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arXiv:quant-ph/9905001 · Physical Review A

Bogoliubov dispersion relation and the possibility of superfluidity for weakly interacting photons in a two-dimensional photon fluid

R. Y. Chiao, Jack Boyce

Published Nov 1, 1999• 115 citations
arXivHTMLPDF

Abstract

The Bogoliubov dispersion relation for the elementary excitations of the weakly interacting Bose gas is shown to hold for the case of the weakly interacting photon gas (the ``photon fluid'') in a nonlinear Fabry-Perot cavity. The chemical potential of a photon in the two-dimensional photon fluid does not vanish. The Bogoliubov relation, which is also derived by means of a linearized fluctuation analysis in classical nonlinear optics, implies the possibility of a new, superfluid state of light. The theory underlying an experiment in progress to observe sound waves in the photon fluid is described, and another experiment to measure the critical velocity of this superfluid is proposed.

DOI
10.1103/physreva.60.4114

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The Bogoliubov dispersion relation for the elementary excitations of the weakly interacting Bose gas is shown to hold for the case of the weakly interacting photon gas (the ``photon fluid'') in a nonlinear Fabry-Perot cavity. The chemical potential of a photon in the two-dimensional photon fluid does not vanish. The Bogoliubov relation, which is also derived by means of a linearized fluctuation analysis in classical nonlinear optics, implies the possibility of a new, superfluid state of light. The theory underlying an experiment in progress to observe sound waves in the photon fluid is described, and another experiment to measure the critical velocity of this superfluid is proposed.
The Bogoliubov dispersion relation for the elementary excitations of the weakly-interacting Bose gas is shown to hold for the case of the weakly-interacting photon gas (the ``photon fluid'') in a nonlinear Fabry-Perot cavity. This relation, which is also derived by means of a linearized fluctuation analysis in classical nonlinear optics, implies the possibility of a new superfluid state of light. The theory underlying an experiment in progress to measure this dispersion relation is described, and another experiment to test the prediction of the superfluidity of this state of light is proposed.
We discuss the possibility that photons, which are bosons, can form a 2D superfluid due to Bose-Einstein condensation inside a nonlinear Fabry-Perot cavity filled with atoms in their ground states. A "photon fluid" forms inside the cavity as a result of multiple photon-photon collisions mediated by the atoms during a cavity ring-down time. The effective mass and chemical potential for a photon inside this fluid are nonvanishing. This implies the existence of a Bogoliubov dispersion relation for the low-lying elementary excitations of the photon fluid, and in particular, that sound waves exist for long-wavelength, low-frequency disturbances of this fluid. Possible experiments to test for the superfluidity of the photon fluid based on the Landau critical-velocity criterion will be discussed.
Quantum fluids of light are a photonic counterpart to atomic Bose gases and are attracting increasing interest for probing many-body physics quantum phenomena such as superfluidity. Two different configurations are commonly used: the confined geometry where a nonlinear material is fixed inside an optical cavity and the propagating geometry where the propagation direction plays the role of an effective time for the system. The observation of the dispersion relation for elementary excitations in a photon fluid has proved to be a difficult task in both configurations with few experimental realizations. Here, we propose and implement a general method for measuring the excitations spectrum in a fluid of light, based on a group velocity measurement. We observe a Bogoliubov-like dispersion with a speed of sound scaling as the square root of the fluid density. This Letter demonstrates that a nonlinear system based on an atomic vapor pumped near resonance is a versatile and highly tunable platform to study quantum fluids of light.
We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in DDD dimensions. Using the Landau's two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for D≥2D\ge 2D≥2. To model the recent measurements of the sound velocities in 2D, obtained around the Berezinskii-Kosterlitz-Thouless transition temperature and outside the very weakly-interacting regime, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results are currently unavailable, we find no hybridization, triggering the necessity of future experimental investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in DDD dimensions.
Bogoliubov's description of Bose gases relies on the linear dynamics of noninteracting quasiparticles on top of a homogeneous condensate. Here, we theoretically explore the weakly nonlinear regime of a one-dimensional photon superfluid in which phononlike elementary excitations interact via their backreaction on the background flow. The generalized dispersion relation extracted from spatiotemporal intensity spectra reveals additional branches that correspond to Bogoliubov quasiparticles—phase-locked collective excitations originating from nonresonant harmonic generation and wave-mixing processes. These mechanisms are inherent to fluctuation dynamics and highlight nontrivial scattering channels other than resonant interactions that could be relevant in the emergence of dissipative and turbulent phenomena in superfluids. Published by the American Physical Society 2024
Abstract We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in D dimensions. Using the Landau’s two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for D ⩾ 2. To model the recent measurements of the sound velocities in 2D, obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless transition temperature, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results are currently unavailable, we find no hybridization, triggering the necessity of future investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in D dimensions.