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Moskalenko, C. Riek, D.V. Seletskiy, G. Burkard, and A. Leitenstorfer 1. GEOMETRY OF NONLINEAR MIXING For the nonlinear mixing in the EOX, we select the orientation of Ep parallel to the z-axis. This choice of the polarization direction of the probe field ensures that the maximum signal is detected in the electro-optic detection scheme for a copropagating classical THz electric field polarized perpendicular to the probe electric field [S1]. In the experiment, adjustment is achieved by rotation of the EOX around the [110] axis for fixed, mutually perpendicular polarization directions of the probe and detected electric fields. Also, only one of two possible polarization modes of the detected field [the one perpendicular to the probe field, i.e. oriented parallel to the unit vector es in Fig. 1(b)] contributes to the signal in this geometry. There is no THz field generated by optical rectification of the probe for this orientation of the EOX. The second-order nonlinear mixing of the probe field Ep(t) with the detected THz field ETHz (t) then induces nonlinear polarization in the EOX with the following components [S2-S4]: P(2) x (t) = 4 0dxyzETHz,y(t)Ep,z(t) (S1) and similarly for the y-component with the interchange of indices x ↔ y in Eq. (S1). Here 0 is the vacuum permittivity. For the zincblende-type EOX we adopt as an example, the tensor components dxyz ≡ χ (2) xyz/2 and dyxz ≡ χ (2) yxz/2 are"],"authors":[{"full_name":"Raymer, M.G."},{"full_name":"Cooper, J."},{"full_name":"Carmichael, H.J."},{"full_name":"Beck, M."},{"full_name":"Smithey, D.T."}]}}],"number_of_pages":5,"legacy_creation_date":"2015-10-02","preprint_date":"2015-08-27","author_count":5,"public_notes":[{"source":"arXiv","value":"10 pages, 6 figures"}],"earliest_date":"2015-08-27","refereed":true,"external_system_identifiers":[{"schema":"ADS","value":"2015PhRvL.115z3601M"}],"facet_author_name":["1912857_S.A. Moskalenko","1971768_Guido Burkard","1998800_Denis V. Seletskiy","2029388_A. Leitenstorfer","2169869_Claudius Riek"],"license":[{"imposing":"arXiv","url":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/"},{"license":"arXiv nonexclusive-distrib 1.0","material":"preprint","url":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/"}],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:1395724","updated":"2025-10-02T15:08:58.337221"},"journal_title_variants":["Phys. Rev. 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Bottom left corner: time profiles of the NIR intensity envelope $I_{_\\mathrm{NIR\\!}}(t)$ and a representative multi-THz vacuum field $E_{_\\mathrm{THz\\!}}(t)$.  After collimation by a lens (L), the modified NIR field is analyzed using a quarter-wave plate $\\left(\\!\\frac{\\lambda}{4}\\!\\right)_{\\!a}$, a Wollaston prism (WP) and balanced detectors (D$_s$,D$_z$) measuring the difference in the photon flux for the split components. (b) Spatial directions determining the electro-optic effect in the zincblende-type EOX and the following ellipsometry analysis.","label":"Fig:Geometry","source":"arxiv","key":"10a2195976ceac2bd65b56b19ea8aa1a","url":"https://inspirehep.net/files/10a2195976ceac2bd65b56b19ea8aa1a"},{"filename":"fig2.png","material":"preprint","caption":"(color online) (a) Calculated integrand function $\\Omega\\, (n/n_{_\\Omega}) |R(\\Omega)|^2$ entering Eq.~\\eqref{Eq:variance_THz_final}. (b) Double-logarithmic plot of the ratio $\\Delta \\mathcal{S}/N$ in dependence on $N$.  Black dotted (red dashed) line shows the bare SN (multi-THz vacuum) contribution. (c)  Increase of $(\\Delta\\mathcal{S}-\\Delta\\mathcal{S}_{\\mathrm{sn}})/\\Delta\\mathcal{S}_{\\mathrm{sn}}$ with $N$.  Parameters are defined in the main text.","label":"Fig:signal_vacuum","source":"arxiv","key":"fc0746e6f94b7264a58bd8506d482dd6","url":"https://inspirehep.net/files/fc0746e6f94b7264a58bd8506d482dd6"},{"filename":"fig3.png","material":"preprint","caption":"(color online) (a) Frequency dependence of the squeeze factor $r$. Squeezing correlates $\\Omega$ and $2\\Omega_\\mathrm{c}-\\Omega$ modes (as indicated by arrows).   (b) Error contour in the complex-amplitude plane for PV (gray circle) and SV with $\\theta\\!=\\!0/\\theta\\!=\\!\\pi$ (red/green ellipse with reduced uncertainty in the phase/amplitude quadrature $Y$/$X$).  (c) Normalized (with respect to the constant PV level, solid black line) EOS variance in dependence on the time delay $\\tau$ of the probe NIR pulse for SV with $\\theta\\!=\\!0/\\theta\\!=\\!\\pi$ (solid red line\\;/\\;dashed green line).","label":"Fig:squeezing","source":"arxiv","key":"b2f1de3821663905ed479cb93e11e937","url":"https://inspirehep.net/files/b2f1de3821663905ed479cb93e11e937"},{"filename":"temp_profile.png","material":"preprint","caption":"Temporal profile of the intensity (red line) and its envelope (blue line) of the NIR probe pulse used in our calculations.","label":"Fig:temp_profile","source":"arxiv","key":"1c5132ac43214eb18fa32621c2c90861","url":"https://inspirehep.net/files/1c5132ac43214eb18fa32621c2c90861"},{"filename":"n_THz_NIR.png","material":"preprint","caption":"Dispersion of the refractive index in the THz (solid red line) and NIR (dashed blue line) range. Inset shows the dispersion with a higher frequency resolution in the range of small THz frequencies.","label":"Fig:n_omega","source":"arxiv","key":"783a8a19fda4f8d85dcd27f4495c0ea5","url":"https://inspirehep.net/files/783a8a19fda4f8d85dcd27f4495c0ea5"},{"filename":"R_function.png","material":"preprint","caption":"Calculated response function $R(\\Omega)$ without the low-frequency cutoff (solid black line) and with the low-frequency cutoff (dashed red line).","label":"Fig:R_function","source":"arxiv","key":"3e2514fb3d3d3c412ec58825c67eb255","url":"https://inspirehep.net/files/3e2514fb3d3d3c412ec58825c67eb255"}],"legacy_version":"20160122162508.0","inspire_categories":[{"term":"General Physics"},{"term":"Quantum Physics","source":"arxiv"}],"first_author":{"emails":["andrey.moskalenko@uni-konstanz.de"],"full_name":"Moskalenko, Andrey S.","last_name":"Moskalenko","first_name":"Andrey S.","recid":1912857},"control_number":1395724,"dois":[{"value":"10.1103/PhysRevLett.115.263601"},{"material":"publication","source":"arXiv","value":"10.1103/PhysRevLett.115.263601"}],"document_type":["article"],"texkeys":["Moskalenko:2015sra"],"abstracts":[{"source":"APS","value":"Direct detection of vacuum fluctuations and analysis of subcycle quantum properties of the electric field are explored by a paraxial quantum theory of ultrafast electro-optic sampling. The feasibility of such experiments is demonstrated by realistic calculations adopting a thin ZnTe electro-optic crystal and stable few-femtosecond laser pulses. We show that nonlinear mixing of a short near-infrared probe pulse with the multiterahertz vacuum field leads to an increase of the signal variance with respect to the shot noise level. The vacuum contribution increases significantly for appropriate length of the nonlinear crystal, short pulse duration, tight focusing, and a sufficiently large number of photons per probe pulse. If the vacuum input is squeezed, the signal variance depends on the probe delay. Temporal positions with a noise level below the pure vacuum may be traced with subcycle resolution.","abstract_source_suggest":{"input":"APS"}},{"source":"arXiv","value":"Direct detection of vacuum fluctuations and analysis of sub-cycle quantum properties of the electric field are explored by a paraxial quantum theory of ultrafast electro-optic sampling. The feasibility of such experiments is demonstrated by realistic calculations adopting a thin ZnTe electro-optic crystal and stable few-femtosecond laser pulses. We show that nonlinear mixing of a short near-infrared probe pulse with multi-terahertz vacuum field modes leads to an increase of the signal variance with respect to the shot noise level. The vacuum contribution increases significantly for appropriate length of the nonlinear crystal, short probe pulse durations, tight focusing, and sufficiently large number of photons per probe pulse. If the vacuum input is squeezed, the signal variance depends on the probe delay. Temporal positions with noise level below the pure vacuum may be traced with a sub-cycle accuracy.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Paraxial Theory of Direct Electro-Optic Sampling of the Quantum 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Calvo</string-name>, <string-name>A. Picón</string-name>, and <string-name>E. Bagan</string-name></person-group>, <article-title>Quantum field theory of photons with orbital angular momentum,</article-title> <source>Phys. Rev. A</source> <volume>73</volume>, <page-range>013805</page-range> (<year>2006</year>)<issn>1050-2947</issn><pub-id pub-id-type=\"doi\" specific-use=\"suppress-display\" assigning-authority=\"crossref\">10.1103/PhysRevA.73.013805</pub-id>.</mixed-citation></ref>"}]},{"reference":{"label":"32","misc":["The presented solution is equivalent to evolving the electric-field operator in the Heisenberg picture, as shown in [20]. The corresponding evolution Hamiltonian may be found in [22]. Note that the Heisenberg equation for the generated electric field is also given by Maxwell's equations with the nonlinear polarizations as sources"]},"raw_refs":[{"schema":"JATS","source":"APS","value":"<ref id=\"c32\"><label>[32]</label><mixed-citation publication-type=\"misc\"><object-id>32</object-id>The presented solution is equivalent to evolving the electric-field operator in the Heisenberg picture, as shown in <styled-content><xref ref-type=\"bibr\" rid=\"c20\">[20]</xref></styled-content>. The corresponding evolution Hamiltonian may be found in <styled-content><xref ref-type=\"bibr\" rid=\"c22\">[22]</xref></styled-content>. Note that the Heisenberg equation for the generated electric field is also given by Maxwell's equations with the nonlinear polarizations as sources.