How to exploit driving and dissipation to stabilize and manipulate quantum many-body states

May combine two claims.

These effectively attractive interactions keep the condensate localized in space with a soliton-like shape and reduce the condensation threshold with respect to condensation into the expanding positive-mass states at the bottom of the band.

“These keep the condensate localized in space with a soliton-like shape [112,113] and, in this way, reduce the condensation threshold with respect to condensation into the expanding positive-mass states at the bottom of the band.”

• cites [112] [112] Tanese, D.; Flayac, H.; Solnyshkov, D. D.; Amo, Alberto; Lemaître, Aristide; Galopin, Elisabeth; Braive, R.; Senellart, Pascale; Sagnes, Isabelle; Malpuech, Guillaume et al. Polariton condensation in solitonic gap states in a one-dimensional periodic potential, Nat. Commun., Volume 4 (2013) no. 1, 1749 sourcePartly supported

  The Results section (‘Condensation in bound GS states under cw excitation’; page unavailable) reports a localized gap state with a soliton-like profile and says it condenses instead of lower-energy band states because its overlap with the reservoir makes it kinetically favored. It does not report a comparative condensation threshold for expanding positive-mass states, so the claimed threshold reduction is not established by this paper. (LLM, conf=0.85)

  Experimental — accuracy not yet measured
• cites [113] [113] Baboux, Florent; De Bernardis, Daniele; Goblot, Valentin; Gladilin, V. N.; Gomez, Carmen; Galopin, Elisabeth; Le Gratiet, Luc; Lemaître, Aristide; Sagnes, Isabelle; Carusotto, Iacopo; Wouters, Michiel; Amo, Alberto; Bloch, Jacqueline Unstable and stable regimes of polariton condensation, Optica, Volume 5 (2018) no. 10, pp. 1163-1170 sourceDisputed

  The Theoretical Framework (p. 2) says negative-mass states can form stable condensates of arbitrarily large size, and the Conclusion (p. 7) describes them as extended—not soliton-like localized. The paper attributes dynamical instability, rather than stable localization, to effective attractive interactions in positive-mass condensates. It does not report the claimed threshold reduction. (LLM, conf=0.78)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Early works assessed thermality in terms of the momentum distribution approaching or not a Bose-Einstein distribution at a well-defined temperature and chemical potential, while recent works have highlighted the need to establish thermalization in terms of rigorous fluctuation-dissipation relations and frequency-dependent observables.

“While early works have assessed thermality in terms of the momentum distribution approaching or not a Bose-Einstein distribution at a well defined temperaturefoot_3 and chemical potential [119,120], recent works have highlighted the need to establish thermalization in terms of rigorous fluctuation-dissipation relations and frequency-dependent observables [121].”

• cites [119] [119] Bajoni, Daniele; Senellart, Pascale; Lemaître, Aristide; Bloch, Jacqueline Photon lasing in GaAs microcavity: similarities with a polariton condensate, Phys. Rev. B, Volume 76 (2007), 201305 sourcePartly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured
• cites [120] [120] Sun, Yongbao; Wen, Patrick; Yoon, Yoseob; Liu, Gangqiang; Steger, Mark; Pfeiffer, Loren N.; West, Ken; Snoke, David W.; Nelson, Keith A. Bose–Einstein condensation of long-lifetime polaritons in thermal equilibrium, Phys. Rev. Lett., Volume 118 (2017) no. 1, 016602 sourceDisputed

  Split into 2 atoms — 1 confirmed, 0 partially supported, 1 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured
• cites [121] [121] Chiocchetta, Alessio; Gambassi, Andrea; Carusotto, Iacopo Laser operation and Bose–Einstein condensation: analogies and differences, Universal themes of Bose–Einstein condensation, Cambridge University Press, 2017, pp. 409-423 sourceSupported

May combine two claims.

Incoherent pumping overcomes losses and a coherent fluid of light is spontaneously generated in the cavity via a nonequilibrium condensation mechanism analogous to lasing.

“a most interesting physics occurs when incoherent pumping overcomes losses and a coherent fluid of light is spontaneously generated in the cavity via a nonequilibrium condensation mechanism analogous to lasing [8]”

• cites [8] [8] Bloch, Jacqueline; Carusotto, Iacopo; Wouters, Michiel Non-equilibrium Bose–Einstein condensation in photonic systems, Nat. Rev. Phys., Volume 4 (2022) no. 7, pp. 470-488 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Different configurations to obtain frequency-dependent pumping were proposed using parametric emission processes.

“different configurations to obtain a frequency-dependent pumping were proposed in [63] using parametric emission processes.”

• cites [63] [63] Kapit, Eliot; Hafezi, Mohammad; Simon, Steven H. Induced self-stabilization in fractional quantum Hall states of light, Phys. Rev. X, Volume 4 (2014), 031039 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Atomic gases enjoy extraordinary cleanness and control at the microscopic level, permitting quantitative comparison with ab initio theoretical calculations.

“atomic gases enjoy an extraordinary level of cleanness and control at the microscopic level, which permits a quantitative comparison with ab initio theoretical calculations.”

