blue line depicts $\\Gamma$ for the full quantum treatment according to Eq.~\\eqref{result}. It is given by the sum of the classical contribution $\\Gamma_\\mathrm{I}$ [black line, cf. Eq.~\\eqref{gammaI}], the  contribution stemming from the quantum susceptibilities $\\Gamma_\\mathrm{II}$ [dashed orange line, cf. Eqs.~\\eqref{gammaII}] and the cascading contribution $\\Gamma_\\mathrm{III}$ [dashed green line, cf. Eqs.~\\eqref{gammaIII}]. The inset shows a zoom-in on the interval $0.9\\pi\\leq\\theta\\leq 1.1\\pi$. (b), off-resonant case, where $\\omega,\\Omega\\ll \\omega'_{g'g},\\omega'_{fg}$. The length $L$ of the nonlinear medium with respect to the strength of the nonlinear susceptibilities is chosen such that the maximal value of $\\Gamma$ can still be regarded as a small correction to the shot noise (in this case a maximum contribution of $0.2N$ was adopted). (c), ratio of the absolute strength of the quantum contribution $|\\Gamma_\\mathrm{II}|$ to the combined absolute strengths of each contribution $G=|\\Gamma_\\mathrm{I}|+|\\Gamma_\\mathrm{II}|+|\\Gamma_\\mathrm{III}|$ for the level scheme shown in Fig.~\\ref{Fig1}(b). The normally-ordered second moment $\\Gamma$ is almost entirely determined by the quantum contribution $\\Gamma_\\mathrm{II}$ at $\\theta$ being close to the half-wave plate configuration, $\\theta=\\pi$.","label":"Fig3","source":"arxiv","key":"c4b5a2f9398a5156fd768b3df29d4360","url":"https://inspirehep.net/files/c4b5a2f9398a5156fd768b3df29d4360"},{"filename":"Fig4.png","material":"preprint","caption":"Spectral filtering in electro-optic sampling and effects of the cascading processes. (a), the spectral filtering introduced in the detection window. For $\\tilde{\\omega}/(2\\pi)=217.5$~THz, the lower half of the probe spectrum is being measured while  $\\tilde{\\omega}/(2\\pi)=292.5$~THz constitutes a measurement of the upper half of the probe spectrum. (b), comparison of the normally-ordered second moment $\\Gamma$ according to Eq.~\\eqref{signalcut} between the classical treatment (black line), where only $\\Gamma_\\mathrm{I}$ is taken into account, and the full quantum treatment (blue line) involving also the cascading processes.","label":"Fig4","source":"arxiv","key":"bd73546f37232bfbab9292300021ffa7","url":"https://inspirehep.net/files/bd73546f37232bfbab9292300021ffa7"},{"filename":"Fig5.png","material":"preprint","caption":"Statistics of the measured electro-optic signal $\\hat{\\mathcal{S}}(\\theta)$ [cf. Eq.~\\eqref{signal}] and reconstructed statistics of the THz vacuum. (a), contour plot of the probability distribution of the electro-optic signal $\\hat{\\mathcal{S}}(\\theta(\\varphi))$. The blue line depicts the probability distribution according to Eq.~\\eqref{result}, the black line shows the probability distribution resulting from the classical treatment, and the black dashed line depicts the probability distribution of the shot noise of the probe.  (b), reconstructed statistics of the THz vacuum with $E_\\mathrm{norm}=\\frac{c_0}{L\\omega_\\mathrm{p}\\chi^{(2)}_{+--}}$ (the nonlinearity is independent of the frequency entries in the off-resonant case and can be treated as a constant prefactor). The blue line in the inset depicts the probability distribution of $\\hat{\\mathcal{S}}(\\theta=\\pi/2)$ and the dashed black line corresponds to the shot noise of the probe. Deconvolution of the two should provide the statistics of the THz vacuum.","label":"Fig5","source":"arxiv","key":"999d39fcb8c46760b3b6b6c9e145ab78","url":"https://inspirehep.net/files/999d39fcb8c46760b3b6b6c9e145ab78"},{"filename":"FigB1.png","material":"preprint","caption":"Complete set of superoperator diagrams contributing to $\\Gamma$[cf. Eq.