</mixed-citation></ref>"}]},{"reference":{"dois":["10.1103/PhysRevA.102.041701"],"label":"33","publication_info":{"journal_volume":"102","artid":"041701","year":2020,"journal_record":{"$ref":"https://inspirehep.net/api/journals/1613967"},"journal_title":"Phys.Rev.A"},"title":{"title":"Theory of polaritonic quantum-vacuum detection,"},"misc":["(R) "],"authors":[{"inspire_role":"author","full_name":"Lindel, F."},{"inspire_role":"author","full_name":"Bennett, R."},{"inspire_role":"author","full_name":"Buhmann, S.Y."}]},"raw_refs":[{"schema":"JATS","source":"APS","value":"<ref id=\"c33\"><label>[33]</label><mixed-citation publication-type=\"journal\"><object-id>33</object-id><person-group person-group-type=\"author\"><string-name>F. Lindel</string-name>, <string-name>R. Bennett</string-name>, and <string-name>S. Y. 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Lindel</string-name>, <string-name>R. Bennett</string-name>, and <string-name>S. Y. Buhmann</string-name></person-group>, <article-title>Macroscopic quantum electrodynamics approach to nonlinear optics and application to polaritonic quantum-vacuum detection,</article-title> <source>Phys. Rev. A</source> <volume>103</volume>, <page-range>033705</page-range> (<year>2021</year>)<issn>2469-9926</issn><pub-id pub-id-type=\"doi\" specific-use=\"suppress-display\" assigning-authority=\"crossref\">10.1103/PhysRevA.103.033705</pub-id>.</mixed-citation></ref>"}]},{"reference":{"label":"35","misc":["For a continuous set of modes parametrized by ζ, one has |{0}ω〉=limΔζ→0⨂k|0〉kΔζ. The MIR vacuum state is constructed by having the frequency and polarization as the mode parameter (ζs/z=Λ) and selecting only frequencies in the MIR range for the tensor product"]},"raw_refs":[{"schema":"JATS","source":"APS","value":"<ref id=\"c35\"><label>[35]</label><mixed-citation publication-type=\"misc\"><object-id>35</object-id>For a continuous set of modes parametrized by <inline-formula><math><mi>ζ</mi></math></inline-formula>, one has <inline-formula><math><mrow><msub><mrow><mo>|</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow><mi>ω</mi></msub><mrow><mo>〉</mo><mo>=</mo></mrow><msub><mo movablelimits=\"true\" form=\"prefix\">lim</mo><mrow><mi mathvariant=\"normal\">Δ</mi><mi>ζ</mi><mo>→</mo><mn>0</mn></mrow></msub><msub><mo>⨂</mo><mi>k</mi></msub><msub><mrow><mo>|</mo><mn>0</mn><mo>〉</mo></mrow><mrow><mi>k</mi><mi mathvariant=\"normal\">Δ</mi><mi>ζ</mi></mrow></msub></mrow></math></inline-formula>. The MIR vacuum state is constructed by having the frequency and polarization as the mode parameter (<inline-formula><math><mrow><msub><mi>ζ</mi><mrow><mi>s</mi><mo>/</mo><mi>z</mi></mrow></msub><mo>=</mo><mi mathvariant=\"normal\">Λ</mi></mrow></math></inline-formula>) and selecting only frequencies in the MIR range for the tensor product.</mixed-citation></ref>"}]},{"reference":{"label":"36","misc":["For similar reasons, if the two beams reach the NX with some displacement between the centers of their waists, making G a function of this displacement, the decay length should be of the same magnitude as the beam waists [17]"]},"raw_refs":[{"schema":"JATS","source":"APS","value":"<ref id=\"c36\"><label>[36]</label><mixed-citation publication-type=\"misc\"><object-id>36</object-id>For similar reasons, if the two beams reach the NX with some displacement between the centers of their waists, making <inline-formula><math><mi>G</mi></math></inline-formula> a function of this displacement, the decay length should be of the same magnitude as the beam waists <styled-content><xref ref-type=\"bibr\" rid=\"c17\">[17]</xref></styled-content>.</mixed-citation></ref>"}]},{"reference":{"label":"37","misc":["Through the Wiener-Khintchine theorem, the main (autocorrelation) term in G(τ) provides information about the spectrally resolved gating function, i.e., G(Ω)∝Ω|R(Ω)|2/nΩ [34,38,39]. While Ω|R(Ω)|2 reflects the sampled range of frequencies, the gating function can incorporate nonlinear-polarization effects of quantum character through Pockels effect [20,24]. This fact is a consequence of dispersion and similar in effect to a beam splitter carrying vacuum fluctuations from its free port"]},"raw_refs":[{"schema":"JATS","source":"APS","value":"<ref id=\"c37\"><label>[37]</label><mixed-citation publication-type=\"misc\"><object-id>37</object-id>Through the Wiener-Khintchine theorem, the main (autocorrelation) term in <inline-formula><math><mrow><mi>G</mi><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></math></inline-formula> provides information about the spectrally resolved gating function, i.e., <inline-formula><math><mrow><mi>G</mi><mrow><mo>(</mo><mi mathvariant=\"normal\">Ω</mi><mo>)</mo></mrow><mo>∝</mo><msup><mrow><mi mathvariant=\"normal\">Ω</mi><mo>|</mo><mi>R</mi><mrow><mo>(</mo><mi mathvariant=\"normal\">Ω</mi><mo>)</mo></mrow><mo>|</mo></mrow><mn>2</mn></msup><mo>/</mo><msub><mi>n</mi><mi mathvariant=\"normal\">Ω</mi></msub></mrow></math></inline-formula> <styled-content><xref ref-type=\"bibr\" rid=\"c34 c38 c39\">[34,38,39]</xref></styled-content>. While <inline-formula><math><msup><mrow><mi mathvariant=\"normal\">Ω</mi><mo>|</mo><mi>R</mi><mrow><mo>(</mo><mi mathvariant=\"normal\">Ω</mi><mo>)</mo></mrow><mo>|</mo></mrow><mn>2</mn></msup></math></inline-formula> reflects the sampled range of frequencies, the gating function can incorporate nonlinear-polarization effects of quantum character through Pockels effect <styled-content><xref ref-type=\"bibr\" rid=\"c20 c24\">[20,24]</xref></styled-content>. 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Res.","Phys.Rev.Res."],"arxiv_eprints":[{"categories":["quant-ph","physics.optics"],"value":"2202.03353"}],"referenced_authors_bais":["A.H.SafaviNaeini.1","S.Hill.2","F.Marquardt.1","L.E.Allen.1","T.C.Ralph.1","M.Beck.3","T.L.M.Guedes.1","C.B.Moller.1","M.Boissonneault.1","M.Aspelmeyer.1","J.T.Hill.1","S.Mukamel.1","T.P.M.Alegre.1","H.P.Robertson.1","T.G.Philbin.2","Klemens.Hammerer.1","T.J.Kippenberg.1","S.Schreppler.1","N.C.H.Spethmann.1","P.Krauspe.1","E.Polzik.1","J.Kohler.6","S.Onoe.1","C.Maissen.1","J.F.Schmidt.1","K.E.Dorfman.1","Y.Tsaturyan.1","S.J.Robertson.1","K.Jensen.2","Robert.Raussendorf.1","M.Van.den.Nest.2","F.Y.Khalili.9","Yanbei.Chen.1","A.Krause.1","R.J.C.Spreeuw.1","A.M.Herter.1","T.Farrelly.1","S.Eckart.1","D.P.DiVincenzo.1","P.Bertet.1","A.Schliesser.1","T.L.d.Guedes.1","I.C.BeneaChelmus.1","E.Zeuthen.1","D.M.StamperKurn.1","S.Y.Buhmann.3","J.Faist.1","M.W.Beijersbergen.1","U.Leonhardt.1","D.Vion.1","F.Lindel.1","F.Schlawin.1","A.Blais.1","G.Vasilakis.1","D.E.Browne.1","Chen.Hsun.Chan.1","S.A.Moskalenko.1","L.F.Buchmann.1","G.Burkard.1","M.Kizmann.1","B.M.Terhal.3","M.V.Balabas.1","R.A.Thomas.1","C.Riek.1","Huan.Yang.1","F.R.Ong.1","Hai.Xing.Miao.1","S.Eggert.2","D.Esteve.1","W.Dur.2","M.Seeger.1","R.F.Werner.1","D.V.Seletskiy.1","R.Bennett.1","A.C.Doherty.1","H.J.Briegel.2","P.Sulzer.1","C.Kuklewicz.2","O.Painter.1","F.F.Settembrini.1","J.P.Woerdman.1","A.Leitenstorfer.1","G.Scalari.1","F.Konig.2","C.H.Bennett.1"],"figures":[{"filename":"New_main_fig4.png","material":"preprint","caption":"(a) Orientation of the NX and field components. The probe $\\vec{E}_\\mathrm{p}$ is polarized along $\\vec{e}_z$ and propagates with wave vector $\\vec{k}_\\omega = k_\\omega \\vec{e}_k$. The tensor components of the nonlinear susceptibility are such that only field components along $\\vec{e}_x$ and $\\vec{e}_y$ can mix with the probe, generating new quantum-field components along $\\vec{e}_s$ and $\\vec{e}_k$ (a nonpropagating component). (b) Scheme of an EO measurement. $\\vec{E}_\\mathrm{p}$ changes its ellipticity in the NX due to the nonlinearly generated $\\vec{e}_s$-polarized field component, resulting in $\\vec{E}'$. A quarter-wave plate ($\\lambda/4$) shifts the phase of the $\\vec{e}_a$ component of $\\vec{E}'$ by $\\pi/2$, leading to $\\vec{E}''$, which has its ${E}''_z$ and ${E}''_s$ components spatially split by a Wollaston prism (WP) before independent photon counting. (c) Illustration of the state evolution under the nonlinear interaction~\\cite{Suppl_Mat}. The states include $z$ and $s$ polarizations (in-plane and out-of-plane panels) and two frequency bands, MIR and NIR (left and right panels), with the $z$-polarized NIR coherent probe represented as a blue pool of photons. Red (green) contours represent annihilation (creation) of photons (golden spheres) and the arrows show the directions of the energy transfers. The 1st diagram (uppermost) shows the lowest-order perturbation of the initial state, with $s$-polarized MIR and NIR photons being created through annihilation of a probe photon. The 2nd and 3rd diagrams show the 2nd-order processes that lead to no BA in the MIR, since the photons created by the 1st-order process are annihilated. The last two diagrams show the remaining 2nd-order processes, which cause additional BA in the MIR via generation of extra photons.","label":"fig1","source":"arxiv","key":"daa95d62184203ecaf3340944687cce3","url":"https://inspirehep.net/files/daa95d62184203ecaf3340944687cce3"},{"filename":"Figure_1_abcd_2021_6.png","material":"preprint","caption":"(a), (b) Ratio $\\Delta \\mathcal{S}/N$ (with the rms signal $\\Delta \\mathcal{S}={\\langle\\hat{\\mathcal{S}}^2\\rangle}^{1/2}$) in dependence of the number of photons per probe pulse $N$. The solid blue lines represent the total rms signal per photon, the dotted black lines represent the base-SN contribution, the dashed red lines show the main EO rms signal and the green [purple] dot-dashed lines account for $\\langle [\\hat{\\mathcal{S}}^{(2)}_{\\text{eo}}]^2\\rangle$ [$\\langle \\hat{\\mathcal{S}}^{(1)}_{\\text{eo}}\\hat{\\mathcal{S}}^{(3)}_{\\text{eo}}+\\hat{\\mathcal{S}}^{(3)}_{\\text{eo}}\\hat{\\mathcal{S}}^{(1)}_{\\text{eo}}\\rangle$]. The