• cites [1] [1] Pitaevskiĭ, Lev P.; Stringari, Sandro Bose–Einstein condensation and superfluidity, International Series of Monographs on Physics, 164, Oxford University Press, 2016, 512 pages sourceNot checked — no full text of the source
• cites [2] [2] Gross, Christian; Bloch, Immanuel Quantum simulations with ultracold atoms in optical lattices, Science, Volume 357 (2017) no. 6355, pp. 995-1001 sourceNot checked — no full text of the source
• cites [3] [3] Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm Many-body physics with ultracold gases, Rev. Mod. Phys., Volume 80 (2008) no. 3, pp. 885-964 sourceSupported
• cites [4] [4] Cooper, N. R.; Dalibard, Jean; Spielman, I. B. Topological bands for ultracold atoms, Rev. Mod. Phys., Volume 91 (2019) no. 1, 015005 sourcePartly supported

  The Introduction describes cold atomic gases as controlled experimental settings, and the Outlook says disorder can be negligible in their optical lattices. These passages support the claim about control and cleanness, but our copy does not establish the further claim that this permits quantitative comparison with ab initio calculations. (LLM, conf=0.82)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

Such a parametric strategy was experimentally put into practice to generate a Mott insulator state of impenetrable photons.

“Such a strategy was experimentally put into practice in [64] to generate a Mott insulator state of impenetrable photons.”

• cites [64] [64] Ma, Ruichao; Saxberg, Brendan; Owens, Clai; Leung, Nelson; Lu, Yao; Simon, Jonathan; Schuster, David I. A dissipatively stabilized Mott insulator of photons, Nature, Volume 566 (2019) no. 7742, pp. 51-57 sourcePartly supported

  Section III (pp. 6–7) reports experimental stabilization of a photonic Mott insulator with strongly suppressed on-site number fluctuations. But the paper describes the preparation strategy as coherent driving combined with engineered dissipation, not as a parametric strategy; it also does not establish that the photons are strictly impenetrable. (LLM, conf=0.83)

  Experimental — accuracy not yet measured

May combine two claims.

The overall magnitude of these driven-dissipative fluctuations roughly corresponds to a temperature of the order of the interaction energy g_nl |ψ|^2, and they display interesting correlation properties.

“The overall magnitude of these fluctuations roughly corresponds to a temperature of the order of the interaction energy g nl |ψ| 2 and also display interesting correlation properties [93].”

• cites [93] [93] Busch, Xavier; Carusotto, Iacopo; Parentani, Renaud Spectrum and entanglement of phonons in quantum fluids of light, Phys. Rev. A, Volume 89 (2014) no. 4, 043819 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

In nonlinear dynamics, very similar equations are called complex Ginzburg-Landau equations.

“The very similar equations that are considered in the context of nonlinear dynamics typically go under the name of complex Ginzburg-Landau equations [76,77].”

• cites [76] [76] Cross, Mark C.; Hohenberg, Pierre C. Pattern formation outside of equilibrium, Rev. Mod. Phys., Volume 65 (1993) no. 3, pp. 851-1112 sourceNot checked — no full text of the source
• cites [77] [77] Aranson, Igor S.; Kramer, Lorenz The world of the complex Ginzburg–Landau equation, Rev. Mod. Phys., Volume 74 (2002) no. 1, pp. 99-143 sourceSupported

May combine two claims.

A spatially resolved experimental characterization of the Bogoliubov modes on the two sides of the horizon has shown the transition from sub- to super-sonic flow as the horizon is crossed, with supersonic flow signalled by the positive-norm branch of the Bogoliubov dispersion being pushed down to negative frequencies.

“A spatiallyresolved experimental characterization of the Bogoliubov modes on the two sides of the horizon has been performed in [98], explicitly showing the transition from a sub-to a super-sonic flow as the horizon is crossed: in the experiment, a super-sonic flow is signalled by the positive-norm branch of the Bogoliubov dispersion being pushed down to negative frequencies.”

• cites [98] [98] Falque, Kévin; Delhom, Adrià; Glorieux, Quentin; Giacobino, Élisabeth; Bramati, Alberto; Jacquet, Maxime J. Polariton fluids as quantum field theory simulators on tailored curved spacetimes, Phys. Rev. Lett., Volume 135 (2025), 023401, 7 pages sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

While subtracting commutators is trivial for single-time operator products, it poses serious challenges for multi-time quantities.

“While this is a quite trivial step for single-time operator products, it poses serious challenges for calculation multi-time quantities [83].”

• cites [83] [83] Berg, B.; Plimak, L. I.; Polkovnikov, Anatoli; Olsen, M. K.; Fleischhauer, Michael; Schleich, W. P. Commuting Heisenberg operators as the quantum response problem: time-normal averages in the truncated Wigner representation, Phys. Rev. A, Volume 80 (2009), 033624 sourceSupported

May combine two claims.

In incoherent pumping configurations, a higher noise level is found, with additional fluctuations from spontaneous events in the pumping process, given by ⟨ξ*ξ⟩ = 1/2 (γ_loss + γ_pump(1+|ψ|^2/n_S)) δ^(2)(r-r') δ(t-t').

“Of course, a higher noise level is found in incoherent pumping configurations [80] where additional fluctuations are given by spontaneous events in the pumping process, ξ * (r ∥ , t ) ξ(r ′ ∥ , t ′ ) = 1 2 γ loss + γ pump 1 + |ψ| 2 /n S δ (2) (r ∥ -r ′ ∥ ) δ(t -t ′ ).”

• cites [80] [80] Wouters, Michiel; Savona, Vincenzo Stochastic classical field model for polariton condensates, Phys. Rev. B, Volume 79 (2009) no. 16, 165302 sourcePartly supported

  Equation (33), in the passage labeled (28), includes both inscattering and loss in the stochastic noise correlation; the passage labeled (35) also discusses spontaneous inscattering. But the paper gives the noise in terms of scattering kernels and does not give the quoted local formula with γ_pump(1+|ψ|²/n_S), nor establish the stated comparison with coherent pumping. (LLM, conf=0.85)

  Experimental — accuracy not yet measured

May combine two claims.

