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arXiv:1603.04898 · Physical Review Letters

Inflationary Quasiparticle Creation and Thermalization Dynamics in Coupled Bose-Einstein Condensates

Anna Posazhennikova, Mauricio Trujillo-Martinez, Johann Kroha

Published Jun 2, 2016• 24 citations
arXivHTMLPDF

Abstract

A Bose gas in a double-well potential, exhibiting a true Bose-Einstein condensate (BEC) amplitude and initially performing Josephson oscillations, is a prototype of an isolated, nonequilibrium many-body system. We investigate the quasiparticle (QP) creation and thermalization dynamics of this system by solving the time-dependent Keldysh-Bogoliubov equations. We find avalanchelike QP creation due to a parametric resonance between BEC and QP oscillations, followed by slow, exponential relaxation to a thermal state at an elevated temperature, controlled by the initial excitation energy of the oscillating BEC above its ground state. The crossover between the two regimes occurs because of an effective decoupling of the QP and BEC oscillations. This dynamics is analogous to elementary particle creation in models of the early universe. The thermalization in our setup occurs because the BEC acts as a grand canonical reservoir for the quasiparticle system.

DOI
10.1103/physrevlett.116.225304

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A Bose gas in a double-well potential, exhibiting a true Bose-Einstein condensate (BEC) amplitude and initially performing Josephson oscillations, is a prototype of an isolated, nonequilibrium many-body system. We investigate the quasiparticle (QP) creation and thermalization dynamics of this system by solving the time-dependent Keldysh-Bogoliubov equations. We find avalanchelike QP creation due to a parametric resonance between BEC and QP oscillations, followed by slow, exponential relaxation to a thermal state at an elevated temperature, controlled by the initial excitation energy of the oscillating BEC above its ground state. The crossover between the two regimes occurs because of an effective decoupling of the QP and BEC oscillations. This dynamics is analogous to elementary particle creation in models of the early universe. The thermalization in our setup occurs because the BEC acts as a grand canonical reservoir for the quasiparticle system.
Abstract If and how an isolated quantum system thermalizes despite its unitary time evolution is a long‐standing, open problem of many‐body physics. The eigenstate thermalization hypothesis (ETH) postulates that thermalization happens at the level of individual eigenstates of a system's Hamiltonian. However, the ETH requires stringent conditions to be validated, and it does not address how the thermal state is reached dynamically from an initial non‐equilibrium state. We consider a Bose‐Einstein condensate (BEC) trapped in a double‐well potential with an initial population imbalance. We find that the system thermalizes although the initial conditions violate the ETH requirements. We identify three dynamical regimes. After an initial regime of undamped Josephson oscillations, the subsystem of incoherent excitations or quasiparticles (QP) becomes strongly coupled to the BEC subsystem by means of a dynamically generated, parametric resonance. When the energy stored in the QP system reaches its maximum, the number of QPs becomes effectively constant, and the system enters a quasi‐hydrodynamic regime where the two subsystems are weakly coupled. In this final regime the BEC acts as a grand‐canonical heat reservoir for the QP system (and vice versa), resulting in thermalization. We term this mechanism dynamical bath generation (DBG).
Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence: While some show dissipation-free Josephson oscillations, others find strong damping. Such damping in isolated BECs cannot be understood on the level of the coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral formalism, we describe the time-dependent system dynamics by means of a multimode BEC coupled to fluctuations (single-particle excitations) beyond the Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite an excess of fluctuations when the effective Josephson frequency ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ is in resonance with the effective fluctuation energy ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$, where both ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{J}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}}_{m}$ are strongly renormalized with respect to their noninteracting values. By evaluating and using the model parameters for the respective experiments, we describe quantitatively the presence or absence of damping.
The time-dependent non-equilibrium dynamics of a Bose–Einstein condensate (BEC) typically generates incoherent excitations out of the condensate due to the finite frequencies present in the time evolution. We present a detailed derivation of a general non-equilibrium Greenʼs function technique that describes the coupled time evolution of an interacting BEC and its single-particle excitations in a trap, based on an expansion in terms of the exact eigenstates of the trap potential. We analyze the dynamics of a Bose system in a small double-well potential with initially all particles in the condensate. When the trap frequency is larger than the Josephson frequency, , the dynamics changes at a characteristic time, , abruptly from the slow Josephson oscillations of the BEC to fast Rabi oscillations driven by quasiparticle excitations in the trap. For times , the Josephson oscillations are undamped, in agreement with the experiments. We analyze the physical origin of the finite scale as well as its dependence on the trap parameter Δ .
Cosmological reheating describes the transition of the postinflationary universe to a hot and thermal state. In order to shed light on the underlying dynamics of this process, we propose to quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. In our setup, the excitations on top of an atomic Bose-Einstein condensate play the role of the particles produced by the decaying inflaton field after inflation. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the nonrelativistic limit by a time dependence of the atomic interactions, which can be tuned experimentally via Feshbach resonances. As we illustrate by means of classical-statistical simulations for the case of two spatial dimensions, the dynamics of the atomic system exhibits the characteristic stages of far-from-equilibrium reheating, including the amplification of fluctuations via parametric instabilities and the subsequent turbulent transport of energy towards higher momenta. The transport is governed by a nonthermal fixed point showing universal self-similar time evolution as well as a transient regime of prescaling with time-dependent scaling exponents. While the classical-statistical simulations can capture only the earlier stages of the dynamics for weak couplings, the proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.
In this paper, we formulate quantum field theory on an analogue curved spacetime in a Bose-Einstein condensate where quantum particles on curved spacetime are equated with Bogoliubov quasi-particle excitations on the Bose-Einstein condensate. By using our formulation, we numerically investigate a particle creation in analogue expanding Universe which can be expressed as Bogoliubov quasiparticles in an expanding Bose-Einstein condensate and obtain its spectrum which shows the thermal Maxwell-Boltzmann distribution, the temperature of which can be experimentally accessible. This is the first direct numerical simulation for the particle creation and its spectrum on analogue curved spacetime by using the system of Bose-Einstein condensates.
An attempt is made to determine the difference between Bose–Einstein condensation of particles and quasiparticles. An equation is obtained for the number of particles in a Bose–Einstein condensate as a function of the total number of particles in the system. This equation is also written for quasiparticles taking account of their creation by external pumping and the presence of equilibrium thermal excitations in the system. Analyzing both equations, the chemical potential of the pumped quasiparticles and their number in the condensate are found as a function of the pumping intensity. A condition under which the Bose–Einstein condensation of low-energy quasiparticle excitations starts and occurs at any, including quite high, temperatures is found.