background gradient illustrates the transition between the effectively BA-free, shot-noise dominated (SN) and the BA-dominated (BA) regimes. (c), (d) Increase of $(\\Delta \\mathcal{S}-\\Delta \\mathcal{S}_{\\mathrm{sn}})/\\Delta \\mathcal{S}_{\\mathrm{sn}}$ with $N$. The solid (dotted) blue lines contain up to 4th(2nd)-order contributions. Left (right) plots correspond to parameter set 1 (set 2), see main text.","label":"Noise","source":"arxiv","key":"f90b07e0a8e7a895ac3786af1c4c7237","url":"https://inspirehep.net/files/f90b07e0a8e7a895ac3786af1c4c7237"},{"filename":"TOTAL_autocorrelation2.png","material":"preprint","caption":"(a) Illustration of an EO measurement with two channels ($\\mathrm{ch1}$ and $\\mathrm{ch2}$), with $\\lambda/4$, WP and $G(\\tau)$ representing the quarter-wave plate, the Wollaston prism and the correlation register. (b) Total 2nd- (red) and 4th-order (green) contributions to $g(\\tau)$ for $N=10^{11}$, representing signal autocorrelations in the two-channel measurements.","label":"autocorrelation","source":"arxiv","key":"0eee329b8e32f8b8f0a8b880830a51d8","url":"https://inspirehep.net/files/0eee329b8e32f8b8f0a8b880830a51d8"},{"filename":"Figure_2_2.png","material":"preprint","caption":"(a), (b) Minimum of $\\Delta \\mathcal{S} /N$ as a function of $w_0$. The solid blue line shows the total $\\Delta {\\mathcal{S}} /N$ value. The dotted black (dashed red) lines represent the SN (main EO) contributions. The insets show how the probe photon number that minimizes $\\Delta \\mathcal{S} /N$, $N_\\text{min}$, varies as a function of $w_0$ (also normalized as $L/w_0)$. Left (right) plots correspond to parameter set 1 (set 2), apart from the value of $w_0$.","label":"photonnumber","source":"arxiv","key":"8d4f6084c544d9b84d735b8106cc16e6","url":"https://inspirehep.net/files/8d4f6084c544d9b84d735b8106cc16e6"},{"filename":"V22a.png","material":"preprint","caption":" : width=7cm","label":"photonnumber","source":"arxiv","key":"e8c10c0e1595a94990296887ca3e6fa4","url":"https://inspirehep.net/files/e8c10c0e1595a94990296887ca3e6fa4"},{"filename":"V22b.png","material":"preprint","caption":" : width=7cm : Caption not extracted","label":"photonnumber","source":"arxiv","key":"ca2240c10296449bd07abea940495765","url":"https://inspirehep.net/files/ca2240c10296449bd07abea940495765"},{"filename":"V22c.png","material":"preprint","caption":"Top left: $V^{(a)}_{\\{2,2\\}}(\\tau)/N^3$. Top right: $V^{(b)}_{\\{2,2\\}}(\\tau)/N^3$. Bottom: $V^{(c)}_{\\{2,2\\}}(\\tau)/N^3$.","label":"V22_independentplots","source":"arxiv","key":"72ec37370ccc96c9c4558a36b2156231","url":"https://inspirehep.net/files/72ec37370ccc96c9c4558a36b2156231"},{"filename":"V13a.png","material":"preprint","caption":" : width=7cm","label":"V13_independentplots","source":"arxiv","key":"bc212055458f7149acd98cb5bee1857a","url":"https://inspirehep.net/files/bc212055458f7149acd98cb5bee1857a"},{"filename":"V13b.png","material":"preprint","caption":" : Left: $V^{(a)}_{\\{1,3\\}}(\\tau)/N^3$. Right: $V^{(b)}_{\\{1,3\\}}(\\tau)/N^3$. : Caption not extracted","label":"V13_independentplots","source":"arxiv","key":"256ba11df1e41cb28c4203fa85f1de0f","url":"https://inspirehep.net/files/256ba11df1e41cb28c4203fa85f1de0f"},{"filename":"V04c.png","material":"preprint","caption":"$V^{(c)}_{\\{0,4\\}}(\\tau)/N^3$ profile.","label":"V04_independentplots","source":"arxiv","key":"a69ddec9285ddbd8facdaaed92409ef5","url":"https://inspirehep.net/files/a69ddec9285ddbd8facdaaed92409ef5"},{"filename":"ResponseA.png","material":"preprint","caption":"(Full cyan) Gating function $|R(\\Omega)|^2\\Omega/\\omega^{(\\text{set}1)}_\\mathrm{p}$ for the first set of parameters considered (scaled up by factor $15$). (Dotted gray) Corresponding phase-matching function $|\\zeta_{\\omega,\\Omega}|/(d\\frac{L \\omega}{2c_0 n })$.","label":"gatingA","source":"arxiv","key":"20125f330aaa17e7ec98bc165bf10251","url":"https://inspirehep.net/files/20125f330aaa17e7ec98bc165bf10251"},{"filename":"ResponseF.png","material":"preprint","caption":"(Full cyan) Gating function $ |R(\\Omega)|^2 \\text{Abs}(\\Omega)\\Omega/\\omega^{(\\text{set}2)}_\\mathrm{p}$ for the second set of parameters considered (scaled up by 1500). (Dotted gray) Corresponding phase-matching function $|\\zeta_{\\omega,\\Omega}|/(d\\frac{L \\omega}{2c_0 n })$.","label":"gatingF","source":"arxiv","key":"d34feac52f8b0db629ea750aba5cc592","url":"https://inspirehep.net/files/d34feac52f8b0db629ea750aba5cc592"}],"inspire_categories":[{"term":"Quantum Physics","source":"arxiv"},{"term":"General Physics","source":"arxiv"}],"first_author":{"full_name":"Guedes, T.L.M.","last_name":"Guedes","first_name":"T.L.M.","recid":2029387},"control_number":2029383,"dois":[{"material":"publication","source":"APS","value":"10.1103/PhysRevResearch.5.013151"},{"source":"APS","value":"10.1103/PhysRevResearch.5.013151"}],"document_type":["article"],"texkeys":["Guedes:2022znb"],"abstracts":[{"source":"APS","value":"The influence of measurement back action on electro-optic sampling of electromagnetic quantum fluctuations is investigated. Based on a cascaded treatment of the nonlinear interaction between a near-infrared coherent probe and the mid-infrared vacuum, we account for the generated electric-field contributions that lead to detectable back action. Specifically, we theoretically address two realistic setups, exploiting one or two probe beams for the nonlinear interaction with the quantum vacuum, respectively. The setup parameters at which back action starts to considerably contaminate the measured noise profiles are determined. We find that back action starts to detrimentally affect the signal once the fluctuations due to the coupling to the mid-infrared vacuum become comparable to the base shot noise. Due to the vacuum fluctuations entering at the beam splitter, the shot noise of two incoming probe pulses in different channels is uncorrelated. Therefore, even when the base shot noise dominates the output of the experiment, it does not contribute to the correlation signal itself. However, we find that further contributions due to nonlinear shot-noise enhancement are still present. Ultimately, a regime in which electro-optic sampling of quantum fields can be considered as effectively back-action free is found.","abstract_source_suggest":{"input":"APS"}},{"source":"arXiv","value":"The influence of measurement back action on electro-optic sampling of electromagnetic quantum fluctuations is investigated. Based on a cascaded treatment of the nonlinear interaction between a near-infrared coherent probe and the mid-infrared vacuum, we account for the generated electric-field contributions that lead to detectable back action. Specifically, we theoretically address two realistic setups, exploiting one or two probe beams for the nonlinear interaction with the quantum vacuum, respectively. The setup parameters at which back action starts to considerably contaminate the measured noise profiles are determined. Due to the vacuum fluctuations entering at the beam splitter, the shot noise of two incoming probe pulses in different channels is uncorrelated. This leads to the absence of the base-level shot noise in the correlation, while further contributions due to nonlinear shot-noise enhancement are still present. Ultimately, the regime in which electro-optic sampling of quantum fields can be considered as effectively back-action free is found.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"APS","title":"Back action in quantum electro-optic sampling of electromagnetic vacuum fluctuations"},{"source":"arXiv","title":"Back action in quantum electro-optic sampling of electromagnetic vacuum fluctuations"}],"imprints":[{"date":"2023-02-27"}],"curated":false},"id":"2029383"},{"links":{"bibtex":"https://inspirehep.net/api/literature/2850542?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/2850542?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/2850542?format=latex-us","json":"https://inspirehep.net/api/literature/2850542?format=json","json-expanded":"https://inspirehep.net/api/literature/2850542?format=json-expanded","cv":"https://inspirehep.net/api/literature/2850542?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A2850542"},"created":"2024-11-22T10:03:06.526002+00:00","updated":"2025-10-05T13:29:53.612999+00:00","metadata":{"citation_count":0,"citation_count_without_self_citations":0,"authors":[{"raw_affiliations":[{"value":"femtoQ Lab, Department of Engineering Physics, Polytechnique Montr éal, Montr éal, Qu ébec H3T 1J4, Canada"},{"value":"Tempo Optics Inc., Montr éal, Qu ébec H3T 1W9, Canada"}],"full_name_unicode_normalized":"liu, shilong","full_name":"Liu, Shilong","record":{"$ref":"https://inspirehep.net/api/authors/2133833"},"ids":[{"schema":"INSPIRE BAI","value":"S.Liu.66"}],"last_name":"Liu","uuid":"86dc1fcb-33f5-4d60-963c-47a0732ff2f4","first_name":"Shilong","recid":2133833},{"full_name_unicode_normalized":"virally, stéphane","full_name":"Virally, Stéphane","record":{"$ref":"https://inspirehep.net/api/authors/1998798"},"ids":[{"schema":"INSPIRE BAI","value":"S.Virally.1"}],"last_name":"Virally","uuid":"2d1be147-8367-4367-a7ad-df8e2eea634e","first_name":"Stéphane","recid":1998798},{"raw_affiliations":[{"value":"femtoQ Lab, Department of Engineering Physics, Polytechnique Montr éal, Montr éal, Qu ébec H3T 1J4, Canada"}],"full_name_unicode_normalized":"demontigny, gabriel","full_name":"Demontigny, Gabriel","record":{"$ref":"https://inspirehep.net/api/authors/1878270"},"ids":[{"schema":"INSPIRE BAI","value":"G.Demontigny.1"}],"last_name":"Demontigny","uuid":"b78e1f25-5293-4400-915f-7b5d458c6aa3","first_name":"Gabriel","recid":1878270},{"raw_affiliations":[{"value":"femtoQ Lab, Department of Engineering Physics, Polytechnique Montr éal, Montr éal, Qu ébec H3T 1J4, Canada"}],"full_name_unicode_normalized":"cusson, patrick","full_name":"Cusson, Patrick","record":{"$ref":"https://inspirehep.net/api/authors/1998799"},"ids":[{"schema":"INSPIRE BAI","value":"P.Cusson.1"}],"last_name":"Cusson","uuid":"ff078bbb-8245-417d-a17e-1b52bcc98133","first_name":"Patrick","recid":1998799},{"raw_affiliations":[{"value":"femtoQ Lab, Department of Engineering Physics, Polytechnique Montr éal, Montr éal, Qu ébec H3T 1J4, Canada"}],"full_name_unicode_normalized":"seletskiy, denis v.","full_name":"Seletskiy, Denis V.","record":{"$ref":"https://inspirehep.net/api/authors/1998800"},"ids":[{"schema":"INSPIRE BAI","value":"D.V.Seletskiy.1"}],"last_name":"Seletskiy","uuid":"31241979-2ea3-4875-828b-e5b63269ee97","first_name":"Denis V.","recid":1998800}],"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","references":[{"reference":{"dois":["10.1364/OL.25.000025"],"label":"1","publication_info":{"journal_volume":"25","page_end":"27","year":2000,"page_start":"25","journal_title":"Opt.Lett."