Extra fluctuations induced by the driven-dissipative nature lead to stimulation of the Hawking processes and reinforcement of the overall magnitude of the correlation signal.

“Note that the extra fluctuations induced by the driven-dissipative nature [93] lead to a stimulation of the Hawking processes and, then, a reinforcement of the overall magnitude of the correlation signal.”

• cites [93] [93] Busch, Xavier; Carusotto, Iacopo; Parentani, Renaud Spectrum and entanglement of phonons in quantum fluids of light, Phys. Rev. A, Volume 89 (2014) no. 4, 043819 sourcePartly supported

  “Quantum fluctuations in the steady state” (p. 5) says environmental fluctuations heat the phonon state, and “Weak dissipation” (p. 8) reports correlations associated with dissipation. But the paper does not establish that these fluctuations stimulate Hawking processes or increase the magnitude of a Hawking correlation signal; the Conclusions (p. 12) present Hawking emission as a subject for future study. (LLM, conf=0.85)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

In topological photonic systems, new phenomena stemming from non-trivial band topology have been observed, such as unidirectionally propagating chiral edge states.

“a strong interest is being devoted to the so-called topological photonic systems where new phenomena stemming from the non-trivial band topology of the photonic states have been observed, e.g.unidirectionally propagating chiral edge states [103].”

• cites [103] [103] Ozawa, Tomoki; Price, Hannah M.; Amo, Alberto; Goldman, Nathan; Hafezi, Mohammad; Lu, Ling; Rechtsman, Mikael C.; Schuster, David I.; Simon, Jonathan; Zilberberg, Oded; Carusotto, Iacopo Topological photonics, Rev. Mod. Phys., Volume 91 (2019) no. 1, 015006 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Alternatively, the downstream region can be left unpumped so that the photon fluid ballistically expands into this region; this configuration was experimentally realized.

“Alternatively, the downstream region can be left unpumped so that the photon fluid is able to ballistically expand into this region.This latter configuration was experimentally realized in [97].”

• cites [97] [97] Nguyen, Hai Son; Gerace, Dario; Carusotto, Iacopo; Sanvitto, Daniele; Galopin, Elisabeth; Lemaître, Aristide; Sagnes, Isabelle; Bloch, Jacqueline; Amo, Alberto Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons, Phys. Rev. Lett., Volume 114 (2015) no. 3, 036402 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Further sources of quantum noise may stem from interaction of the Bogoliubov modes of the photon fluid with phonon modes in the solid-state crystal hosting the fluid of light.

“Further sources of quantum noise may stem from the interaction of the Bogoliubov modes of the photon fluid with phonon modes in the solid-state crystal hosting the fluid of light [81].”

• cites [81] [81] Frérot, Irénée; Vashisht, Amit; Morassi, Martina; Lemaître, Aristide; Ravets, Sylvain; Bloch, Jacqueline; Minguzzi, Anna; Richard, Maxime Bogoliubov excitations driven by thermal lattice phonons in a quantum fluid of light, Phys. Rev. X, Volume 13 (2023) no. 4, 041058 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

A sonic horizon separating an upstream sub-sonic flow (c_u > v_u) from a downstream supersonic flow (v_d > c_d) displays strong analogies with light propagation near a black hole, and upon quantization, sonic analogs of Hawking radiation have been anticipated to be emitted by the acoustic horizon.

“From the point of view of sound propagation, this configuration displays strong analogies with light propagation in the neighborhood of a black hole in gravitational physics and, upon quantization, sonic analogs of Hawking radiation have been anticipated to be emitted by the acoustic horizon [95].”

• cites [95] [95] Barcelo, Carlos; Liberati, Stefano; Visser, Matt Analogue gravity, Living Rev. Relativ., Volume 14 (2011), pp. 1-159 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Detailed experimental studies of the Bogoliubov dispersion in different pumping regimes have been carried out by pump-probe spectroscopy.

“Detailed experimental studies of the Bogoliubov dispersion in the different pumping regimes have been carried out by pump-probe spectroscopy in [92].”

• cites [92] [92] Claude, Ferdinand; Jacquet, Maxime J.; Usciati, Romain; Carusotto, Iacopo; Giacobino, Élisabeth; Bramati, Alberto; Glorieux, Quentin High-resolution coherent probe spectroscopy of a polariton quantum fluid, Phys. Rev. Lett., Volume 129 (2022) no. 10, 103601 sourceSupported

May combine two claims.

While particle-number conservation makes it difficult to verify this prediction in atomic condensates at equilibrium, the phase of an optical condensate can be pinned by an additional incident coherent laser, and a clear gap in the Goldstone mode dispersion is observed in experiments.

“While particle-number conservation makes it difficult to verify this prediction in atomic condensates at equilibrium [124], the phase of an optical condensate can be pinned by an additional incident coherent laser [125] and a clear gap in the Goldstone mode dispersion is clearly observed in experiments [106].”

• cites [124] [124] Gunton, J. D.; Buckingham, M. J. Condensation of the ideal Bose gas as a cooperative transition, Phys. Rev., Volume 166 (1968), pp. 152-158 sourceNot checked — no full text of the source
• cites [125] [125] Wouters, Michiel; Carusotto, Iacopo Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime, Phys. Rev. A, Volume 76 (2007), 043807 sourceNot checked — no full text of the source
• cites [106] [106] Claude, Ferdinand; Jacquet, Maxime J.; Glorieux, Quentin; Wouters, Michiel; Giacobino, Élisabeth; Carusotto, Iacopo; Bramati, Alberto Observation of the diffusive Nambu–Goldstone mode of a non-equilibrium phase transition, Nat. Phys., Volume 21 (2025), pp. 924-930 sourcePartly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

May combine two claims.