~\\eqref{Gamma}. Vertical arrows represent the density matrices of a pair molecules $a$ and $b$ as indicated, with the past at the bottom and the future at the top. Horizontal arrows denote interactions with the electric fields. Blue zigzag arrows: generated NIR field $\\hat{E}_{\\mathrm{p},s}$; wavy red lines: THz field $\\hat{E}_{\\mathrm{THz},s}$; straight blue arrows: coherent probe field $\\hat{E}_{\\mathrm{p},z}$. An arrow pointing to the right (left) corresponds to the annihilation (creation) of a photon. The interaction with the THz field (wavy red lines) does not have an arrow since for any interaction it can be pointing either to the right or to the left. The $\\pm$ indices denote the superoperator nature of the corresponding mode of the interacting field. Additional contributing diagrams are given by flipping all field arrows attributed to molecule $a$ and/or molecule $b$. Note that flipping the field arrows at both molecules results in the Hermitian conjugation of the corresponding terms. The first row describes the classical DFG response contribution to $\\Gamma$ if the THz arrows are chosen to point outwards at each molecule while the classical SFG is obtained when all of the THz arrows point inwards. Here, the intermolecular time ordering does not play any role. The second and third rows represent the quantum corrections to the classical response. Terms with the superscript $(\\mathrm{q})$ denote processes involving quantum susceptibilities on molecule $b$ (note the two $'-'$-type interactions) while terms with the superscript $(\\mathrm{casc})$ describe cascading processes.  For the second and third row, the intermolecular time ordering is important since the interaction with the THz field on molecule $a$ has to always occur after the THz interaction with molecule $b$.","label":"S1","source":"arxiv","key":"b295f7476f55cfd58f7074a33c11840f","url":"https://inspirehep.net/files/b295f7476f55cfd58f7074a33c11840f"}],"inspire_categories":[{"term":"Quantum Physics","source":"arxiv"},{"term":"Condensed Matter","source":"arxiv"},{"term":"General Physics","source":"arxiv"}],"preprint_date":"2021-03-13","author_count":5,"first_author":{"full_name":"Kizmann, Matthias","last_name":"Kizmann","first_name":"Matthias","recid":1869214},"public_notes":[{"source":"arXiv","value":"28 pages, 6 figures"}],"control_number":3058448,"earliest_date":"2021-03-13","document_type":["article"],"texkeys":["Kizmann:2021zvg"],"abstracts":[{"source":"arXiv","value":"Electro-optic sampling has emerged as a new quantum technique enabling measurements of electric field fluctuations on subcycle time scales. Probing a second-order nonlinear material with an ultrashort coherent laser pulse imprints the fluctuations of a terahertz field onto the resulting near-infrared electrooptic signal. We describe how the statistics of this time-domain signal can be calculated theoretically, incorporating from the onset the quantum nature of the electric fields involved in the underlying interactions. To this end, a microscopic quantum theory of the electro-optic process is developed using an ensemble of non-interacting three-level systems as a model for the nonlinear material. We find that the response of the nonlinear medium can be separated into a classical part sampling the terahertz field and quantum contributions independent of the state of the probed terahertz field. The quantum response is caused by interactions between the three-level systems mediated by the terahertz vacuum fluctuations. It arises due to cascading processes and contributions described by quantum susceptibilities solely accessible via quantum light. We show that the quantum contributions can be substantial and might even dominate the total response. We also determine the conditions under which the classical response serves as a good approximation of the electro-optic process and demonstrate how the statistics of the sampled terahertz field can be reconstructed from the statistics of the electro-optic signal. In a complementary regime, electro-optic sampling can serve as a spectroscopic tool to study the pure quantum susceptibilities of materials.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Quantum susceptibilities in time-domain sampling of electric field fluctuations"}],"facet_author_name":["1869214_Matthias Kizmann","1912857_S.A. Moskalenko","1971768_Guido Burkard","2029388_A. 