},"misc":["Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm"],"authors":[{"full_name":"Ranka, J.K."},{"full_name":"Windeler, R.S."},{"full_name":"Stentz, A.J."}]},"raw_refs":[{"schema":"text","source":"arXiv","value":"1. 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E. & Nocedal, J. An interior point algorithm for large-scale nonlinear programming. SIAM J. on Optim. 9, 877–900 (1999)."}]}],"referenced_authors_bais":["L.L.SanchezSoto.1","R.H.Stolen.1","E.Santamato.1","L.F.Mollenauer.1","E.Bolduc.1","R.W.Boyd.1","J.Gordon.1","K.Huang.26","P.Balcou.1","S.Liu.66","P.L.McMahon.1","Paul.B.Corkum.1","E.Karimi.1","Anne.LHuillier.1","M.S.Najafabadi.1","B.A.Malomed.1","Y.M.Ivanov.1","E.Karimi.3","Y.Cui.4","G.Leuchs.2","J.Laurat.1","Ferenc.Krausz.1","M.Lewenstein.1","H.L.Jeannic.1","Yi.Yun.Zhang.1","N.Bent.1"],"figures":[{"filename":"Fig_1.png","material":"preprint","caption":"Framework for spectro-temporal engineering using \\Red{physics-embedded} convolutional neural network (P-CNN). (a) Schematic setup including dispersion and nonlinear engineering, supercontinuum generation, and measurement stages. (b) Mapping between input parameter spaces and observations via a nonlinear angle \\(\\theta\\). (c) \\Red{The architecture of the physics neural networks, incorporating parameters space, physics embedded CNN, and observations}","label":"F1","source":"arxiv","key":"31a3b1f5955e20989ac3dc3cd5fb63c1","url":"https://inspirehep.net/files/31a3b1f5955e20989ac3dc3cd5fb63c1"},{"filename":"Fig_2.png","material":"preprint","caption":"Performance of \\Red{physics embedded networks}. (a) and (b) Linear regression analysis for the predicted \\(\\mathrm{I_{pred}}\\) from the FNN and P-CNN against the target \\(\\mathrm{I_{tar}}\\) obtained from GNLSE simulations. (c) Schematic representation of the phase \\(\\Phi(\\omega)\\) with added noise \\(\\Delta \\Phi(\\omega)\\) (top-left panel) and its impact on the SC outputs (\\(I(\\omega)\\)) across three approaches: FNN (top), GNLSE (middle), and P-CNN (bottom). The Euclidean distance (\\(d\\)) with maximum probability quantifies the deviation of the noisy SC output from the noiseless target spectrum, with values of \\(\\bar{d}_{E,0} = 0.13\\), \\(\\bar{d}_{E,1} = 1.17\\), \\(\\bar{d}_{E,0} = 1.08\\) , and \\(\\bar{d}_{E,2} = 0.46\\), respectively, for GNLSE, FNN, P-FNN and P-CNN. (d) Statistical distributions of the Euclidean distance for 1000 noisy phase inputs.","label":"F1-2","source":"arxiv","key":"eddc272d65f721c6438d40100bca933b","url":"https://inspirehep.net/files/eddc272d65f721c6438d40100bca933b"},{"filename":"Fig_3.png","material":"preprint","caption":"Spectral control of the supercontinuum. (a) Evolution of the SC spectra as a function of the input phase, controlled by the 4$f$ shaper. (b) Calculated nonlinear conversion efficiency defined in Eq. \\ref{E_R} quantifies energy transfer from the soliton (Net-S) to dispersive wave (Net-D) spectral regions. The P-CNN enables engineering of the dispersive wave parameters: (c) The center wavelength oscillation with a target 3.7\\% modulation around 1070 nm and (d) linear tunability in bandwidth for DW.","label":"F2","source":"arxiv","key":"59f2bb3d749cd1aa4bbd559f8faf6315","url":"https://inspirehep.net/files/59f2bb3d749cd1aa4bbd559f8faf6315"},{"filename":"Fig_4.png","material":"preprint","caption":"Temporal pulse duration engineering. (a) Ordinates the measured relationship between the pulse duration (left ordinate axis) and second-order dispersion distance ($X_2$), with the right axis displaying the nonlinear compression factor. (b) The reconstructed temporal intensity at five positions marked in (a). (c)-(e) The measured and reconstructed FROG traces for positions (1), (3), and (5) as indicated in panel (a), where the reconstructed spectral amplitude and phase are provided in the corresponding right-side panels.","label":"F3","source":"arxiv","key":"4b3a7ecfe05bfd7793f66c7a7863763c","url":"https://inspirehep.net/files/4b3a7ecfe05bfd7793f66c7a7863763c"},{"filename":"Fig_5.png","material":"preprint","caption":"Spectro-temporal correlations for high-order soliton formation. (a) Bandwidth (3dB) of target functions (P-CNN) and measurements, ranging from 10 to 70 nm. (b)-(c) Spectra of high-order solitons for soliton numbers $N$=3 and $N$=4, with the top panels showing simulated target states and the bottom panels presenting experimental measurements. (d) Dispersion length, nonlinear length, and soliton number for a soliton with $N$=4. (e)-(f) Temporal intensity profiles reconstructed via FROG for various soliton sequences.","label":"F4","source":"arxiv","key":"66075739445bdc83ab09341b52486c4c","url":"https://inspirehep.net/files/66075739445bdc83ab09341b52486c4c"},{"filename":"Fig_6.png","material":"preprint","caption":"Setup and Simulations for Supercontinuum and Few-cycle pulse Generation. (a) Mode-locked fiber laser (MLF): The core laser source for generating initial soliton pulses. (b) EDFA-1: Includes an Erbium-doped fiber (EDF) \\(L_0\\) of 1.1 m, and single-mode fiber (SMF) $\\sim$ 2.6 m. (c) Pulse Shaper: Comprises two symmetric optical gratings (940 grooves /\\ mm) and lenses (focal length $\\sim$ 150 mm) positioned on either side of a Spatial Light Modulator (SLM, Santec SLM-100: 1440 $\\times $1050 pixels). (d) EDFA-2: Consists of a forward SMF \\(L_1\\) of 1.2 m, an Er-doped fiber \\(L_2\\) of 2 m, and an attached SMF \\(L_3\\) of 0.8 m. (e) Supercontinuum generation: utilized with a Highly Nonlinear Fiber (HNF) of the length \\(L_4\\) of $\\sim$ 4 cm. (f) and (g) Dynamics of the Pulse and Spectral Intensity in simulations: Traces the evolution of the pulse and its spectral intensity through SMF (\\(L_1\\)), EDFA-2 (\\(L_2\\)), and SMF (\\(L_3\\)). (h) Temporal Intensity Profile: Displays the temporal intensity at the position where SMF \\(L_3\\) is approximately 0.8 m, with the resultant pulse width around 46 fs. (i) Calculated SC Spectrum: Shows the supercontinuum from 1 to 2.5 $\\mathrm{\\mu m}$ at a propagation length of 3.5 cm. (j) and (k) Dynamics of SC: Depicts the spectral and temporal intensity variations of the SC along the HNF from 0 to 5 cm.","label":"Fig-setup","source":"arxiv","key":"b351278996ac5ab4f0ed908192652344","url":"https://inspirehep.net/files/b351278996ac5ab4f0ed908192652344"},{"filename":"Fig_7.png","material":"preprint","caption":"Structure and Performance of P-CNN in Regression Tasks. (a) Structure of the P-CNN: Illustrates the comprehensive architecture. (b) Layer Actions: Details the specific operations performed at each layer of the CNN. (c) Training Loss: Charts the loss throughout the training process, highlighting model convergence. (d) Error Reduction in Euclidean distance : Compares the effectiveness of the constrained nonlinear multivariable (CNM) function and the gradient descent algorithm (GDA) in optimizing solutions, with initial conditions set to random values and inverted solutions derived from the trained CNN. The inset panel displays the target and measured spectra at the final iteration.","label":"Fig-CNN-1","source":"arxiv","key":"71750edf545a31879a0854c456a3904a","url":"https://inspirehep.net/files/71750edf545a31879a0854c456a3904a"}],"inspire_categories":[{"term":"General Physics","source":"arxiv"},{"term":"Math and Math Physics","source":"arxiv"},{"term":"Quantum Physics","source":"arxiv"}],"preprint_date":"2024-11-21","author_count":5,"first_author":{"emails":["dr.shilongliu@gmail.com"],"full_name":"Liu, Shilong","last_name":"Liu","first_name":"Shilong","recid":2133833},"public_notes":[{"source":"arXiv","value":"Will be published in Ultrafast Science"}],"control_number":2850542,"earliest_date":"2024-11-21","document_type":["article"],"texkeys":["Liu:2024sho"],"abstracts":[{"source":"arXiv","value":"Frequency synthesis and spectro-temporal control of optical wave packets are central to ultrafast science, with supercontinuum (SC) generation standing as one remarkable example. Through passive manipulation, femtosecond (fs) pulses from nJ-level lasers can be transformed into octave-spanning spectra, supporting few-cycle pulse outputs when coupled with external pulse compressors. While strategies such as machine learning have been applied to control the SC's central wavelength and bandwidth, their success has been limited by the nonlinearities and strong sensitivity to measurement noise. Here, we propose and demonstrate how a physics-embedded convolutional neural network (P-CNN) that embeds spectro-temporal correlations can circumvent such challenges, resulting in faster convergence and reduced noise sensitivity. This innovative approach enables on-demand control over spectro-temporal features of SC, achieving few-cycle pulse shaping without external compressors. This approach heralds a new era of arbitrary spectro-temporal light state engineering, with implications for ultrafast photonics, photonic neuromorphic computation, and AI-driven optical systems.