Restricting the incoherent pump to a limited region of space allows control of the condensate shape via the volcano effect: condensation mostly occurs at the center of the pump spot, and coherent particles are expelled by repulsive interactions to form a macroscopic outward-expanding radial flow.

“restricting the incoherent pump to a limited region of space allows to control the shape of the condensate via the so-called volcano effect: condensation mostly occurs at the center of the pump spot, and then the coherent particles get expelled by the repulsive interactions and form a macroscopic outward-expanding radial flow.”

• cites [108] [108] Richard, Maxime; Kasprzak, J.; Romestain, R.; Andre, R.; Dang, L. S. Spontaneous coherent phase transition of polaritons in CdTe microcavities, Phys. Rev. Lett., Volume 94 (2005) no. 18, 187401 sourceNot checked — no full text of the source
• cites [109] [109] Wouters, Michiel; Carusotto, Iacopo; Ciuti, Cristiano Spatial and spectral shape of inhomogeneous nonequilibrium exciton-polariton condensates, Phys. Rev. B, Volume 77 (2008), 115340 sourceSupported
• cites [110] [110] Wertz, E.; Ferrier, L.; Solnyshkov, D. D.; Johne, R.; Sanvitto, Daniele; Lemaître, Aristide; Sagnes, Isabelle; Grousson, R.; Kavokin, Alexey V.; Senellart, Pascale; Malpuech, Guillaume; Bloch, Jacqueline Spontaneous formation and optical manipulation of extended polariton condensates, Nat. Phys., Volume 6 (2010) no. 11, pp. 860-864 sourcePartly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

Classified as probably not a substantial claim.

A naive application of the Landau criterion would predict that an impurity moving across the fluid experiences significant friction for any flow speed v, with no specific feature at the equilibrium speed of sound c_s = sqrt(g_nl |ψ|^2 / m).

“A naive application of the Landau criterion for superfluidity [1,105] would then predict that an impurity moving across a fluid will experience a significant friction force for any value of the flow speed v, with no specific feature at the (equilibrium) speed of sound c s = g nl |ψ| 2 /m.”

• cites [1] [1] Pitaevskiĭ, Lev P.; Stringari, Sandro Bose–Einstein condensation and superfluidity, International Series of Monographs on Physics, 164, Oxford University Press, 2016, 512 pages sourceNot checked — no full text of the source
• cites [105] [105] Carusotto, Iacopo; Rousseaux, Germain The Cerenkov effect revisited: from swimming ducks to zero modes in gravitational analogues, Analogue gravity phenomenology: analogue spacetimes and horizons, from theory to experiment (Lecture Notes in Physics), Springer, 2013 no. 870, pp. 109-144 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Further theoretical work has extended the idea to a two-dimensional lattice geometry where impenetrable photons are also subject to a synthetic magnetic field.

“Further theoretical work [150] has extended this idea to a two-dimensional lattice geometry where impenetrable photons are also subject to a synthetic magnetic field.”

• cites [150] [150] Umucalılar, Rifat Onur; Carusotto, Iacopo Fractional quantum Hall states of photons in an array of dissipative coupled cavities, Phys. Rev. Lett., Volume 108 (2012), 206809 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

A closely related experiment has been explored: strong interactions between photons are obtained by coupling light to optically dressed atoms in a Rydberg-EIT configuration, and a synthetic magnetic field in a cylindrically symmetric geometry is obtained by using a twisted optical ring-cavity.

“A closely related idea has been experimentally explored in a recent experiment [152]: strong interactions between photons are obtained by coupling light to optically dressed atoms in a Rydberg-EIT configuration [31,153]; a synthetic magnetic field in a cylindrically symmetric geometry is obtained by using a twisted optical ring-cavity [154].”

• cites [152] [152] Clark, Logan W.; Schine, Nathan; Baum, Claire; Jia, Ningyuan; Simon, Jonathan Observation of Laughlin states made of light, Nature, Volume 582 (2020) no. 7810, pp. 41-45 sourceSupported
• cites [31] [31] Peyronel, Thibault; Firstenberg, Ofer; Liang, Qi-Yu; Hofferberth, Sebastian; Gorshkov, Alexey V.; Pohl, Thomas; Lukin, Mikhail D.; Vuletić, Vladan Quantum nonlinear optics with single photons enabled by strongly interacting atoms, Nature, Volume 488 (2012) no. 7409, pp. 57-60 sourceNot checked — no full text of the source
• cites [153] [153] Gorshkov, Alexey V.; Otterbach, Johannes; Fleischhauer, Michael; Pohl, Thomas; Lukin, Mikhail D. Photon-photon interactions via Rydberg blockade, Phys. Rev. Lett., Volume 107 (2011), 133602 sourceSupported
• cites [154] [154] Schine, Nathan; Ryou, Albert; Gromov, Andrey; Sommer, Ariel; Simon, Jonathan Synthetic Landau levels for photons, Nature, Volume 534 (2016) no. 7609, pp. 671-675 sourceSupported

May combine two claims.

In the Tonks-Girardeau case, the different excited states are labeled by the quasimomenta of the fermionized particles and their energy can be analytically calculated.