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Formation of welldefined 3D islands in different self-assembled patterns was observed by atomic force microscopy (AFM) of uncapped CdSe/ZnSe ensembles. However, high-resolution transmission electron microscopy (HRTEM)based composition mapping revealed that the ZnSe-capped CdSe QDs are essentially undulations in a compositionally inhomogeneous quasi-2D CdZnSe layer with Cd-rich cores. These QDs extend laterally by up to 8 nm. They are separated by approximately 100 nm, corresponding to an areal density of 1010 cm-2. To optimize the interaction probability between optical pulses and single charge carriers in the quantum structure, we use the nanophotonic concept [2] of embedding the QDs in sub-wavelength Al apertures"],"authors":[{"full_name":"Zibik, E.A."},{"full_name":"Grange, T."},{"full_name":"Carpenter, B.A."},{"full_name":"Porter, N.E."},{"full_name":"Ferreira, R."},{"full_name":"Bastard, G."},{"full_name":"Stehr, D."},{"full_name":"Winnerl, S."},{"full_name":"Helm, M."},{"full_name":"Liu, H.Y."},{"full_name":"Skolnick, M.S."},{"full_name":"Wilson, L.R."}]},"raw_refs":[{"schema":"text","source":"arXiv","value":"[33] E. A. Zibik, T. Grange, B. A. Carpenter, N. E. Porter, R. Ferreira, G. Bastard, D. Stehr, S. Winnerl, M. Helm, H. Y. Liu, M. S. Skolnick, and L. R. Wilson, Nat. Materials 8, 803 (2009). Supplemental Material Femtosecond Transfer and Manipulation of Persistent Hot-Trion Coherence in a Single CdSe/ZnSe Quantum Dot P. Henzler, C. Traum, M. Holtkemper, D. Nabben, M. Erbe, D. E. Reiter, T. Kuhn, S. Mahapatra, K. Brunner, D. V. Seletskiy, and A. Leitenstorfer In the following, we provide additional information, supporting measurements, a full derivation of Eq. (1) and an explanation of our theoretical model, as referred to in the main paper. Sample Structures In the main paper, we investigate a negatively charged CdSe/n-ZnSe quantum dot (QD) grown by molecular beam epitaxy on a GaAs (001) substrate by a Te-mediated self-assembly process [1]. Formation of welldefined 3D islands in different self-assembled patterns was observed by atomic force microscopy (AFM) of uncapped CdSe/ZnSe ensembles. However, high-resolution transmission electron microscopy (HRTEM)based composition mapping revealed that the ZnSe-capped CdSe QDs are essentially undulations in a compositionally inhomogeneous quasi-2D CdZnSe layer with Cd-rich cores. These QDs extend laterally by up to 8 nm. They are separated by approximately 100 nm, corresponding to an areal density of 1010 cm-2 . 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Physics","source":"arxiv"},{"term":"Condensed Matter","source":"arxiv"},{"term":"General Physics","source":"arxiv"}],"preprint_date":"2016-11-21","author_count":7,"first_author":{"full_name":"Riek, Claudius","last_name":"Riek","first_name":"Claudius","recid":2169869},"public_notes":[{"source":"arXiv","value":"19 pages, 4 figures"}],"control_number":3034919,"dois":[{"material":"publication","source":"arXiv","value":"10.1038/nature21024"}],"earliest_date":"2016-11-21","document_type":["article"],"texkeys":["Riek:2016ujf"],"abstracts":[{"source":"arXiv","value":"Besides their stunning physical properties which are unmatched in a classical world, squeezed states of electromagnetic radiation bear advanced application potentials in quantum information systems and precision metrology, including gravitational wave detectors with unprecedented sensitivity. Since the first experiments on such nonclassical light, quantum analysis has been based on homodyning techniques and photon correlation measurements. These methods require a well-defined carrier frequency and photons contained in a quantum state need to be absorbed or amplified. They currently function in the visible to near-infrared and microwave spectral ranges. Quantum nondemolition experiments may be