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["physics.optics"],"titles":[{"source":"arXiv","title":"Engineering spectro-temporal light states with physics-embedded deep learning"},{"source":"arXiv","title":"Engineering spectro-temporal light states with physics-trained deep learning"}],"facet_author_name":["2133833_Shilong Liu","1878270_Gabriel Demontigny","1998798_Stéphane Virally","1998799_Patrick Cusson","1998800_Denis V. 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A mirror (M1) reflects the beam back into the crystal for additional nonlinear interaction. The PPLN is positioned so that the pump's focal plane is at the second pass. The beam is collimated by a concave mirror (CM1) with a focal length of \\SI{150}{\\mm}. The signal twin (\\SI{1.37}{\\um}, \\SI{100}{\\fs}), idler twin (\\SI{4.0}{\\um}, \\SI{100}{\\fs}) and pump are separated using a pair of dichroic mirrors (DM1 and DM2). The signal twin is then sent towards measurement devices, while the idler is not studied in this work. b) Average number of signal photons generated per pulse as a function of the average number of pump photons. The dashed line is a fit of the expected number of generated signal photons, showing signs of saturation for $\\ev{N_{\\rm P}}> \\num{1.4e13}$.","source":"arxiv","label":"fig:fig1","key":"139e583513f62e3d5c3f82586660c4cb","url":"https://inspirehep.net/files/139e583513f62e3d5c3f82586660c4cb"},{"filename":"Figure_2.png","material":"preprint","caption":"\\justifying a) Signal photon number probability density histogram for 2 981 607 recorded events. An average of $\\langle N_{\\rm S} \\rangle= 1.296 \\times 10^8$ photons per pulse with a standard deviation of $\\sigma_{N_{\\rm S}}=1.265 \\times 10^8$ photons was measured, giving a parametric gain of $G \\simeq 10.3$, Such values give a $g^{(2)}(0)$ value of $1.95 \\pm 0.03$, close to the expected $g^{(2)}(0)=2$ for a single-mode thermal state. From this value, a number of spatio-temporal mode of $K_{g2}=1.05 \\pm0.03$ was calculated. The dashed line is a guide to the eye showing a perfect thermal (negative-exponential) statistics. b) Second-order correlation function $g^{(2)}(0)$ (right axis, black) and the corresponding linear modal entropy $S^{g2}_\\mathrm{mod} = (K_{g2}-1)/K_{g2}$ (left axis, red) as a function of mean signal photon number per pulse. Near single-mode operation ($S^{g2}_\\mathrm{mod} < 0.1$) is maintained over three orders of magnitude in brightness. The shaded region marks pump levels at which the single-mode sinh² scaling of Fig.~\\ref{fig:fig1}b breaks down. The mapping $g^{(2)}(0) \\to S^{g2}_\\mathrm{mod}$ does not apply in this regime, and the $S^{g2}_\\mathrm{mod}$ axis is therefore omitted within the shaded region. The modest rise of $S^{g2}_\\mathrm{mod}$ as the shaded boundary is approached from below is attributed to tail-flattening of $P(N)$ by parasitic $\\chi^{(2)}$ effects (e.g., SHG of pump or signal) rather than to modal repopulation (see text).","source":"arxiv","label":"fig:fig2","key":"426a648c8a4ca4ccc735ca00c7f18d01","url":"https://inspirehep.net/files/426a648c8a4ca4ccc735ca00c7f18d01"},{"filename":"Figure_3.png","material":"preprint","caption":"\\justifying Temporal mode extraction by singular value decomposition on the reduced spectral density matrix of the signal at high-gain. First and second ($\\times 10$) intensity Schmidt modes of the signal. The decomposition yields the Schmidt number $K_\\mathrm{HG} = 1.034 \\pm 0.002$. Inset: reduced spectral density matrix of the signal, displaying near-perfect symmetry, as expected for a single-spatio-temporal mode light.","source":"arxiv","label":"fig:fig3","key":"44c342c0d6133030f1cc4a9fe6a6f87e","url":"https://inspirehep.net/files/44c342c0d6133030f1cc4a9fe6a6f87e"},{"filename":"Figure_4-5.png","material":"preprint","caption":"\\justifying \\textbf{Temporal-mode control by the pump mode} (a) Effect of pump temporal extent on mode purity. Pictorial representation of the vacuum fluctuations available for amplification by SPDC, dictated by the phase matching bandwidth ($\\Delta \\omega_{PM}$) of the nonlinear medium used. For proper single-mode amplification, the pump duration has to be similar to the inverse of $\\Delta \\omega_{PM}$. If the pump temporal extent is increased beyond that criterion by the addition of group delay dispersion, multiple temporal modes can be amplified without changing the spectral content of the pump; (b) Measured linear modal entropy $S^\\mathrm{HG}_\\mathrm{mod} = (K_\\mathrm{HG}-1)/K_\\mathrm{HG}$ as a function of group delay dispersion (GDD) of the pump, with associated pulse duration. Near-unit purity ($S^\\mathrm{HG}_\\mathrm{mod}\\simeq0$) is maintained only for relatively small added GDD, confirming that single spatio-temporal mode operation is only possible near the transform limit. The methodology for the fit is explained in Supplementary Material Sec. S2. A single fit parameter (minimum entropy) was used to take experimental reality into account, as the theory gives $\\min(K_\\mathrm{HG})=1$.","source":"arxiv","label":"fig:fig4","key":"bf46f38835aafd8934f8f47403efe9cc","url":"https://inspirehep.net/files/bf46f38835aafd8934f8f47403efe9cc"}],"preprint_date":"2026-05-14","author_count":9,"first_author":{"emails":["gabriel.demontigny@polymtl.ca"],"full_name":"Demontigny, Gabriel","last_name":"Demontigny","first_name":"Gabriel","recid":1878270},"control_number":3156729,"earliest_date":"2026-05-14","document_type":["article"],"texkeys":["Demontigny:2026olk"],"abstracts":[{"source":"arXiv","value":"We introduce an ultrafast, bright, entangled twin-beam source generated by type-0 parametric down-conversion in periodically-poled lithium niobate at MHz repetition rate, with continuously tunable Schmidt number $K$ set by the pump pulse duration. Photon-number statistics characterization via $g^{(2)}(0)$ and singular-value decomposition of the signal spectral density matrix yield $K\\simeq1.05$ and $K\\simeq1.03$, respectively, maintained over multiple orders of magnitude in brightness. Group-delay dispersion of the pump drives a continuous transition from single-mode operation to a controlled multimode regime, consistent with the temporal gain window departing from the inverse phase-matching bandwidth. Strong non-degeneracy of the source (signal at 1.37 um, idler at 4.0 um, $\\sim 100$ fs duration) decouples a mid-infrared interaction wavelength, which overlaps with molecular vibrational resonances, from a near-infrared detection band, establishing a practical platform for quantum-enhanced metrology, nonlinear interferometry, and mid-infrared spectroscopic sensing. We show that in the bright few-mode limit, the total entanglement resource is clearly separated between modal and occupational degrees of freedom, and that our source allocates up to 95-97% of that resource to the occupational sector.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Single Spatio-Temporal Mode Bright Twin-Beam Source Across the Near- and Mid-Infrared"}],"facet_author_name":["1878270_Gabriel Demontigny","1951539_Maria V. Chekhova","1998798_Stéphane Virally","1998799_Patrick Cusson","1998800_Denis V. Seletskiy","2771244_Andrei Rasputnyi","3156731_Amauri Perraton Elorza","3156732_Esteban Murillo Zapata","3156733_Eli Martel"],"license":[{"license":"CC BY 4.0","material":"preprint","url":"http://creativecommons.org/licenses/by/4.0/"}],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:3156729","updated":"2026-07-03T04:10:41.617654"},"curated":false,"arxiv_eprints":[{"categories":["quant-ph","physics.optics"],"value":"2605.15385"}]},"id":"3156729"},{"links":{"bibtex":"https://inspirehep.net/api/literature/2680445?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/2680445?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/2680445?format=latex-us","json":"https://inspirehep.net/api/literature/2680445?format=json","json-expanded":"https://inspirehep.net/api/literature/2680445?format=json-expanded","cv":"https://inspirehep.net/api/literature/2680445?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A2680445"},"created":"2023-07-26T03:08:07.579916+00:00","updated":"2026-02-09T13:16:57.455063+00:00","metadata":{"citation_count":7,"citation_count_without_self_citations":7,"authors":[{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/05f8d4e86"}],"raw_affiliations":[{"value":"femtoQ Lab, Department of Engineering Physics, Polytechnique Montréal, Montréal, QC H3T 1J4, Canada"}],"full_name_unicode_normalized":"onoe, sho","full_name":"Onoe, Sho","record":{"$ref":"https://inspirehep.net/api/authors/1949829"},"ids":[{"schema":"INSPIRE BAI","value":"S.Onoe.1"}],"affiliations":[{"curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/institutions/904305"},"value":"Montreal, Ecole Polytechnique"}],"last_name":"Onoe","uuid":"5a4b7040-fc00-428e-97d0-ad6b82df85ec","first_name":"Sho","recid":1949829},{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/05f8d4e86"}],"raw_affiliations":[{"value":"femtoQ Lab, Department of Engineering Physics, Polytechnique Montréal, Montréal, QC H3T 1J4, Canada"}],"full_name_unicode_normalized":"virally, stéphane","full_name":"Virally, Stéphane","record":{"$ref":"https://inspirehep.net/api/authors/1998798"},"ids":[{"schema":"INSPIRE BAI","value":"S.Virally.1"}],"affiliations":[{"curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/institutions/904305"},"value":"Montreal, Ecole Polytechnique"}],"last_name":"Virally","uuid":"7d7c4d41-82f5-49eb-b7e8-fd5b22adb0f2","first_name":"Stéphane","recid":1998798},{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/05f8d4e86"}],"raw_affiliations":[{"value":"femtoQ Lab, Department of Engineering Physics, Polytechnique Montréal, Montréal, QC H3T 1J4, Canada"}],"full_name_unicode_normalized":"seletskiy, denis v.","full_name":"Seletskiy, Denis V.","record":{"$ref":"https://inspirehep.net/api/authors/1998800"},"ids":[{"schema":"INSPIRE BAI","value":"D.V.Seletskiy.1"}],"affiliations":[{"curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/institutions/904305"},"value":"Montreal, Ecole Polytechnique"}],"last_name":"Seletskiy","uuid":"a7b4b950-9885-42e5-a323-7fd8bad2bb5f","first_name":"Denis V.","recid":1998800}],"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","references":[{"reference":{"texkey":"PhotonCounting1963","dois":["10.1103/PhysRev.130.2529"],"label":"1","publication_info":{"journal_volume":"130","artid":"2529","year":1963,"page_start":"2529","journal_title":"Phys.Rev."