“In the specific Tonks-Girardeau case, the different excited states are labeled by the quasimomenta of the (fermionized) particles and their energy can be analytically calculated [147].”

• cites [147] [147] Castin, Yvan Simple theoretical tools for low dimension Bose gases, J. Phy. IV France, Volume 116 (2004), pp. 89-132 sourceSupported

May combine two claims.

In the numerical spectra of the steady-state total population for a driven cavity chain, at low incident intensity the spectrum has a single main peak corresponding to the 1-photon transition to the k=0 orbital, and at growing intensities additional peaks appear at frequencies corresponding to higher N=2,3,... photon transitions.

“at low intensity (blue line), the spectrum is characterized by a single main peak corresponding to the 1-photon transition to the k = 0 orbital.At growing intensities, additional peaks at frequencies corresponding to the higher N = 2, 3, . . .photon transitions appear.”

• cites [145] [145] Carusotto, Iacopo; Gerace, Dario; Tureci, H. E.; De Liberato, Simone; Ciuti, Cristiano; Imamoğlu, A. Fermionized photons in an array of driven dissipative nonlinear cavities, Phys. Rev. Lett., Volume 103 (2009), 033601 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

The idea of using coherent drive to realize a Tonks-Girardeau gas of impenetrable photons in a one-dimensional chain of coupled cavities was theoretically explored.

“As a first example, this idea was theoretically explored in view of realizing a Tonks-Girardeau gas of impenetrable photons in a one-dimensional chain of coupled cavities [145].”

• cites [145] [145] Carusotto, Iacopo; Gerace, Dario; Tureci, H. E.; De Liberato, Simone; Ciuti, Cristiano; Imamoğlu, A. Fermionized photons in an array of driven dissipative nonlinear cavities, Phys. Rev. Lett., Volume 103 (2009), 033601 sourceSupported

May combine two claims.

Combining these elements, a two-photon Laughlin state is selectively created using a coherent laser pump with finite angular momentum and its microscopic structure is probed by looking at correlation functions of the emitted light at different spatial positions and in different orbital angular momentum channels.

“Combining these elements, a two-photon Laughlin state is selectively created using a coherent laser pump with finite angular momentum and its microscopic structure is probed by looking at the correlation functions of the emitted light at different spatial positions and in different orbital angular momentum channels.”

• cites [152] [152] Clark, Logan W.; Schine, Nathan; Baum, Claire; Jia, Ningyuan; Simon, Jonathan Observation of Laughlin states made of light, Nature, Volume 582 (2020) no. 7810, pp. 41-45 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The radiative loss feature has been exploited in experimental studies of correlation properties across the phase transition and in the recent observation of KPZ universal behaviours in a one-dimensional configuration.

“This feature has been exploited in experimental studies of the correlation properties across the phase transition and, in particular, for the recent observation of KPZ universal behaviours in a one-dimensional configuration [133].”

• cites [133] [133] Fontaine, Quentin; Squizzato, Davide; Baboux, Florent; Amelio, Ivan; Lemaître, Aristide; Morassi, Martina; Sagnes, Isabelle; Le Gratiet, Luc; Harouri, Abdelmounaim; Wouters, Michiel; Carusotto, Iacopo; Amo, Alberto; Richard, Maxime; Minguzzi, Anna; Canet, Léonie; Ravets, Sylvain; Bloch, Jacqueline Kardar–Parisi–Zhang universality in a one-dimensional polariton condensate, Nature, Volume 608 (2022) no. 7924, pp. 687-691 sourcePartly supported

  The Method section describes measuring coherence from light emitted by a one-dimensional polariton condensate, and the paper reports experimental KPZ scaling in that coherence. Its below- and above-threshold measurements concern emission spectra; the passages do not establish a study of correlation properties across the phase transition. (LLM, conf=0.83)

  Experimental — accuracy not yet measured

May combine two claims.

For pump frequency above the bare resonance (ω_inc > ω_0) and g_nl > 0, bistability effects are apparent, with two values of density |ψ|^2 available for the same pump intensity, and the intermediate branch is dynamically unstable.

“in the latter case, bistability effects are apparent, with two values of the density |ψ| 2 being available for the same value of the pump intensity |E inc | 2 (the intermediate branch is dynamically unstable).”

• AssumptionThe authors state this as an assumption: The nonlinear interaction parameter g_nl is positive.

May combine two claims.

Away from the sonic operating point, the Bogoliubov dispersion may display finite gaps (D, E) and even precursors (A) or fully fledged (B, C') dynamical instabilities.

“Away from this point, the dispersion may display finite gaps (D, E) and, even, precursors (A) or fully fledged (B, C') dynamical instabilities.”

May combine two claims.

Specific calculations have predicted that in one dimension the long-range order does not survive long-wavelength fluctuations and is replaced by an exponential decay of the same-time coherence, yet on relatively long distance scales.

“specific calculations have predicted [126] that in one dimension the long range order does not survive the long-wavelength fluctuations and is replaced by an exponential decay of the same-time coherence, yet on relatively long distance scales.”

• cites [126] [126] Graham, R.; Haken, H. Laserlight–first example of a second-order phase transition far away from thermal equilibrium, Z. Phys. A, Hadrons Nuclei, Volume 237 (1970), pp. 31-46 sourceNot checked — no full text of the source

May combine two claims.

Under E_inc = 0, the equation of motion (39) has a global U(1) symmetry ψ → ψ e^{iφ}; this symmetry is spontaneously broken above threshold, where the field selects a specific uniform phase across the whole system and its time evolution displays a monochromatic oscillation at frequency ω = ω_0 + g |ψ|^2.