performed at the expense of excess fluctuations in another quadrature. Here we generate mid-infrared time-locked patterns of squeezed vacuum noise. After propagation through free space, the quantum fluctuations of the electric field are studied in the time domain by electro-optic sampling with few-femtosecond laser pulses. We directly compare the local noise amplitude to the level of bare vacuum fluctuations. This nonlinear approach operates off resonance without absorption or amplification of the field that is investigated. Subcycle intervals with noise level significantly below the pure quantum vacuum are found. Enhanced fluctuations in adjacent time segments manifest generation of highly correlated quantum radiation as a consequence of the uncertainty principle. Together with efforts in the far infrared, this work opens a window to the elementary quantum dynamics of light and matter in an energy range at the boundary between vacuum and thermal background conditions.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Subcycle Quantum Electrodynamics"}],"facet_author_name":["1912857_S.A. Moskalenko","1971768_Guido Burkard","1998800_Denis V. Seletskiy","2029388_A. Leitenstorfer","2169869_Claudius Riek","2226088_M. 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The inset at the bottom right shows the harmonic oscillator of the {UDW} detector, with dashed lines representing the different energy levels with constant gap $\\hbar \\omega_u$. The vacuum modes of the field are represented by the gray curly lines in the bottom-left corner. The UDW detector follows the trajectory shown via the bold black line. It interacts with the vacuum during a very short time interval {defined by} the switching function (represented by the blue line). In the Schrödinger picture, both the UDW detector and the vacuum states are affected by this interaction. The orange curvy lines represent the evolved modes of the field that are no longer in the initial vacuum state.","label":"FigVisualUnruh","source":"arxiv","key":"ebb3fc09aa408ad207a04f1b93911264","url":"https://inspirehep.net/files/ebb3fc09aa408ad207a04f1b93911264"},{"filename":"SubCycleStatistics.png","material":"preprint","caption":"Numerical plot of the $Q$- and $P$-quadrature variances for the subcycle mode $g$, Eq. \\eqref{EqnDefoffPOmega_a}, in dependence of the normalized inverse time extension of the Gaussian profile, $\\sigma/\\omega_0$. The top solid line (red) represents the {$P$-quadrature} variance, while the bottom solid line (blue) corresponds to the {$Q$-quadrature} variance. The dashed line represents the {$Q$-quadrature} variance one would obtain by assuming that both variances would characterize a single-mode (minimum-uncertainty) squeezed state (MUS), i.e. {$\\langle \\hat{Q}^2_g(\\sigma)\\rangle_{\\text{MUS}} = 1/\\langle \\hat{P}^2_g (\\sigma)\\rangle$}. The difference between the dashed and the bottom solid line can be attributed to extra thermal photons within $\\hat{a}_g$ . It can be seen from the graph that the {$Q$- and $P$-quadrature} variances start to deviate from quantum shot noise (i.e. variance of $1$) at around $\\sigma \\approx 0.45 \\omega_0$, when the Gaussian-profile mode enters the subcycle regime.","label":"FigPlotSubcycle","source":"arxiv","key":"573c7a1b0c1d6968746598c63b8bef99","url":"https://inspirehep.net/files/573c7a1b0c1d6968746598c63b8bef99"},{"filename":"WaveFormElectroOptic.png","material":"preprint","caption":"(a) Amplitude of the scalar-field mode for the probed waveform $f_{\\widetilde{\\omega}}(\\Omega)$, as given by Eqs. \\eqref{phi_discrete}-\\eqref{f_of_ai}. The green solid lines represent the envelope of the probed subcycle mode, $\\pm\\big|\\sqrt{\\frac{1}{\\varepsilon_0}}\\Phi_{\\widetilde\\omega}(t,0)\\big|$. Its real part is given by the dashed green line. (b) The purple solid lines show $\\pm|E_p(t,0)|$, the envelope of the probe pulse that drives the interaction, with a dashed purple line representing its real part. We have set {$t_p=0$ and} $\\widetilde{\\omega}=\\omega_p+1.5\\sigma_p$, where {$\\omega_p/(2\\pi)=255$ ~THz}, $\\sigma_p=\\sqrt{2 {\\log 2}}/t_{1/2}$ and {$t_{1/2}=5.8$ ~fs}.","label":"FigWaveFormElectroOptic","source":"arxiv","key":"6593b1c109803aa9c1af8c2bfdb23c79","url":"https://inspirehep.net/files/6593b1c109803aa9c1af8c2bfdb23c79"},{"filename":"Ellipsometry.png","material":"preprint","caption":"The electric field propagates through the {electro-optic crystal} (EOX) for the coherent pulse to induce an interaction with the vacuum. The outgoing field propagates through a narrow band-pass filter (BPF), filtering out outside the narrow-band frequency window $\\widetilde\\omega-\\Delta \\omega/2 \\leqslant \\omega \\leqslant \\widetilde\\omega+\\Delta \\omega/2$. This is followed by a $\\phi_z$ wave-plate, which applies to the field a $\\phi$-phase shift in the {$z$-polarization}. Then the field passes through a half-wave plate ($\\lambda/2$) at an angle of $\\pi/8$ from the horizontal (see diagonal light-grey line) and a Wollaston prism (WP), which physically splits the s and z components of the field. Each output is detected by a photon counter.","label":"FigExperimentalSetup","source":"arxiv","key":"91a3bee1db9a83a15393ee60e42cddc4","url":"https://inspirehep.net/files/91a3bee1db9a83a15393ee60e42cddc4"},{"filename":"PlotPRL.png","material":"preprint","caption":"Numerical plot of the {$Q$- and $P$-}quadrature variances {obtained} with the first-order unitary evolution method. The top line (solid red) is the {$P$-quadrature} variance, while the bottom line (solid blue) represents the {$Q$-quadrature} one. The dashed lines represent the numerical result when we utilize the standard first-order perturbation theory. In this plot, there is a vertical line near $\\omega_p$. To the right of it, the electro-optic sampling can be modelled as {a UDW} detector.Numerical plot of the X and P quadrature with the first order perturbation theory. The top line (the darker green) is the P-quadrature, while the bottom line (the lighter green) is the X-quadrature. It is found that the P-quadrature does not beat shot noise. It is worth noting that the lack of symmetry relative to the central probe frequency in Fig. \\ref{FigPlot1stOrd} (vertical dotted line) is a consequence of the {asymmetric} $\\omega$ dependence of the probe waveform we chose (note the $\\sqrt{|\\omega|}$ factor in Eq. \\eqref{waveformE}).","label":"FigPlot1stOrd","source":"arxiv","key":"e997ce2101724158310d4e8455d8811a","url":"https://inspirehep.net/files/e997ce2101724158310d4e8455d8811a"},{"filename":"Plot2Ord.png","material":"preprint","caption":"Numerical plot of the X and P quadrature variance for both first and second-order unitary evolution theory. The top line (the red line) is the P-quadrature variance, while the bottom line (the blue line) is the X-quadrature variance. The dotted line corresponds to the second order results.","label":"FigPlot2ndOrd","source":"arxiv","key":"095475d069d7129882819f62771f5477","url":"https://inspirehep.net/files/095475d069d7129882819f62771f5477"},{"filename":"RefractiveIndex.png","material":"preprint","caption":"The frequency dependent refractive index of the EOX crystal is plotted. We have utilized the (simplified) model of \\cite{Andrey} for the MIR regime. For the NIR regime, we have utilized the fit provided by \\cite{Marple1964}. We have continuously connected the two models.","label":"FigRefractiveIndex","source":"arxiv","key":"3b1894cb321c1d71c29707c15699ae46","url":"https://inspirehep.net/files/3b1894cb321c1d71c29707c15699ae46"},{"filename":"BalancedHomodyne.png","material":"preprint","caption":"The electric field passes through the $EOX$ for the signal to induce an interaction with the vacuum. The output goes through a band-pass filter, which filters all frequency except $\\widetilde\\omega+\\eta/2\\leq \\omega \\leq \\widetilde\\omega-\\eta/2$). The $\\phi$-waveplate in the z-polarization allows a homodyne detection of arbitrary phase, this