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arXiv:1811.12135 · Physical Review A

Early-time dynamics of Bose gases quenched into the strongly interacting regime

A. Muñoz de las Heras, Meera M. Parish, Francesca Maria Marchetti

Published Feb 21, 2019• 17 citations
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Abstract

The crossover from shallow to deep interaction quenches of the very early-time dynamics of a degenerate Bose gas is analyzed by using a time-dependent variational formalism, which self-consistently describes the excitation of particles out of the condensate in pairs only. In the unitary regime, the model leads to a universal scaling behavior of the typical growth time of the momentum distribution in agreement with recent experimental observations.

DOI
10.1103/physreva.99.023623

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The crossover from shallow to deep interaction quenches of the very early-time dynamics of a degenerate Bose gas is analyzed by using a time-dependent variational formalism, which self-consistently describes the excitation of particles out of the condensate in pairs only. In the unitary regime, the model leads to a universal scaling behavior of the typical growth time of the momentum distribution in agreement with recent experimental observations.
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We explore the dynamics of a Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. Within a self-consistent Bogoliubov analysis we find that after the initial condensate-quasiparticle Rabi oscillations, at long time scales the gas is characterized by a nonequilibrium steady-state momentum distribution function, with depletion, condensate density, and contact that deviate strongly from their corresponding equilibrium values. These are in a qualitative agreement with recent experiments on 85{}^{85}85Rb by Makotyn et al. Our analysis also suggests that for sufficiently deep quenches close to the resonance the nonequilibrium state undergoes a phase transition to a fully depleted state, characterized by a vanishing condensate density.
We study the dynamics of an initially degenerate homogeneous Bose gas after an interaction quench to the unitary regime at a magnetic Feshbach resonance. As the cloud decays and heats, it exhibits a crossover from degenerate- to thermal-gas behavior, both of which are characterized by universal scaling laws linking the particle-loss rate to the total atom number N. In the degenerate and thermal regimes, the per-particle loss rate is ∝N^{2/3} and N^{26/9}, respectively. The crossover occurs at a universal kinetic energy per particle and at a universal time after the quench, in units of energy and time set by the gas density. By slowly sweeping the magnetic field away from the resonance and creating a mixture of atoms and molecules, we also map out the dynamics of correlations in the unitary gas, which display a universal temporal scaling with the gas density, and reach a steady state while the gas is still degenerate.
We study a degenerate Bose gas quenched to unitarity by solving a many-body model including three-body losses and correlations up to second order. As the gas evolves in this strongly interacting regime, the buildup of correlations leads to the formation of extended pairs bound purely by many-body effects, analogous to the phenomenon of Cooper pairing in the BCS regime of the Fermi gas. Through fast sweeps away from unitarity, we detail how the correlation growth and formation of bound pairs emerge in the fraction of unbound atoms remaining after the sweep, finding quantitative agreement with experiment. We comment on the possible role of higher-order effects in explaining the deviation of our theoretical results from experiment for slower sweeps and longer times spent in the unitary regime.
We address the physics of equilibration in ultracold atomic gases following a quench of the interaction parameter. Our work is based on a bath model which generates damping of the bosonic excitations. We illustrate this dissipative behavior through the momentum distribution of the excitations nk{n}_{k}nk​, observing that larger kkk modes have shorter relaxation times $\ensuremath{\tau}(k)$; they will equilibrate faster, as has been claimed in recent experimental work. We identify three time regimes. At short times nk{n}_{k}nk​ exhibits oscillations; these are damped out at intermediate times where the system appears to be in a false or slowly converging equilibrium. Finally, at longer times, full equilibration occurs. This false equilibrium is, importantly, associated with the kkk dependence in $\ensuremath{\tau}(k)$ and has implications for experiment.
We explore the dynamics of a resonant Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. For such deep quenches, we utilize a self-consistent dynamic field approximation and find that after an initial regime of many-body Rabi-type oscillations between the condensate and finite-momentum quasiparticle pairs, at long times, the gas reaches a prethermalized nonequilibrium steady state. We explore the resulting state through its broad stationary momentum distribution function, that exhibits a power-law high-momentum tail. We study the dynamics and steady-state form of the associated enhanced depletion, quench-rate-dependent excitation energy, Tan's contact, structure function, and radio-frequency spectroscopy. We find these predictions to be in a qualitative agreement with recent experiments.