“Under the E inc = 0 condition, the equation of motion (39) displays in fact a global U (1) symmetry ψ → ψ e i ϕ for arbitrary ϕ and this symmetry is spontaneously broken above threshold where the field ψ selects a specific and uniform phase across the whole system and its time-evolution displays a monochromatic oscillation at the intensity-dependent frequency ω = ω 0 + g |ψ| 2 .”

May combine two claims.

The transition between the diffusive and propagating regimes is typically associated with an exceptional point in the dispersion, whose position is determined by the departure from equilibrium, namely the loss rates: the larger γ_loss, the wider the diffusive plateau.

“The transition between the two regimes is typically associated to an exceptional point in the dispersion, whose position is determined by the strength of the departure from equilibrium, namely by the value of the loss rates: the larger γ loss , the wider the diffusive plateau.”

May combine two claims.

The difference between non-interacting and impenetrable photons translates to the shape of g^(2): for non-interacting photons it has a position-independent value equal to 1; for impenetrable photons, its same-point value is much suppressed with respect to its different-point value, g^(2)(i1=i2) ≪ g^(2)(i1≠i2).

“for non-interacting photons it has a position-independent value equal to 1; for impenetrable photons, its same-point value is much suppressed with respect to its differentpoint value, g (2) (i 1 = i 2 ) ≪ g (2) (i 1 ̸ = i 2 ).”

May combine two claims.

Losses in usual devices are linear in the field amplitude and have an approximately frequency- and wavevector-independent rate, so they can be described by Markovian Lindblad terms.

“Losses in usual devices are linear in the field amplitude and have an approximately frequencyand wavevector-independent rate, so that they can be described at the level of the master equation for the density operator”

• AssumptionRests on an assumption: The cavities used for quantum fluid of light experiments are far from the ultrastrong light-matter coupling regime.

May combine two claims.

Radiative losses transfer all properties of the in-cavity field to the emitted light, so the quantum state of the fluid of light can be reconstructed in real time from the quantum optical properties of the emitted radiation.

“radiative losses transfer all properties of the in-cavity field to the emitted light [51], so that the quantum state of the fluid of light can be reconstructed in real time just by looking at the quantum optical properties of the emitted radiation.”

• cites [51] [51] Walls, D. F.; Milburn, Gerard J. Quantum optics, Graduate Texts in Physics, Springer, 2008, 425 pages sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The mean-field approximation is accurate as long as fluctuations around the mean-field are small, which is generally the case if interactions between particles are weak.

“Usually, this factorization assumption is accurate as long as the fluctuations around the mean-field are small, which is generally the case if interactions between the particles are weak.”

• AssumptionThe authors state this as an assumption: The fluctuations around the mean-field are small.

May combine two claims.

If the in-cavity field is weak enough not to affect the population inversion, gain saturation is not significant and the effective incoherent pumping rate is γ_eff,0 = 4Ω_R^2/Γ_P.

“If we further assume that the in-cavity field is weak enough not to affect the population inversion, gain saturation is not significant and we obtain an effective incoherent pumping of the form (19) with a rate”

• AssumptionThe authors state this as an assumption: The in-cavity field is weak enough not to affect the population inversion.

Probably not a substantial claim: may not pass S3 (load-bearing).

Application of the mean-field factorization to the conservative Hamiltonian leads to the Gross-Pitaevskii equation for an interacting Bose-Einstein condensate.

“Application of this procedure to the conservative Hamiltonian (15) leads to the Heisenberg equation”

• Also stated in: § 3.1. Mean-field approximation · plain

  “gives the usual Gross-Pitaevskii equation for an interacting Bose-Einstein condensate,”

Probably not a substantial claim: may not pass S3 (load-bearing).

Photon-photon interactions in a nonlinear optical medium are encoded in the χ(3) optical nonlinearity, which describes a dielectric polarization proportional to the cube of the applied electric field.

“binary photon-photon interactions are encoded in the χ (3) optical nonlinearity of the medium, which describes a dielectric polarization proportional to the cube of the applied electric field.”

• cites [42] [42] Butcher, P. N.; Cotter, D. The elements of nonlinear optics, Cambridge Studies in Modern Optics, 9, Cambridge University Press, 2008, xiv+344 pagesNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [43] [43] Boyd, R. W. Nonlinear optics, Academic Press Inc., 2008, xix+613 pagesNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The nonequilibrium nature of the fluid of light opens the way to new physical phenomena and offers tools for stabilization, manipulation, and diagnostics of the fluid.

“the nonequilibrium nature of the fluid opens the way to new physical phenomena and offers a wide variety of novel experimental tools for the stabilization, the manipulation and the diagnostics of the fluid.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

In some physical models of lasing, the frequency dependence of gain is crucial to theoretically recover stable laser operation at the bottom of the photon band as observed in experiment.

“In some physical models of lasing, such a frequency-dependence of gain is crucial to theoretically recover a stable laser operation at the bottom of the photon band as observed in the experiment.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

In nonlinear optics, the analogous equation is called the Lugiato-Lefever equation, originally formulated in [78] and still a powerful workhorse for optical devices based on Kerr cavity solitons and frequency combs.

“In the nonlinear optics literature, they go under the name of Lugiato-Lefever equation: originally formulated in [78], this equation is still now a powerful workhorse for the description of optical devices based on Kerr cavity solitons and frequency combs [73].”

