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arXiv:2301.06028 · Physical Review A

Quench dynamics of thermal Bose gases across wide and narrow Feshbach resonances

Xiaoyi Yang, Ren Zhang

Published Jun 21, 2023• 1 citation
arXivHTMLPDF

Abstract

Using high-temperature virial expansion, we study the quench dynamics of the thermal Bose gases near wide, narrow, and intermediate Feshbach resonances. Our results show that the shallow bound state near Feshbach resonances leads to oscillation of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\mathbf{k}}$. Near the wide Feshbach resonance, the long-time momentum distribution ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\mathbf{k}}$ oscillates when the scattering length ${a}_{s}$ is quenched to large but with finite positive values. The oscillation frequency is determined by the bound-state energy. When ${a}_{s}$ is quenched to infinity or negative value, the oscillation vanishes. Near the narrow Feshbach resonance, when the background scattering length ${a}_{\mathrm{bg}}$ is larger than de Broglie wave length $\ensuremath{\lambda}$, there is an oscillation, and the frequency is determined by the energy of the shallow bound state in the open channel. When ${a}_{\mathrm{bg}}<0$ or $0<{a}_{\mathrm{bg}}\ensuremath{\ll}\ensuremath{\lambda}$, there is no shallow bound state in the open channel, and hence no oscillation. We check our conclusion using some realistic systems, and the results are consistent with our conclusion.

DOI
10.1103/physreva.107.063310

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Using high-temperature virial expansion, we study the quench dynamics of the thermal Bose gases near wide, narrow, and intermediate Feshbach resonances. Our results show that the shallow bound state near Feshbach resonances leads to oscillation of n\ifmmode^\elseˆ\fik{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\mathbf{k}}n\ifmmode^\elseˆ\fik​. Near the wide Feshbach resonance, the long-time momentum distribution n\ifmmode^\elseˆ\fik{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\mathbf{k}}n\ifmmode^\elseˆ\fik​ oscillates when the scattering length as{a}_{s}as​ is quenched to large but with finite positive values. The oscillation frequency is determined by the bound-state energy. When as{a}_{s}as​ is quenched to infinity or negative value, the oscillation vanishes. Near the narrow Feshbach resonance, when the background scattering length abg{a}_{\mathrm{bg}}abg​ is larger than de Broglie wave length \ensuremathλ\ensuremath{\lambda}\ensuremathλ, there is an oscillation, and the frequency is determined by the energy of the shallow bound state in the open channel. When abg<0{a}_{\mathrm{bg}}<0abg​<0 or 0<abg\ensuremath≪\ensuremathλ0<{a}_{\mathrm{bg}}\ensuremath{\ll}\ensuremath{\lambda}0<abg​\ensuremath≪\ensuremathλ, there is no shallow bound state in the open channel, and hence no oscillation. We check our conclusion using some realistic systems, and the results are consistent with our conclusion.
High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this Letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from noninteracting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for the low-momentum part with k<k^{*}, and increases for high-momentum part with k>k^{*}, where k^{*} is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of k^{*}λ that agrees perfectly with the experiment, with λ being the thermal de Broglie wavelength. We also find a jump of the halfway relaxation time across k^{*}λ and the nonmonotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the longtime steady state thermalizes or not, and we find that this state reaches a partial thermalization, namely, it thermalizes for the low-energy part with kλ≲1 but does not thermalize for the very high momentum tail with kλ≫1. Our framework can also be applied to quench dynamics in other systems.
Quench experiments on a unitary Bose gas around a broad Feshbach resonance have led to the discovery of universal dynamics. This universality manifests in the measured atomic momentum distributions, where, asymptotically, a quasiequilibrated metastable state is found in which both the momentum distribution and the timescales are determined by the particle density. In this Letter we present counterpart studies for the case of a very narrow Feshbach resonance of Cs 133 atoms with a width of 8.3 mG. In dramatic contrast to the behavior reported earlier, a rapid quench of an atomic condensate to unitarity is observed to ultimately lead to coherent oscillations involving dynamically produced condensed and noncondensed molecules and atoms. The same characteristic frequency, determined by the Feshbach coupling, is observed in all types of particles. To understand these quench dynamics and how these different particle species are created, we develop a beyond Hartree-Fock-Bogoliubov dynamical framework including a type of cross-correlation between atoms and molecules. This leads to quantitative consistency with the measured frequency. Our results, which can be applied to the general class of bosonic superfluids associated with narrow Feshbach resonances, establish a alternate paradigm for universal dynamics dominated by quantum many-body interactions.
Recent advances in the tunability of ultracold atomic gases have created opportunities for studying interesting quantum many-body systems. Fano-Feshbach resonances, in particular, allow experimenters to freely adjust the scattering of atoms by controlling an external magnetic field. By rapidly changing this field near a resonance, it is possible to drive systems out of equilibrium towards novel quantum states where correlations between atoms change dynamically. In this thesis, we take a wave-function-based approach to theoretically examine the response of several interesting systems to suddenly-switched, or "quenched", interactions.\nWe first calculate the time evolution of a Bose-Einstein condensate that is quenched to the unitarity regime, where the scattering length 'a' diverges. Working within the time-dependent variational formalism, we find that the condensate does not deplete as quickly as the usual Bogoliubov theory would suggest. We also make a quantitative prediction for the dynamics of short-range pair correlations, encoded in Tan's contact. We then consider the dynamics of these correlations for quenches to small 'a', and we find that bound states can cause high-contrast oscillations of the contact. These dynamics can be modelled quantitatively at short times by using a properly-chosen two-body model. Finally, we characterize the nonlocal correlation waves that are generated by an interaction quench in arbitrary dimensionality. Our analysis demonstrates that the large-momentum limit of the post-quench momentum distribution can sometimes include contributions from both the short range and the long range, depending on the quench protocol.
Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value by many-body effects. When the scattering length as{a}_{s}as​ of the atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However, at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse.
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.
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.