We present a theoretical study of the quantum depletion of microcavity polaritons that are excited with a resonant laser pulse. The dynamics of the quantum fluctuations are interpreted in the context of quantum quenches in general and in terms of the dynamical Casimir effect in particular. We compute the time evolution of the first- and second-order correlation functions of the polariton condensate. Our theoretical modeling is based on the truncated Wigner approximation for interacting Bose gases. For homogeneous systems, analytical results are obtained in the linearized Bogoliubov approximation. Inhomogeneous systems are studied numerically by Monte Carlo simulations.
We present a theoretical study of the quantum depletion of microcavity polaritons that are excited with a resonant laser pulse. The dynamics of the quantum fluctuations are interpreted in the context of quantum quenches in general and in terms of the dynamical Casimir effect in particular. We compute the time evolution of the first- and second-order correlation functions of the polariton condensate. Our theoretical modeling is based on the truncated Wigner approximation for interacting Bose gases. For homogeneous systems, analytical results are obtained in the linearized Bogoliubov approximation. Inhomogeneous systems are studied numerically by Monte Carlo simulations.
The statistics of the condensed polaritons is described in terms of the Wigner function. In the framework of the truncated Wigner method, the Wigner function obeys a Fokker-Planck equation, which is solved analytically. The second-order correlations in the stationary state are in excellent agreement with those obtained from the numerical solution of the master equation and show a qualitative and, well above threshold, also quantitative agreement with recent experiments. Furthermore, the contributions of the different noise effects that influence the polariton ground-state statistics are explicitly defined. Exploiting the equivalence between Fokker-Planck and Langevin descriptions of stochastic processes, the time-dependent correlations of the polaritons close to the stationary state are derived. An explicit expression for the polariton linewidth is obtained, whose numerical values reproduce qualitatively the experimental ones. Finally, the limit of validity of the truncated Wigner method in the present model is discussed.
We theoretically investigate the nonequilibrium dynamics of homogeneous ultracold Bose gases of microwave-shielded polar molecules following a sudden quench of the scattering length at zero temperature. We calculate in particular the quantum depletion, the anomalous density, the condensate fluctuations, and the pair-correlation function using both the time-dependent Bogoliubov approach and the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation. During their time evolution, these quantities exhibit slow or fast oscillations depending on the strength of the shielding interactions. We find that at long timescales the molecular condensate is characterized by nonequilibrium steady-state momentum distribution functions, with depletion, anomalous density, and correlations that deviate from their corresponding equilibrium values. We demonstrate that the pair correlations expand diffusively at short times while they spread ballistically at long times.
The demonstration of coherent polariton emission from a CdTe microcavity structure [1] has provided a new system for the study of condensate physics. Unlike atomic condensates, the microcavity system is not in equilibrium; the polariton life-time in the cavity is only ∼ 2ps, so the population has to be maintained by pumping. This raises interesting questions about how the properties of such a non-equilibrium condensate differ from those of an equilibrium system. Recent experimental measurements of the first (g(1)) and second (g(2)) order correlation functions of the emitted light have shown that the decay times of both are ∼ 100−200ps, much longer than the cavity life-time. In this work, we present a theroetical treatment which provides a quantitative explanation of these results, and shows that the ultimate cause of the coherence decay is interactions between polaritons in the condensate. The microcavity polariton condensate is a mesoscopic quantum system, consisting of N ∼ 102 po-laritons within the finite size excitation spot. As a result, number fluctuations of ∼ N 1 2 are expected. For a finite equilibrium condensate of interacting particles, it is straight forward to show that the decay
The fundamental mechanisms which control the phase coherence of the polariton Bose-Einstein condensate (BEC) are determined. It is shown that the combination of number fluctuations and interactions leads to decoherence with a characteristic Gaussian decay of the first-order correlation function. This line shape, and the long decay times ( approximately 150 ps) of both first- and second-order correlation functions, are explained quantitatively by a quantum-optical model which takes into account interactions, fluctuations, and gain and loss in the system. Interaction limited coherence times of this type have been predicted for atomic BECs, but are yet to be observed experimentally.
Polariton condensates provide a versatile platform for exploring non-equilibrium phase transitions and collective phenomena in open quantum systems. Near the condensation threshold, these systems are particularly sensitive to fluctuations and instabilities, which can strongly influence the condensate formation. Using optical trapping and homodyne detection, we directly access the photon statistics and second-order correlation function g(2)(0) of the condensate. We show that polariton condensation near the threshold is not a purely static transition, but instead undergoes a dynamical regime characterized by stochastic hopping between condensed and non-condensed states. These intermittent dynamics are accompanied by a gradual reduction of g(2)(0) towards unity, revealing the progressive build-up of coherence even in the presence of strong temporal fluctuations. Numerical simulations, based on a stochastic Truncated Wigner description of the driven-dissipative polariton field, reproduce these dynamics and capture the essential role of noise and reservoir interactions. This work demonstrates that the observed temporal hopping is an intrinsic feature of polariton condensation, providing a dynamical perspective that goes beyond static descriptions of the condensation phase transition.
The semiclassical approach consisting of Boltzmann equations for the excited states and the ground state supplemented by a Master equation for the probability distribution of the condensate population is solved for picosecond pulsed microcavity polaritons. With the simple birth- and death-type Master equation for the condensate population that disregards the condensate phase, one gets results, which, compared to quasistationary solutions, are in better agreement with the experiments. First, the time-dependent solutions show the influence of the change to the coherent state already at pump powers close above the condensate threshold. Second, and even more important for the interpretation of corresponding pulsed experiments, the time-dependent solution give results for the second-order correlation function with seemingly larger correlations above threshold, although no polariton-polariton interaction in the ground state has been included.