• cites [78] [78] Lugiato, Luigi A.; Lefever, René Spatial dissipative structures in passive optical systems, Phys. Rev. Lett., Volume 58 (1987) no. 21, 2209 sourceNot checked — no full text of the source
• cites [73] [73] Lugiato, Luigi A.; Prati, Franco; Brambilla, Enrico; Gatti, Alessandra The cavity Kerr medium model and the surprising history around it, Quantum fluids of light and matter (Proceedings of the International School of Physics “Enrico Fermi”), IOS Press, 2025 no. 209, pp. 5-21 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

Available temperatures in atomic gases are typically still too high to observe the most exciting strongly correlated states of matter.

“Still, the available values of the temperature are typically still too high to observe the most exciting strongly correlated states of matter.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Equations analogous to the generalized nonequilibrium Gross-Pitaevskii equation (39) have been derived in several other contexts from different points of view.

“equations analogous to (39) have been derived in several other contexts from different points of view.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In electronic systems with conserved electron number, ν can be fixed by tuning the magnetic field B or the electronic density n_2D with gates so as to fix the Fermi energy between two Landau levels.

“In electronic systems where the number of electrons is conserved, the value of ν can be fixed by tuning the externally applied magnetic field B or the electronic density n 2D with suitable gates, so as to fix the Fermi energy between two Landau levels.”

May combine two claims.

Linear loss and incoherent pumping produce linear, phase-insensitive gain and loss terms, and if γ_pump > γ_loss with no gain saturation, unlimited exponential growth may arise.

“from which it is immediate to see how an unlimited exponential growth may arise if γ pump > γ loss and no gain saturation mechanism is included in the model.”

Probably not a substantial claim: may not pass S3 (load-bearing).

As typical of Wigner representations, statistical averaging over noise gives information on symmetrized products of quantum operators, so commutators must be subtracted to obtain normal-ordered quantities.

“As typical of Wigner representations [55], for any product of fields ψ(r ∥ ) and ψ * (r ′ ∥ ), the statistical average over the noise provides information on the corresponding symmetrized product of quantum operators Ψ(r ∥ ) and Ψ † (r ′ ∥ ), so commutators have to be subtracted to obtain the more standard normal-ordered quantities.”

• cites [55] [55] Gardiner, Crispin W.; Zoller, Peter Quantum noise, Springer Series in Synergetics, Springer, 2004, xxii+450 pagesNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

In the presence of a strong and uniform synthetic magnetic field, photonic modes closely resemble Landau levels and skipping orbits appear on the edges.

“in the presence of a strong and uniform synthetic magnetic field, photonic modes closely resemble Landau levels and skipping orbits appear on the edges.”

May combine two claims.

With proper design of device geometry, e.g. ring resonators, related parametric processes can be induced into modes at different frequencies, causing the density modulation to move continuously in space and produce temporally periodic oscillations in emitted light intensity while preserving long-time phase coherence of the emission.

“With a proper design of the device geometry, e.g. in ring resonators, related parametric processes can be induced into modes at different frequencies: in this case, the density modulation continuously moves in space and gives temporally periodic oscillations in the emitted light intensity, while preserving a long-time phase coherence of the emission.”

May combine two claims.

Depending on the relative value of the energy bandwidth ∆ω_band and the loss rate γ_loss, one can transition from an integer quantum Hall regime where γ_loss ≫ ∆ω_band and coherent pumping uniformly drives all states within the band, to an anomalous Hall regime where γ_loss < ∆ω_band and the coherent drive frequency selects a set of resonant states.

“depending on the relative value of the energy bandwidth ∆ω band and of the loss rate γ loss , one can in fact transition from a IQH regime where γ loss ≫ ∆ω band and the coherent pumping uniformly drives all states within the band, to an anomalous Hall regime where γ loss < ∆ω band and the frequency of the coherent drive specifically selects a set of resonant states.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Equivalently, in real space, condensation is signalled by the onset of long-range order in the correlation function G^(1)(r,r') = ⟨Ψ†(r)Ψ(r')⟩, which tends to a non-zero value at long distances |r-r'| → ∞.

“Equivalently, from a real-space perspective, condensation is instead signalled by the onset of long-range order in the correlation function G (1) (r, r ′ ) = Ψ † (r) Ψ(r ′ )(50) which tends to a non-zero value at long distances |rr ′ | → ∞ [122].”

• cites [122] [122] Cohen-Tannoudji, Claude Lectures at Collège de France (1999-2000) https://www.phys.ens.fr/...Not checked yet

  Not checked in the free run.

May combine two claims.

In the anomalous Hall regime, the lateral shift is no longer quantized and is determined by the averaged value of the Berry curvature over the set of resonant states.

“In this latter case, the lateral shift is no longer quantized and is determined by the averaged value of the Berry curvature over the set of resonant states.”

Probably not a substantial claim: may not pass S3 (load-bearing).

An experiment exploiting driving and dissipation for a comprehensive study of anomalous and integer quantum Hall effect in a photonic Haldane model using a frequency-encoded synthetic dimension platform based on an optical fiber loop was recently reported.

“An experiment that exploits driving and dissipation for a comprehensive study of anomalous and integer quantum Hall effect in a photonic Haldane model using a frequency-encoded synthetic dimension platform based on an optical fiber loop was recently reported in [104].”

• cites [104] [104] Chénier, Alexandre; d’Aligny, Bosco; Pellerin, Félix; Blanchard, Paul-Édouard; Ozawa, Tomoki; Carusotto, Iacopo; St-Jean, Philippe Quantized Hall drift in a frequency-encoded photonic Chern insulator (2024) sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The SO(2) rotational symmetry spontaneously broken by the ferromagnetic transition of the xy model is mathematically equivalent to the U(1) group describing the Ψ → Ψ e^{iφ} symmetry spontaneously broken at the condensation transition.

