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arXiv:1509.05264 · Cambridge University Press eBooks

Disorder, Synchronization, and Phase-locking in Nonequilibrium Bose-Einstein Condensates

P. R. Eastham, Bernd Rosenow

Published Oct 4, 2018• 3 citations
arXivHTMLPDF

Abstract

We review some theories of non-equilibrium Bose-Einstein condensates in potentials, in particular of the Bose-Einstein condensate of polaritons. We discuss such condensates, which are steady-states established through a balance of gain and loss, in the complementary limits of a double-well potential and a random disorder potential. For equilibrium condensates, the former corresponds to a Josephson junction, whereas the latter is the setting for the superfluid/Bose glass transition. We explore the non-equilibrium generalization of these phenomena, and highlight connections with mode selection and synchronization.

DOI
10.1017/9781316084366.025

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We review some theories of non-equilibrium Bose-Einstein condensates in potentials, in particular of the Bose-Einstein condensate of polaritons. We discuss such condensates, which are steady-states established through a balance of gain and loss, in the complementary limits of a double-well potential and a random disorder potential. For equilibrium condensates, the former corresponds to a Josephson junction, whereas the latter is the setting for the superfluid/Bose glass transition. We explore the non-equilibrium generalization of these phenomena, and highlight connections with mode selection and synchronization.
Quantum phase transitions realized in inhomogeneous potentials is a topic of major importance in condensed matter physics. It involves non-trivial matter states, as Josephson oscillations for double potential wells [55], Mott insulators for periodic potentials [56], and Bose glasses for disorder potentials [57]. The case of disorder potentials is a crucial matter both for the intrinsic interest of phase transitions and for the unavoidable disorder in real systems. It is worth the effort to address this issue for the case of polariton condensates.
Abstract In an equilibrium three-dimensional (3D) disordered condensate, it is well established that disorder can generate an amount of normal fluid ρ n equaling to of ρ ex , where ρ ex is a sum of interaction-induced quantum depletion and disorder-induced condensate deformation. The concept that the superfluid is more volatile to the existence of disorder than the condensate is crucial to the understanding of the Bose glass phase. In this work, we show that, by bringing a weakly disordered 3D condensate to non-equilibrium regime via a quantum quench in the interaction, disorder can destroy superfluid significantly more, leading to a steady state of Hamiltonian H f in which the ρ n far exceeds of the ρ ex . This suggests the possibility of engineering Bose glass in the dynamic regime. Here, we refer to the dynamical Bose glass as the case where in the steady state of quenched condensate , the superfluid density goes to zero while the condensate density remains finite. As both the ρ n and ρ ex are measurable quantities, our results allow an experimental demonstration of the dramatized interplay between the disorder and interaction in the non-equilibrium scenario.
We demonstrate that the synchronization of a lattice of solid-state condensates when intersite tunneling is switched on depends strongly on the weak local disorder. This finding is vital for implementation of condensate arrays as computation devices. The condensates here are nonlinear bosonic fluids of exciton-polaritons trapped in a weakly disordered Bose-Hubbard potential, where the nearest-neighboring tunneling rate (Josephson coupling) can be dynamically tuned. The system can thus be tuned from a localized to a delocalized fluid as the number density or the Josephson coupling between nearest neighbors increases. The localized fluid is observed as a lattice of unsynchronized condensates emitting at different energies set by the disorder potential. In the delocalized phase, the condensates synchronize and long-range order appears, evidenced by narrowing of momentum and energy distributions, new diffraction peaks in momentum space, and spatial coherence between condensates. Our paper identifies similarities and differences of this nonequilibrium crossover to the traditional Bose-glass to superfluid transition in atomic condensates.
We derive a theory for Bose condensation in nonequilibrium steady states of bosonic quantum gases that are coupled both to a thermal heat bath and to a pumped reservoir (or gain medium), while suffering from loss. Such a scenario describes photonic many-body systems such as exciton-polariton gases. Our analysis is based on a set of kinetic equations for a gas of noninteracting bosons. By identifying a dimensionless scaling parameter controlling the boson density, we derive a sharp criterion for which system states become selected to host a macroscopic occupation. We show that with increasing pump power, the system generically undergoes a sequence of nonequilibrium phase transitions. At each transition, a state either becomes or ceases to be Bose selected (i.e., to host a condensate): The state which first acquires a condensate when the pumping exceeds a threshold is the one with the largest ratio of pumping to loss. This intuitive behavior resembles simple lasing. In the limit of strong pumping, the coupling to the heat bath becomes dominant so that eventually the ground state is selected, corresponding to equilibrium(like) Bose condensation. For intermediate pumping strengths, several states become selected, giving rise to fragmented nonequilibrium Bose condensation. We compare these predictions to experimental results obtained for exciton polaritons in a double-pillar structure [M. Galbiati et al., Phys. Rev. Lett. 108, 126403 (2012)] and find good agreement. Our theory, moreover, predicts that the reservoir occupation is clamped at a constant value whenever the system hosts an odd number of Bose condensates.
We study driven-dissipative Bose-Einstein condensates in a two-mode Josephson system, such as a double-well potential, with asymmetrical pumping. We investigate nonlinear effects on the condensate populations and mode transitions. The generalized Gross-Pitaevskii equations are modified in order to treat pumping of only a single mode. We characterize the steady-state solutions in such a system as well as criteria for potential trapping of a condensate mode. There are many possible steady states, with different density and/or phase profiles. Transitions between different condensate modes can be induced by varying the parameters of the junction or the initial conditions, or by applying external fields.
The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles, and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state; but the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.