is followed by a wollaston prism in the diagonal plane. The electric field is then detected with a photon counter for each polarisation.","label":"FigExperimentalSetupHomodyne","source":"arxiv","key":"ccafc0ebb0a8edf84b3f9db9f3f1b505","url":"https://inspirehep.net/files/ccafc0ebb0a8edf84b3f9db9f3f1b505"}],"legacy_version":"20210420063644.0","inspire_categories":[{"term":"General Physics","source":"arxiv"},{"term":"General Physics"},{"term":"Quantum Physics","source":"arxiv"}],"first_author":{"emails":["sho.onoe@uqconnect.edu.au"],"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/00rqy9422"}],"full_name":"Onoe, Sho","last_name":"Onoe","first_name":"Sho","recid":1949829},"control_number":1854046,"dois":[{"material":"publication","source":"APS","value":"10.1103/PhysRevD.105.056023"},{"source":"APS","value":"10.1103/PhysRevD.105.056023"},{"material":"publication","source":"arXiv","value":"10.1103/PhysRevD.105.056023"}],"document_type":["article"],"texkeys":["Onoe:2021tjc"],"abstracts":[{"source":"APS","value":"A new theoretical framework to describe the experimental advances in electro-optic detection of broadband quantum states, specifically the quantum vacuum, is devised. Electro-optic sampling is a technique in ultrafast photonics which, when transferred into the quantum domain, can be utilized to resolve properties of a sampled quantum state via its interaction with a strong coherent probe pulse at ultrafast timescales. By making use of fundamental concepts from quantum field theory on spacetime metrics, the nonlinear interaction behind the electro-optic effect is shown to be equivalent to a stationary Unruh-DeWitt detector coupled to a conjugate field during a very short time interval. When the coupling lasts for a time interval comparable to the oscillation periods of the detected field mode (i.e., the subcycle regime), virtual particles inhabiting the field vacuum are transferred to the detector in the form of real excitation. We demonstrate that this behavior can be rigorously translated to the scenario of electro-optic sampling of the quantum vacuum, in which the (spectrally filtered) probe works as an Unruh-DeWitt detector, with its interaction-generated photons arising from virtual particles inhabiting the electromagnetic vacuum. Our analysis accurately encapsulates the quantum nature of the vacuum, and we propose the specific working regime in which we can experimentally verify the existence of virtual photons with quantum correlations in the electromagnetic ground state.","abstract_source_suggest":{"input":"APS"}},{"source":"arXiv","value":"A new theoretical framework to describe the experimental advances in electro-optic detection of broadband quantum states, specifically the quantum vacuum, is devised. By making use of fundamental concepts from quantum field theory on spacetime metrics, the nonlinear interaction behind the electro-optic effect can be reformulated in terms of an Unruh-DeWitt detector coupled to a conjugate field during a very short time interval. When the coupling lasts for a time interval comparable to the oscillation periods of the detected field mode (i.e. the subcycle regime), virtual particles inhabiting the field vacuum are transferred to the detector in the form of real excitations. We demonstrate that this behavior can be rigorously translated to the scenario of electro-optic sampling of the quantum vacuum, in which the (spectrally filtered) probe works as an Unruh-DeWitt detector, with its interaction-generated photons arising from virtual particles inhabiting the electromagnetic vacuum. We discuss the specific working regime of such processes, and the consequences through characterization of the quantum light involved in the detection.