Observation of the Bogoliubov Dispersion in a Fluid of Light

Abstract

Quantum fluids of light are 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 study 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.Superfluidity is one of the most striking manifestation of quantum many-body physics. Initially observed in liquid Helium [1,2], the realization of atomic Bose-Einstein condensates (BEC) has allowed detailed investigations of this macroscopic quantum phenomenon exploiting the precise control over the system parameters. Recently, another kind of quantum fluid made of interacting photons in a nonlinear cavity has brought new perspectives to the study of superfluidity in drivendissipative systems, with many fascinating developments [3] such as the observation of polariton BEC [4,5] and the demonstration of exciton-polariton superfluidity [6,7]. A different photon fluid configuration, initially proposed by Pomeau and Rica more than twenty years ago [8] but long ignored experimentally, relies on the propagation of a intense laser beam through some nonlinear medium. In this 2D+1 geometry (2 transverse spatial dimensions and 1 propagation dimension analogous to an effective time), the negative third-order Kerr nonlinearity is interpreted as a photon-photon repulsive interaction. Few theoretical works addressing mostly hydrodynamic effects using this geometry have been recently proposed [9,10] and investigated in photorefractive crystals [11], thermo-optic media [12,13] and hot atomic vapors [14].The theoretical framework used to describe quantum fluids of light relies on the analogy with weakly interacting Bose gases where the mean field solution has originally been derived by Bogoliubov [15,16]. A fundamental property of the Bogoliubov dispersion relation is the linear dependence in the excitation wavevector at long wavelengths (sound-like) and the quadratic dependence at short wavelengths (free-particle like). Although this dispersion has been well characterized in atomic BEC experiments [17][18][19][20], a direct measurement of this dispersion in a fluid of light remains elusive [12,21]. In this letter, we propose a general method to experimentally access the dispersion of elementary density excitation...

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