},"misc":["The quantum theory of optical coherence"],"authors":[{"full_name":"Glauber, R.J."}]},"raw_refs":[{"schema":"text","source":"arXiv","value":"[1]R. 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(a) The pulse-intensity evolution in five FDLs, where the initial pulse is set to be an L\\'{e}vy distribution, $A\\cdot \\mathcal{L}_{1.2,1}(t/T_{0})/|\\mathcal{L}_{1.2,1}(t/T_{0})|$, see Eq. ( \\protect\\ref{E-Levy}). Here, $T_{0}$ is $60.1$ fs, $A=18.76$, and $\\protect \\alpha =1.2$. The inserted fragmented white line shows the half-pulse width, which is $85$ fs in the output. (b) The pulse amplitude for the produced fractional soliton with $\\protect\\alpha =1.2$ and the conventional soliton (the dashes red profile) are displayed for comparison. (c) The scheme for the implementation of FNLSE in optics: the extra-cavity setup ($R=0$), and the intra-cavity one ($R>0$). (d) The experimental setup of the intra-cavity is designed to emulate FNLSE. Here the labels are defined as follows: pump-1(2): the pump laser operating at $980$ nm; \\SL{EDFA-1(2): erbium-doped fiber amplifiers}; PC: the polarization controller; SLM: the spatial light modulator; ISO: the fiber isolator; SA: the saturable absorber; SMF: the single-mode fiber.","source":"arxiv","label":"F1","key":"25fd1171dc2f1f1ca4a587be1234c6cd","url":"https://inspirehep.net/files/25fd1171dc2f1f1ca4a587be1234c6cd"},{"filename":"Fig_2-eps-converted-to.png","material":"preprint","caption":"The spectral-temporal analysis of the soliton pulses produced by the mode-locked fiber laser. (a) The stability analysis produced by varying LI ($\\protect\\alpha $) and dispersion length ($L_{\\mathrm{dis}}$). Data points indicate the boundary between stable and unstable soliton states; the dashed line represents the fractional-dispersion length (FDL) for $T_{0}=250$ fs. Insets show the measured and simulated (left and right sides, respectively) spectra for specific parameter settings: [$\\protect\\alpha $, $L_{\\mathrm{dis} }$] = [$0,0$], [$1,10$ m], and [$0.05,142$ m], respectively. (b) The comparison of the pulse amplitude produced by the experiment and simulations. The experimental profiles were reconstructed by the FROG system.","source":"arxiv","label":"F2","key":"0c9ae18fd8a04d9ffd95f4edb7ff7194","url":"https://inspirehep.net/files/0c9ae18fd8a04d9ffd95f4edb7ff7194"},{"filename":"Fig_3-eps-converted-to.png","material":"preprint","caption":"Spectral responses to varying the EDFA's pump power in the extra-cavity regime. (a1)-(a4): Recorded spectra produced by the flat [$ \\protect\\alpha =0,L_{\\mathrm{dis}}=0$], second-order [$\\protect\\alpha =2,L_{ \\mathrm{dis}}=1.7L_{\\protect\\alpha ,\\mathrm{FDL}}$], fractional-order [$\\protect\\alpha =1,L_{\\mathrm{dis}}=2.42L_{\\protect\\alpha ,\\mathrm{FDL}}$] and [$\\protect \\alpha =0.2,L_{\\mathrm{dis}}=0.88L_{\\protect\\alpha ,\\mathrm{FDL}}$] GVD, respectively. The bottom panels show the temporal intensity reconstructed by the FROG system for the pump power in 240 mW. (b1)-(b4): Showcasing the spectral valleys with multiple lobes, under the action of the segmented fractional phase, as indicated at the top of each panel and defined in Eqs. \\protect\\ref{E7}- \\protect\\ref{E10} , respectively. (c1)-(c4): The corresponding spectra, as obtained in the simulations.","source":"arxiv","label":"F3","key":"8e3e8a0a24c9aa6f33648c73bc669237","url":"https://inspirehep.net/files/8e3e8a0a24c9aa6f33648c73bc669237"},{"filename":"Fig_4-eps-converted-to.png","material":"preprint","caption":"The application of the spectral valleys to high-dimensional data encoding. (a): The pulse transmission regime for the data encoding from binary to quinary by using five spectral-valley modes. It includes a `soliton' pulse from a mode-locked fiber laser, the `write' section operated by a pulse shaper, a `nonlinear' SPM section, a `linear' fiber link of the length $\\simeq 100$ km, and a `read' section including a photodetector and oscilloscope. (b): Stretched temporal profiles recorded by the oscilloscope for modes of $ \\mathrm{\\{1\\}}$, $\\mathrm{\\{2\\}}$, and $\\mathrm{\\{3\\}}$, respectively. (c): The recorded temporal profiles of \\{25412, 33142, 35243, 4152, 14313\\} strings, as realized with $25$ holograms and produced by the oscilloscope for one round trip.","source":"arxiv","label":"F4","key":"5888121fc9948272b402979536fdc9a6","url":"https://inspirehep.net/files/5888121fc9948272b402979536fdc9a6"},{"filename":"Fig_5-eps-converted-to.png","material":"preprint","caption":"Simulations and experiments for pulse's spectra under the action of FGVD and nonlinearity. (a) and (d): The normalized temporal intensity and {gradient ($ -\\partial I/\\partial t$). (b) and (e): The corresponding temporal phase and gradient ($-\\partial \\protect\\phi /\\partial t$)}. (c) The summary effective force for $B=\\protect\\pi /2$. (f) The calculated spectral intensity for $C_{0}$ varying between $-3$ to $+3$. (g)-(h): The calculated three forces for $C_{0}=+\\protect\\pi /4$ and $C_{0}=-\\protect\\pi /4$, respectively. {(i) The measured spectral intensity for $ C_{0}$ varying from $-1.8$ to $1.8$.}","source":"arxiv","label":"F5","key":"5d657273355099282426325ef6a763fb","url":"https://inspirehep.net/files/5d657273355099282426325ef6a763fb"}],"first_author":{"emails":["shilong.liu@polymtl.ca","dr.shilongliu@gmail.com"],"full_name":"Liu, Shilong","last_name":"Liu","ids":[{"schema":"ORCID","value":"0000-0002-6308-4059"},{"schema":"INSPIRE BAI","value":"S.Liu.66"}],"first_name":"Shilong","recid":2133833},"control_number":2726573,"dois":[{"source":"WILEY","value":"10.1002/lpor.202401714"}],"document_type":["article"],"texkeys":["Liu:2023pwp"],"abstracts":[{"source":"WILEY","value":"A nonlinear optical platform is presented to emulate a nonlinear Lévy waveguide that supports the pulse propagation governed by a generalized fractional nonlinear Schrödinger equation (FNLSE). This approach distinguishes between intra-cavity and extra-cavity regimes, exploring the interplay between the effective fractional group-velocity dispersion (FGVD) and Kerr nonlinearity. In the intra-cavity configuration, stable fractional solitons enabled by an engineered combination of the fractional and regular dispersions in the fiber cavity are observed. The soliton pulses exhibit their specific characteristics, viz., “heavy tails” and a “spectral valley” in the temporal and frequency domain, respectively, highlighting the effective nonlocality introduced by FGVD. Further investigation in the extra-cavity regime reveals the generation of spectral valleys with multiple lobes, offering potential applications to the design of high-dimensional data encoding. To elucidate the spectral valleys arising from the interplay of FGVD and nonlinearity, an innovative “force” model supported by comprehensive numerical analysis is developed. These findings open new avenues for experimental studies of spectral-temporal dynamics in fractional nonlinear systems.","abstract_source_suggest":{"input":"WILEY"}},{"source":"arXiv","value":"We present a nonlinear optical platform to emulate a nonlinear \\textit{Lévy waveguide} that supports the pulse propagation governed by a generalized fractional nonlinear Schrödinger equation (FNLSE). Our approach distinguishes between intra-cavity and extra-cavity regimes, exploring the interplay between the effective fractional group-velocity dispersion (FGVD) and Kerr nonlinearity. In the intra-cavity configuration, we observe stable \\textit{fractional solitons} enabled by an engineered combination of the fractional and regular dispersions in the fiber cavity. The soliton pulses exhibit their specific characteristics, \\textit{viz.}, \"heavy tails\" and a \"spectral valley\" in the temporal and frequency domain, respectively, highlighting the effective nonlocality introduced by FGVD. Further investigation in the extra-cavity regime reveals the generation of spectral valleys with multiple lobes, offering potential applications to the design of high-dimensional data encoding. To elucidate the spectral valleys arising from the interplay of FGVD and nonlinearity, we have developed an innovative \"force\" model supported by comprehensive numerical analysis. These findings open new avenues for experimental studies of spectral-temporal dynamics in fractional nonlinear systems.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["physics.optics"],"titles":[{"source":"WILEY","title":"Experimental Emulator of Pulse Dynamics in Fractional Nonlinear Schrödinger Equation"},{"source":"arXiv","title":"Experimental emulator of pulse dynamics in fractional nonlinear Schrödinger equation"},{"source":"arXiv","title":"Observation of the spectral bifurcation in the Fractional Nonlinear Schrödinger Equation"}],"imprints":[{"date":"2025-04-01"}],"curated":false},"id":"2726573"},{"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"},"created":"2018-07-30T00:00:00+00:00","updated":"2025-11-17T08:22:36.158759+00:00","metadata":{"citation_count":29,"citation_count_without_self_citations":17,"authors":[{"affiliations_identifiers":[{"schema":"GRID","value":"grid.9811.1"}],"raw_affiliations":[{"value":"Department of Physics U. and Center for Applied Photonics - 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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},"id":"1684219"},{"links":{"bibtex":"https://inspirehep.net/api/literature/3094595?