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"APS","title":"Realizing a rapidly switched Unruh-DeWitt detector through electro-optic sampling of the electromagnetic vacuum"},{"source":"arXiv","title":"Realizing an Unruh-DeWitt detector through electro-optic sampling of the electromagnetic vacuum"}],"imprints":[{"date":"2022-03-01"},{"date":"2022-03-29"}],"curated":false},"created":"2021-03-29T00:00:00+00:00","id":"1854046","updated":"2026-02-09T11:50:31.885809+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/1854046?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1854046?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1854046?format=latex-us","json":"https://inspirehep.net/api/literature/1854046?format=json","json-expanded":"https://inspirehep.net/api/literature/1854046?format=json-expanded","cv":"https://inspirehep.net/api/literature/1854046?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1854046"}},{"metadata":{"citation_count":17,"citation_count_without_self_citations":8,"authors":[{"raw_affiliations":[{"value":"Department of Physics and Center for Applied Photonics, University of Konstanz, D-78457 Konstanz, Germany"}],"full_name_unicode_normalized":"guedes, t.l. m.","full_name":"Guedes, T.L. 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General sketch of the {proposed} experimental setup. The classical driving field propagates through a $\\chi^{(2)}$ nonlinear crystal (NX) of small thickness $L$ and unperturbed refractive index $n$, generating ultrabroadband squeezed quantum light. The outgoing light is registered by the detector D. (b) World line of a plane wave mode of the quantum electric field within the NX with refractive index modulated by a half-cycle pulse (HCP). The trajectory (blue) is given by Eq.~\\eqref{WL1} with $C_1=0$, $\\alpha/n^2=0.49$ and $n\\zeta =12$. The dotted purple straight line indicates the trajectory of light in the absence of nonlinear effects. After the acceleration has mostly ceased, the world line approaches the dotted green line parallel to the purple one. The process of acceleration is confined to a diamond-like space-time zone (light red parallelogram) of dimensions defined by the duration of the driving transient.","label":"Fig:Worldline","source":"arxiv","key":"c7fa6fab7a1ee81a6ac009689bb0e6d4","url":"https://inspirehep.net/files/c7fa6fab7a1ee81a6ac009689bb0e6d4"},{"filename":"SpectrumCW_G.png","material":"preprint","caption":"{Normalized spectral photon flux density in the case of CW driving ($\\rho_0 \\omega_0=C^2|E_0|^2\\omega^2_0/\\pi^2$)}. Calculations including up to second (blue) and fourth order (red) terms in $\\alpha=dE_0$ have been included. The value of the factor $\\pi^4\\rho_0\\omega_0/4$ governing the smallness of the $\\alpha^4$ term with respect to the $\\alpha^2$ term is 0.02. Although the second order contribution has a parabolic shape in the range of $\\omega/\\omega_0$ from 0 to 1, higher order terms allow for modification of this shape. They also lead to the appearance of photons with frequencies larger than $\\omega_0$ and its harmonics. The dotted curve shows the average spectral photon flux density for a measurement over a finite time interval $\\Delta t = N T$ with $N=50$, where $T=2\\pi/\\omega_0$ is the period of the driving field.","label":"Fig:CW","source":"arxiv","key":"4fdc5ef156bda9747a66f1e9a3805516","url":"https://inspirehep.net/files/4fdc5ef156bda9747a66f1e9a3805516"},{"filename":"SpectrumHC_FC_finalG.png","material":"preprint","caption":"{Normalized spectral photon density (SPD) for the driving HCP (dotted blue) and SCP (solid blue) cases ($\\rho_0=C^2E^2_0\\Gamma/\\pi^2$) {in the leading ($\\alpha^2$) order.} The exponential behavior of the spectra can be better analysed in a logarithmic plot}, presented for the HCP case in the inset (which has the same high-frequency behavior as for the SCP case). The SPD is shown in blue, while the asymptotic dotted straight line represents a fit of the form $Ae^{-\\pi(\\omega/\\Gamma)}$.","label":"Fig:HC_SC","source":"arxiv","key":"e7bc1a0a486b80909351a88cfd12136c","url":"https://inspirehep.net/files/e7bc1a0a486b80909351a88cfd12136c"},{"filename":"VarianceG3.png","material":"preprint","caption":"Dynamics} of the normally ordered variance (NOV), $V(\\tau)$, of the emitted quantum electric field for (a) CW, (b) HCP and (c) SCP driving {(dotted green).