Universal Dynamics of a Degenerate Bose Gas Quenched to Unitarity

Abstract

Motivated by an unexpected experimental observation from the Cambridge group, [Eigen et al., Nature 563, 221 (2018)], we study the evolution of the momentum distribution of a degenerate Bose gas quenched from the weakly interacting to the unitarity regime. For the two-body problem, we establish a relation that connects the momentum distribution at long time to a sub-leading term in the initial wave function. For the many-body problem, we employ the time-dependent Bogoliubov variational wave function and find that, in certain momentum regimes, the momentum distribution at long times displays the same exponential behavior found by the experiment. Moreover, we find that this behavior is universal and independent of the short-range details of the interaction potential. Consistent with the relation found in the two-body problem, we also numerically show that this exponential form is hidden in the same sub-leading term of the Bogoliubov wave function in the initial stages. Our results establish a consistent picture to understand the universal dynamics observed in the Cambridge experiment.

Cumulant theory of the unitary Bose gas: Prethermal and Efimovian dynamics

“…Whether this prethermal steady-state is due to integrable dephasing dynamics, as in the weakly-interacting regime [32], or to ergodic mechanisms is unclear. State-of-the-art integrable theories of the post-quench evolution [33][34][35][36] are by definition unable to capture the relaxation dynamics which must occur in this ergodic system. Additionally, the usual perturbative inclusion of such processes using Boltzmannian approaches [37] is not justified in this regime where the distinctness of collisions is blurred and all rates are on the order of the Fermi scale.…”

Bose-Einstein condensation of Efimovian triples in the unitary Bose gas

“…[33] reveal the existence of pair and triple condensates in the unitary Bose gas. Previous theoretical studies either have not included the necessary Efimovian correlations [37][38][39][40][41][42] or many-body effects [43][44][45], combined only recently in the triplet model of Ref. [46].…”

Maximum Energy Growth Rate in Dilute Quantum Gases

“…where N (t) is a normalization factor, |0 is vacuum of particles, and g 0 and g k are all variational parameters. This approach is not restricted to the short time and has been successfully used in the previous studies of degenerate Bose gas quenched to unitarity [10,13,26]. The evolution of variational parameters g 0 (t) and g k (t) can be obtained from the Euler-Lagrange equation for the Lagrangian…”