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arXiv:2309.04587 · Physical Review Research

Resonance triplet dynamics in the quenched unitary Bose gas

J. van de Kraats, D. J. M. Ahmed-Braun, V. E. Colussi, S. J. J. M. F. Kokkelmans

Published Mar 11, 2024• 4 citations
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Abstract

The quenched unitary Bose gas is a paradigmatic example of a strongly interacting out-of-equilibrium quantum system, whose dynamics become difficult to describe theoretically due to the growth of non-Gaussian quantum correlations. We develop a conserving many-body theory capable of capturing these effects, allowing us to model the postquench dynamics in the previously inaccessible time regime where the gas departs from the universal prethermal stage. Our results show that this departure is driven by the growth of strong lossless three-body correlations, rather than atomic losses, thus framing the heating of the gas in this regime as a fully coherent phenomenon. We uncover the specific few-body scattering processes that affect this heating and show that the expected connection between the two-body and three-body contacts and the tail of the momentum distribution is obscured following the prethermal stage, explaining the absence of this connection in experiments. Our general framework, which reframes the dynamics of unitary quantum systems in terms of explicit connections to microscopic physics, can be broadly applied to any quantum system containing strong few-body correlations. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.l012056

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The quenched unitary Bose gas is a paradigmatic example of a strongly interacting out-of-equilibrium quantum system, whose dynamics become difficult to describe theoretically due to the growth of non-Gaussian quantum correlations. We develop a conserving many-body theory capable of capturing these effects, allowing us to model the postquench dynamics in the previously inaccessible time regime where the gas departs from the universal prethermal stage. Our results show that this departure is driven by the growth of strong lossless three-body correlations, rather than atomic losses, thus framing the heating of the gas in this regime as a fully coherent phenomenon. We uncover the specific few-body scattering processes that affect this heating and show that the expected connection between the two-body and three-body contacts and the tail of the momentum distribution is obscured following the prethermal stage, explaining the absence of this connection in experiments. Our general framework, which reframes the dynamics of unitary quantum systems in terms of explicit connections to microscopic physics, can be broadly applied to any quantum system containing strong few-body correlations. Published by the American Physical Society 2024
We study the quench of a degenerate ultracold Bose gas to the unitary regime, where interactions are as strong as allowed by quantum mechanics. We lay the foundation of a cumulant theory able to simultaneously capture the three-body Efimov effect and ergodic evolution. After an initial period of rapid quantum depletion, a universal prethermal stage is established, characterized by a kinetic temperature and an emergent Bogoliubov dispersion law, while the microscopic degrees of freedom remain far from equilibrium. Integrability is then broken by higher-order interaction terms in the many-body Hamiltonian, leading to a momentum-dependent departure from power law to decaying exponential behavior of the occupation numbers at large momentum. We also find signatures of the Efimov effect in the many-body dynamics and make a precise identification between the observed beating phenomenon and the binding energy of an Efimov trimer. Throughout the paper, our predictions for a uniform gas are quantitatively compared with experimental results for quenched unitary Bose gases in uniform potentials.
This thesis describes studies of out-of-equilibrium dynamics in an interacting homogeneous Bose gas. We use the versatile platform of an ultracold gas of 39^{39}39K, prepared in an optical box trap. The experiment features both tuneable interaction strengths and a homogeneous atomic density. We examine first a weakly interacting near-equilibrium system, followed by far-from-equilibrium dynamics under moderate interactions, and finally combine strong interactions with highly non-equilibrium dynamics in studies of the unitary Bose gas. We start with a theoretical study of the effects of three-body recombination on the temperature of a weakly interacting, partially condensed gas. Contrary to the expectation of heating, we find that for appropriate values of the condensed fraction and gas parameter, the system temperature is expected to decrease. Not only do we predict lower temperatures, however, but also for the condensate fraction to grow. We then present experiments in which we engineer a far-from-equilibrium momentum distribution, and study the dynamics as the gas relaxes. As the distribution evolves, we observe bidirectional dynamic scaling, with a flow of particles to lower momenta while energy is transported to higher ones. These flows are characterised by spatiotemporal scaling exponents, which we find do not vary appreciably over a range of moderate interaction strengths. Finally, we look to the unitary Bose gas, quenching clouds into the strongly interacting regime. This regime offers insight into universal behaviour that depends only on the interparticle spacing, as well as being an avenue for the study of Efimov physics. However, few things come for free; strongly interacting Bose systems are plagued by high atom-loss and heating rates. We study atom-loss rates and the dynamics of correlations in our gases, isolate the coherent effects from the dissipative ones, and identify a quasi-equilibrium state that features a non-zero condensate fraction.
Theoretical treatments of nonequilibrium dynamics in strongly interacting Bose-Fermi mixtures are complicated by the inherent non-Gaussian nature of the vacuum two-body physics, invalidating the typical Hartree-Fock-Bogoliubov approximation. Here we apply the cumulant expansion to study nonequilibrium Bose-Fermi mixtures, which allows us to explicitly include the missing non-Gaussian quantum correlations, leading to a consistent dynamical theory of a Bose-Fermi mixture near an interspecies Feshbach resonance. We first apply our theory to a study of atom-pair coherence in the gas, which is significantly enhanced by the competing influences of the Fermi sea and Bose-Einstein condensation, in agreement with analytical calculations. Then we study the depletion of a degenerate Bose-Fermi mixture following a quench to the unitary regime, characterizing the resulting depletion of the Bose-Einstein condensate, the deformation of the Fermi surface, and the production of molecules. We find that at early times, the population dynamics scale quadratically with the hold time, and define an associated characteristic timescale set by the parameters of the mixture and the width of the Feshbach resonance. Published by the American Physical Society 2024
We study the growth of two- and three-body correlations in an ultracold Bose gas quenched to unitarity. This is encoded in the dynamics of the two- and three-body contacts analyzed in this work. Via a set of relations connecting many-body correlation dynamics with few-body models, signatures of the Efimov effect are mapped out as a function of evolution time at unitarity over a range of atomic densities nnn. For the thermal resonantly interacting Bose gas, we find that atom bunching leads to an enhanced growth of few-body correlations. These atom-bunching effects also highlight the interplay between few-body correlations that occurs before genuine many-body effects enter on Fermi timescales.
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.
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 regime to the unitary regime. For the two-body problem, we establish a relation that connects the momentum distribution at a long time to a subleading 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 is 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 subleading term of the Bogoliubov wave function in the initial stages. Conceptually, our results show that, for quench to the universal regime and coherent quantum dynamics afterward, the universal longtime behavior is hidden in the initial state.