} Contributions up to the first $V^{(1)}(\\tau)$ (blue) and the second $V^{(1)}(\\tau)+V^{(2)}(\\tau)$ (red) order in the squeezing strength $r$ are shown. The NOV is normalized by $V_0=\\hbar\\Gamma^2/(24\\pi\\epsilon_0 c_0n A)$, while time is normalized by $\\Gamma$ ($\\Gamma=\\omega_0$ for CW driving). $r=0.07$ for (a), $0.21$ for (b) and $1.54$ {for (c).","label":"Fig:Variance","source":"arxiv","key":"d08b7b5c968cedba2f44f90dc83ead54","url":"https://inspirehep.net/files/d08b7b5c968cedba2f44f90dc83ead54"},{"filename":"Joint_worldlinesG2.png","material":"preprint","caption":"{World} lines of the modes of quantum light propagating through the NX for HCP (a) and SCP (b) driving. Each world line (blue) is defined by its initial condition, which is given by a certain event at the boundary of the crystal and correspondingly by the amplitude of the driving field {(green)} at this event. Here $\\alpha/n^2=0.49$ and $n\\zeta=12$  (see Ref.~\\cite{Suppl_Mat}).","label":"Fig:Worldlines","source":"arxiv","key":"feb1c32ca5cd05eae7ce4bae38bf8022","url":"https://inspirehep.net/files/feb1c32ca5cd05eae7ce4bae38bf8022"}],"legacy_version":"20200526105635.0","inspire_categories":[{"term":"General Physics","source":"arxiv"},{"term":"Gravitation and Cosmology","source":"arxiv"},{"term":"General Physics"},{"term":"Gravitation and Cosmology"},{"term":"Quantum Physics","source":"arxiv"}],"first_author":{"emails":["thiago.lucena@uni-konstanz.de"],"full_name":"Guedes, T.L. M.","last_name":"Guedes","first_name":"T.L. M.","recid":2029387},"control_number":1699381,"dois":[{"value":"10.1103/PhysRevLett.122.053604"},{"material":"publication","source":"arXiv","value":"10.1103/PhysRevLett.122.053604"}],"document_type":["article"],"texkeys":["Guedes:2018tfs"],"abstracts":[{"source":"APS","value":"We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by coherent-field driving in a thin nonlinear crystal with second-order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. They can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance.","abstract_source_suggest":{"input":"APS"}},{"source":"arXiv","value":"We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-field driving in a thin nonlinear crystal with second order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. These spectra can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Spectra of ultrabroadband squeezed pulses and the finite-time Unruh-Davies effect"}],"imprints":[{"date":"2019-02-09"}],"curated":true},"created":"2018-10-22T00:00:00+00:00","id":"1699381","updated":"2026-02-09T11:04:58.217732+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/1699381?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1699381?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1699381?format=latex-us","json":"https://inspirehep.net/api/literature/1699381?format=json","json-expanded":"https://inspirehep.net/api/literature/1699381?format=json-expanded","cv":"https://inspirehep.net/api/literature/1699381?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1699381"}}],"total":15},"links":{"self":"https://inspirehep.net/api/literature/?q=a%20A.Leitenstorfer.1&size=10&page=1","next":"https://inspirehep.net/api/literature/?q=a%20A.Leitenstorfer.1&size=10&page=2","bibtex":"https://inspirehep.net/api/literature/?q=a%20A.Leitenstorfer.1&size=10&page=1&format=bibtex","latex-eu":"https://inspirehep.net/api/literature/?q=a%20A.Leitenstorfer.1&size=10&page=1&format=latex-eu","latex-us":"https://inspirehep.net/api/literature/?q=a%20A.Leitenstorfer.1&size=10&page=1&format=latex-us","json":"https://inspirehep.net/api/literature/?q=a%20A.Leitenstorfer.1&size=10&page=1&format=json","json-expanded":"https://inspirehep.net/api/literature/?q=a%20A.Leitenstorfer.1&size=10&page=1&format=json-expanded","cv":"https://inspirehep.net/api/literature/?q=a%20A.Leitenstorfer.1&size=10&page=1&format=cv"}}