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/3094595?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/3094595?format=latex-us","json":"https://inspirehep.net/api/literature/3094595?format=json","json-expanded":"https://inspirehep.net/api/literature/3094595?format=json-expanded","cv":"https://inspirehep.net/api/literature/3094595?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A3094595"},"created":"2025-12-22T04:18:34.285762+00:00","updated":"2026-07-15T07:12:19.808055+00:00","metadata":{"citation_count":1,"citation_count_without_self_citations":1,"authors":[{"raw_affiliations":[{"value":"Max Planck Institute for the Science of Light"},{"value":"Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)"}],"full_name_unicode_normalized":"rasputnyi, andrei","full_name":"Rasputnyi, Andrei","record":{"$ref":"https://inspirehep.net/api/authors/2771244"},"last_name":"Rasputnyi","ids":[{"schema":"INSPIRE BAI","value":"A.Rasputnyi.1"}],"uuid":"13228f77-47eb-481b-ab6c-5cd4ba331677","first_name":"Andrei","recid":2771244},{"raw_affiliations":[{"value":"Institut Polytechnique de Paris"}],"full_name_unicode_normalized":"karuseichyk, ilya","full_name":"Karuseichyk, Ilya","record":{"$ref":"https://inspirehep.net/api/authors/1959773"},"last_name":"Karuseichyk","ids":[{"schema":"INSPIRE BAI","value":"I.Karuseichyk.1"}],"uuid":"312fe7e9-fcdb-441a-b067-0f4d22d7fe2e","first_name":"Ilya","recid":1959773},{"raw_affiliations":[{"value":"Max Planck Institute for the Science of Light"},{"value":"Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)"},{"value":"University of Ottawa"}],"full_name_unicode_normalized":"leuchs, gerd","full_name":"Leuchs, Gerd","record":{"$ref":"https://inspirehep.net/api/authors/1951068"},"last_name":"Leuchs","ids":[{"schema":"ORCID","value":"0000-0003-1967-2766"},{"schema":"INSPIRE BAI","value":"G.Leuchs.2"}],"uuid":"3cc9cf3f-d119-4001-b6b1-247169f8f2c6","first_name":"Gerd","recid":1951068},{"raw_affiliations":[{"value":"Max Planck Institute for the Science of Light"},{"value":"University of Lille"}],"full_name_unicode_normalized":"tani, francesco","full_name":"Tani, Francesco","record":{"$ref":"https://inspirehep.net/api/authors/2459178"},"last_name":"Tani","ids":[{"schema":"ORCID","value":"0000-0001-6482-0647"},{"schema":"INSPIRE BAI","value":"F.Tani.1"}],"uuid":"17ab3de2-7b90-43b3-a6d9-e2df8625102b","first_name":"Francesco","recid":2459178},{"raw_affiliations":[{"value":"Polytechnique Montréal"},{"value":"1 University of New Mexico"}],"full_name_unicode_normalized":"seletskiy, denis","full_name":"Seletskiy, 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OPA 1 and OPA 2, 3-mm BBO crystals; DM1 and DM2, dichroic mirrors; ND, neutral density filter; SHG, second-harmonic generation. (b) Two typical single-shot spectra with spectral fringes (incoherent background is subtracted). Each single-shot spectrum contains information about the amplitude $|\\alpha_{2\\omega}|$ and relative phase $\\phi_{2\\omega}$ of the second-harmonic pulse of BSV.","label":"fig:setup","source":"arxiv","key":"948f639b557214b2e3b9120a9f7e8b3f","url":"https://inspirehep.net/files/948f639b557214b2e3b9120a9f7e8b3f"},{"filename":"Figure_2_v2.png","material":"preprint","caption":"(a-c) Experimental and (d-f) simulated Husimi functions for different strengths of the Kerr interaction. The radial coordinate is normalized to the mean amplitude.","label":"fig:husimi","source":"arxiv","key":"65975b2fc67c681fe6f783d8b9858e6b","url":"https://inspirehep.net/files/65975b2fc67c681fe6f783d8b9858e6b"},{"filename":"fig_BSV_mixture.png","material":"preprint","caption":"Schematic representation of BSV as a mixture (red ellipse) of  squeezed coherent states (blue ellipses) in phase space. The dashed circle represents the vacuum state (the shot-noise uncertainty).","label":"fig:husimi","source":"arxiv","key":"0d89bde016c678180fa5067d216af841","url":"https://inspirehep.net/files/0d89bde016c678180fa5067d216af841"},{"filename":"Figure_discussion.png","material":"preprint","caption":"Transformation of the Wigner function due to the Kerr nonlinearity described by unitary transformation $\\hat{S}_{\\operatorname{Kerr}}$ for (a) a coherent state with $|\\alpha|^2=200$ and (b) a phase-squeezed state with the same mean number of photons and degree of squeezing 8 dB. (c) Simulated Wigner negativity volume vs. the number of photons $|\\alpha|^2$ for the fixed Kerr phase $\\phi_{\\operatorname{Kerr}} = 2 \\chi t |\\alpha|^2 = 0.6$. Circles correspond to the lossless case, triangles assume a 5\\%-loss before the Kerr interaction and 5\\% loss after it. Lines visualize an exponential fit of the points.","label":"fig:negativity","source":"arxiv","key":"c24ce6d83edd6a19d63a63c7a802ac39","url":"https://inspirehep.net/files/c24ce6d83edd6a19d63a63c7a802ac39"},{"filename":"Figure1.png","material":"preprint","caption":"(a-c) Spectral intensity covariance maps for different positions of fused silica slab. (d) Probability of occurrence of different spectral modes. (e) The spectral intensity of the fundamental frequency mode. (f) Photon-number probability distribution. Black curve is fit with the Gamma distribution.","label":"fig:stat","source":"arxiv","key":"3e30802b651b56e7c46cf5e63868372d","url":"https://inspirehep.net/files/3e30802b651b56e7c46cf5e63868372d"},{"filename":"Wigner_SV.png","material":"preprint","caption":"Wigner functions of Kerr-evolved squeezed vacuum states and their negativity under loss. The Kerr phase at the mean photon number $n_s$ is $\\phi_{\\mathrm{Kerr}} = 2\\chi t n_s = 0.16$. (a) $n_s = 4$ (low energy, strong nonlinearity $\\chi t = 0.02$). (b) $n_s = 20$ (higher energy, weaker nonlinearity $\\chi t = 0.004$). (c) Wigner negativity volume versus loss after the Kerr interaction: orange curve for case (a), blue curve for case (b).","label":"fig:Wigner_SV_Kerr","source":"arxiv","key":"69d716a9777b785664f33ba191e735f8","url":"https://inspirehep.net/files/69d716a9777b785664f33ba191e735f8"}],"inspire_categories":[{"term":"Quantum Physics","source":"arxiv"}],"first_author":{"full_name":"Rasputnyi, Andrei","last_name":"Rasputnyi","first_name":"Andrei","recid":2771244},"control_number":3094595,"dois":[{"source":"Optica Publishing Group","value":"10.1364/OPTICA.599324"}],"document_type":["article"],"texkeys":["Rasputnyi:2025xjh"],"abstracts":[{"source":"Optica Publishing Group","value":"Characterizing macroscopic quantum states of light is a frontier challenge at the interface of quantum optics and high-intensity photonics. Here, we demonstrate the first, to our knowledge, direct phase-space tomography of a bright, ultrafast quantum state. We adapt a single-shot f-2f interferometer to sample the Husimi Q-function of a 25 fs bright squeezed vacuum (BSV) pulse (mean photon number N∼1012) subject to Kerr nonlinearity. Our measurement reveals a clear transformation from a Gaussian distribution with pronounced quadrature antisqueezing to a characteristic \"S\"-shaped profile as the intensity-dependent nonlinear phase increases. Crucially, we show theoretically that despite optical loss, the state does not degrade into classically modulated light but is rigorously described as a statistical mixture of squeezed coherent states. While global Wigner negativity is masked by technical noise, our results show theoretically that the constituent states individually retain strong Wigner-negative features. This work bridges quantum optics and high-intensity photonics, establishing a platform for diagnosing bright quantum resources.","abstract_source_suggest":{"input":"Optica Publishing Group"}},{"source":"arXiv","value":"Non-Gaussian states of light are a critical resource for fault-tolerant quantum computing and enhanced metrology, but are typically faint and often obtained via post-selection. Here, we demonstrate the deterministic generation of a bright non-Gaussian state by introducing a Kerr nonlinearity to a macroscopic state of light called bright squeezed vacuum (BSV). To characterize the resulting state, we use a single-shot f-2f interferometer to sample its Husimi function. We observe a clear transformation from a 2D Gaussian distribution to an 'S'-shaped non-Gaussian profile, which is the direct statistical evidence of the intensity-dependent nonlinear phase. The negativity of the Wigner function, which is an intrinsic property of any pure non-Gaussian state, cannot be observed because BSV is a mixed state even under minute optical loss. However, we show that BSV can be considered as a mixture of pure squeezed coherent states, for some of which Kerr-induced Wigner-function negativity is quite tolerant to loss. This work bridges the gap between quantum optics and ultrafast nonlinear optics, opening a path to quantum applications that require high photon flux.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"Optica Publishing Group","title":"Kerr-induced non-Gaussianity of a bright ultrafast quantum state"},{"source":"arXiv","title":"Kerr-induced non-Gaussianity of ultrafast bright squeezed vacuum"}],"imprints":[{"date":"2026-07-01"}],"curated":false},"id":"3094595"},{"links":{"bibtex":"https://inspirehep.net/api/literature/2953087?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/2953087?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/2953087?format=latex-us","json":"https://inspirehep.net/api/literature/2953087?format=json","json-expanded":"https://inspirehep.net/api/literature/2953087?format=json-expanded","cv":"https://inspirehep.net/api/literature/2953087?