“More formally, the SO(2) rotational symmetry that is spontaneously broken by the ferromagnetic transition of the x y model is mathematically equivalent to the U (1) group describing the Ψ → Ψ e i φ symmetry that is spontaneously broken at the condensation transition.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The criterion for condensation can be understood in analogy with ferromagnetism, where the ferromagnetic transition is characterized by the magnetization correlation function G^(1)(r,r') = ⟨M(r)M(r')⟩.

“This criterion for condensation can be physically understood in analogy with ferromagnetism where the ferromagnetic transition is characterized in terms of the magnetization correlation function G (1) (r, r ′ ) = ⃗ M (r) ⃗ M (r ′ ) .(51)”

Probably not a substantial claim: may not pass S3 (load-bearing).

In a spatially uniform geometry, condensation is typically associated with the appearance of a sharp and macroscopic k = 0 peak in the momentum distribution n(k) = ⟨Ψ†(k)Ψ(k)⟩.

“condensation in a spatially uniform geometry is typically associated [1,107] to the appearance of a sharp and macroscopic k = 0 peak in the momentum distribution n(k) = Ψ † (k) Ψ(k)”

• cites [1] [1] Pitaevskiĭ, Lev P.; Stringari, Sandro Bose–Einstein condensation and superfluidity, International Series of Monographs on Physics, 164, Oxford University Press, 2016, 512 pages sourceNot checked — no full text of the source
• cites [107] [107] Huang, Kerson Statistical mechanics, John Wiley & Sons, 1987, xiv+498 pagesNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The change in friction behaviour is associated with a singularity in the wavevector of collective excitations emitted by the impurity: at low speed this wavevector is purely imaginary, so the excitation does not transport momentum; at large speeds it acquires a finite real part, associated with momentum dissipated by the impurity into the fluid.

“Such a change in behaviour can be associated to the singularity in the wavevector of the collective excitations emitted by the impurity shown in Figure 4(g)-(h): at low speed, this wavevector is purely imaginary, so the collective excitation generated by the impurity does not transport momentum; at large speeds, instead, this wavevector acquires a finite real part, which is directly associated to”

Classified as probably not a substantial claim. May combine two claims.

As is well known from atomic physics, coherent illumination leads to reversible oscillatory dynamics between different states, with absorption followed by stimulated emission until a steady-state is enforced via spontaneous emission.

“As it is well known from atomic physics [148], a coherent illumination leads to a reversible oscillatory dynamics between the different states, with absorption processes followed by stimulated emission ones until a steady-state is enforced via spontaneous emission processes.”

• cites [148] [148] Cohen-Tannoudji, Claude; Dupont-Roc, Jacques; Grynberg, Gilbert Atom-photon interactions: basic processes and applications, Physics Textbook, John Wiley & Sons, 1998, xxii+656 pages sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The first proposal for strongly correlated photonic matter was the photon blockade effect.

“The first proposal in this direction [144] was the so-called photon blockade effect.”

• cites [144] [144] Imamoğlu, A.; Schmidt, H.; Woods, G.; Deutsch, M. Strongly interacting photons in a nonlinear cavity, Phys. Rev. Lett., Volume 79 (1997) no. 8, pp. 1467-1470 sourceNot checked — no full text of the source

May combine two claims.

N-photon observables are strictly zero on all lower N'<N photon states and, up to moderate incident intensity, only receive a sub-dominant contribution from higher N'>N states.

“Such observables are in fact strictly zero on all lower N ′ < N photon states and, up to moderate values of the incident intensity, only receive a sub-dominant contribution from the higher N ′ > N ones.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

For sufficiently weak interactions, a mean-field theory based on stochastic partial differential equations for classical fields provides an accurate description of the steady-state and dynamics of dilute driven-dissipative systems.

“for sufficiently weak interactions, a mean-field theory based on (stochastic) partial differential equations for classical fields provides an accurate description of the steady-state and of the dynamics of the system.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Moving up to two-dimensional systems is not expected to pose additional conceptual challenges to optical experiments.

“While moving up to two-dimensional systems is not expected to pose additional conceptual challenges to optical experiments, three-and higher-dimensional configurations require the use of synthetic dimension schemes”

May combine two claims.

Independently of the specific geometry, the eigenstates of the nonlinear oscillator Hamiltonian are labelled by photon number and have energy E_n = nħω_o + ħω_nl n(n-1)/2.

“Independently of the specific geometry, the eigenstates of (52) are labelled by the photon number and have an energy”

Probably not a substantial claim: may not pass S3 (load-bearing).

The anharmonicity in the nonlinear cavity is quantified by ω_nl, which is proportional to the χ(3) optical nonlinearity of the nonlinear medium embedded in the cavity.

“where the anharmonicity is quantified by the parameter ω nl proportional to the χ (3) optical nonlinearity of the nonlinear medium embedded in the cavity.”

May combine two claims.

To selectively drive a desired many-body state, the frequency separation from neighboring states must exceed the linewidth; because the separation is typically set by hopping J and interaction ω_int and the broadening grows as N γ_loss, the requirement on γ_loss becomes more stringent as larger N states are targeted.

“In order to be able to selectively drive the desired many-body state, the frequency separation from the neighboring states has to exceed the linewidth: as the separation is typically set by the hopping J and interaction ω int energies and the broadening grows as N γ loss , the requirement on the linewidth γ loss becomes more and more stringent as larger N states are targeted.”