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A2953087"},"created":"2025-07-23T04:26:16.301254+00:00","updated":"2026-10-13T13:10:26.645062+00:00","metadata":{"citation_count":0,"citation_count_without_self_citations":0,"authors":[{"raw_affiliations":[{"value":"Department of Physics, KAIST, Daejeon 34141, Republic of Korea"}],"full_name_unicode_normalized":"kim, sangwon","full_name":"Kim, Sangwon","record":{"$ref":"https://inspirehep.net/api/authors/2135406"},"last_name":"Kim","ids":[{"schema":"INSPIRE BAI","value":"S.S.Kim.2"}],"first_name":"Sangwon","uuid":"04fd4903-8832-4c3b-ba44-14bb0b1ddb02","recid":2135406},{"raw_affiliations":[{"value":"Department of Physics, KAIST, Daejeon 34141, Republic of Korea"},{"value":"Research Center for Natural Sciences, KAIST, Daejeon 34141, Republic of Korea"}],"full_name_unicode_normalized":"ahn, seongjin","full_name":"Ahn, Seongjin","record":{"$ref":"https://inspirehep.net/api/authors/1057536"},"last_name":"Ahn","ids":[{"schema":"INSPIRE BAI","value":"S.H.Ahn.1"}],"first_name":"Seongjin","uuid":"2bff9301-f453-490c-ab5f-4d55d2fab585","recid":1057536},{"raw_affiliations":[{"value":"femtoQ Lab, Department of Engineering Physics, Polytechnique Montréal, Montréal, QC, H3T 1J4, Canada"}],"full_name_unicode_normalized":"seletskiy, denis v.","full_name":"Seletskiy, Denis V.","record":{"$ref":"https://inspirehep.net/api/authors/1998800"},"last_name":"Seletskiy","ids":[{"schema":"INSPIRE BAI","value":"D.V.Seletskiy.1"}],"first_name":"Denis V.","uuid":"58c01cef-2f7e-462a-831a-86aaa0702be9","recid":1998800},{"raw_affiliations":[{"value":"Department of Physics, KAIST, Daejeon 34141, Republic of Korea"}],"full_name_unicode_normalized":"moskalenko, andrey s.","full_name":"Moskalenko, Andrey S.","record":{"$ref":"https://inspirehep.net/api/authors/1912857"},"last_name":"Moskalenko","ids":[{"schema":"INSPIRE BAI","value":"S.A.Moskalenko.1"}],"first_name":"Andrey S.","uuid":"37cb3bec-b5ef-4953-b244-0ac0dfd996f1","recid":1912857}],"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","references":[{"reference":{"label":"1","publication_info":{"journal_volume":"4","artid":"595","year":1987,"page_start":"595","journal_title":"J.Opt.Soc.Am.B"},"misc":["Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases"],"authors":[{"full_name":"McPherson, A."},{"full_name":"Gibson, G."},{"full_name":"Jara, H."},{"full_name":"Johann, U."},{"full_name":"Luk, T.S."},{"full_name":"McIntyre, I.A."},{"full_name":"Boyer, K."},{"full_name":"Rhodes, C.K."}]},"raw_refs":[{"schema":"text","source":"arXiv","value":"[1] A. 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A squeezed vacuum state of light drives electronic transport in a metal tip–surface system. The blue curve depicts the complex trajectory of the tunneling electron, starting with an imaginary time under the barrier and going over to a usual classical trajectory in real time as the electron exits into the classically allowed region. (b) Dynamics of the $P$ quadrature (proportional to the electric field) following from Eq.~(\\ref{Eq:P_dynamics}) for several values of the squeezing parameter $r$ and an initial realization of the $X$ quadrature, $X(t_i) = -2.32$. (c) Phase-space portrait of the field dynamics for $r=1$. This plot shares the vertical axis with (b) and the horizontal axis with (d). As time evolves, the state trajectory follows a clockwise path, exemplified by the selected realization, where it sequentially passes through the points marked by the circle, triangle, square, and cross. The markers correspond to those in (b) and (d), in the same order. (d) Distribution $\\rho(X, t)$ (pseudocolor plot) and Bohmian trajectories $X(t)$ (lines) for the same parameters.","source":"arxiv","label":"fig1","key":"91315d53ebcdc634220ca6c916715e6f","url":"https://inspirehep.net/files/91315d53ebcdc634220ca6c916715e6f"},{"filename":"fig3_final.png","material":"preprint","caption":"Trajectories of the released electrons in the classically allowed region for several values of the squeezing factor $r$ and the optimal initial realization $X(t_i) = X_\\mathrm{peak}$ (visualized in Fig.~\\ref{fig2}). Full red line shows the trajectory for $r=12$ and $X(t_i) = X_\\mathrm{peak}$, whereas the set of trajectories corresponds to less optimal realizations $X(t_i)=X_l$ defined by $\\rho(X_l) \\mathcal{P}(X_l) = (1-l/20) \\rho(X_{\\mathrm{peak}}) \\mathcal{P}(X_{\\mathrm{peak}})$ for $l = 1,2, \\cdots, 19$. As $l$ increases (reflected in the color fading of the lines), the deviations from the trajectory with $X(t_i) = X_\\mathrm{peak}$ grow. Red dotted line indicates $t=\\tau_0$ for all of the trajectories.","source":"arxiv","label":"fig4","key":"575b84a6aea24936b9beaacf70387bf1","url":"https://inspirehep.net/files/575b84a6aea24936b9beaacf70387bf1"},{"filename":"fig2a_final.png","material":"preprint","caption":"Probability distribution $\\rho \\left(X_i\\right)$ of initial realizations for the $X$ quadrature, tunneling probability $\\mathcal{P} \\left(X_i\\right)$ and $\\rho \\left(X_i\\right) \\mathcal{P} \\left(X_i\\right)$ for several values of the squeezing factor. $\\sigma$ denotes the standard deviation of $\\rho(X_i)$, points $X_i=X_\\mathrm{peak}$ where $\\rho \\left(X_i\\right) \\mathcal{P} \\left(X_i\\right)$ is maximized are indicated by purple crosses and the area corresponding to the integral in Eq.~(\\ref{Eq:P_tot}) is colored in blue.","source":"arxiv","label":"fig2","key":"5ab6c4f4cc94ffd17cd9b3c363c9ff0f","url":"https://inspirehep.net/files/5ab6c4f4cc94ffd17cd9b3c363c9ff0f"},{"filename":"fig2b_test.png","material":"preprint","caption":"Dependence of the total tunneling probability of the electron $\\mathcal{P}_\\mathrm{tot}$ evaluated based on Eq.~(\\ref{Eq:P_tot}) on the effective Keldysh parameter $\\gamma_{\\mathrm{peak}}$ introduced in Eq.~(\\ref{Eq:gamma}). From left to right, the corresponding squeezing factor increases from $r = 11$ to $r = 25$. The inset illustrates the dependences of $X_{\\mathrm{peak}}$ and $E_{\\mathrm{peak}}$ on $r$, where purple markers are shared with Fig.~\\ref{fig2}.","source":"arxiv","label":"fig3","key":"4e6b5b041ad5120269df132f0c241327","url":"https://inspirehep.net/files/4e6b5b041ad5120269df132f0c241327"}],"preprint_date":"2025-07-21","author_count":4,"first_author":{"full_name":"Kim, Sangwon","last_name":"Kim","first_name":"Sangwon","recid":2135406},"public_notes":[{"source":"arXiv","value":"7 pages, 4 figures"}],"control_number":2953087,"earliest_date":"2025-07-21","document_type":["article"],"texkeys":["Kim:2025phy"],"abstracts":[{"source":"arXiv","value":"Recent realization of an intense quantum light, namely bright squeezed vacuum, opened a new perspective on quantum light-matter interaction. Several theoretical works have appeared based on coherent state expansions of quantum state of light to investigate non-classical driving of high-harmonic generation in atomic gases and solids, or free-electron dynamics, but their predictions surprisingly coincide with what one could expect from essentially classical interpretations of the light statistics. A deeper theoretical insight into the underlying physics is necessary for understanding of observed experimental findings and predicting emerging effects relying on this new configuration. Here we present a theoretical framework to describe tunneling driven by quantum light, where the properties of such light are captured by a statistical ensemble of classical fields via a hydrodynamic, also referred to as Bohmian, formulation. Generalizing the quasiclassical theory of non-adiabatic tunneling driven by classical light, a single tunneling event is described by a bundle of tunneling solutions, each driven by a classical field corresponding to one realization in the ensemble. Quantum statistics of light are thus imprinted on the measured current. Fully quantum description of light via the Bohmian trajectories of its field provides a perfect fit to the description of the electron (under-) above-barrier dynamics in terms of (complex quasiclassical) real classical trajectories, resulting in a consistent and elegant theoretical approach. To illustrate this, we consider BSV-induced electron transport from the tip to the surface in the tunneling microscope configuration demonstrating the transition from the multiphoton to the direct tunneling regime.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["quant-ph"],"titles":[{"source":"arXiv","title":"Tunneling driven by quantum light described via field Bohmian trajectories"}],"facet_author_name":["2135406_Sung-Soo Kim","1912857_S.A. Moskalenko","1998800_Denis V. Seletskiy","1057536_S.H. Ahn"],"license":[{"license":"arXiv nonexclusive-distrib 1.0","material":"preprint","url":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/"}],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:2953087","updated":"2026-10-13T13:10:26.645062"},"curated":false,"arxiv_eprints":[{"categories":["quant-ph","physics.optics"],"value":"2507.15972"}]},"id":"2953087"}],"total":20},"links":{"self":"https://inspirehep.net/api/literature/?q=a%20D.V.Seletskiy.1&size=10&page=1","next":"https://inspirehep.net/api/literature/?q=a%20D.V.Seletskiy.1&size=10&page=2","bibtex":"https://inspirehep.net/api/literature/?q=a%20D.V.Seletskiy.1&size=10&page=1&format=bibtex","latex-eu":"https://inspirehep.net/api/literature/?q=a%20D.V.Seletskiy.1&size=10&page=1&format=latex-eu","latex-us":"https://inspirehep.net/api/literature/?q=a%20D.V.Seletskiy.1&size=10&page=1&format=latex-us","json":"https://inspirehep.net/api/literature/?q=a%20D.V.Seletskiy.1&size=10&page=1&format=json","json-expanded":"https://inspirehep.net/api/literature/?q=a%20D.V.Seletskiy.1&size=10&page=1&format=json-expanded","cv":"https://inspirehep.net/api/literature/?q=a%20D.V.Seletskiy.1&size=10&page=1&format=cv"}}