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arXiv:2408.08415 · Physical Review Research

Universal coherent atom-molecule oscillations in the dynamics of the unitary Bose gas near a narrow Feshbach resonance

Ke Wang, Zhendong Zhang, Shu Nagata, Zhiqiang Wang, Kathryn Levin

Published Feb 5, 2025• 6 citations
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Abstract

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.

DOI
10.1103/physrevresearch.7.l012025

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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.
The recent observations of a stable molecular condensate emerging from a condensate of bosonic atoms and related ``super-chemical'' dynamics have raised an intriguing set of questions. Here we provide a microscopic understanding of this unexpected stability and dynamics in atom-molecule superfluids; we show one essential element behind these phenomena is an extremely narrow Feshbach resonance in 133Cs^{133}\mathrm{Cs}133Cs at 19.849G. Comparing theory and experiment, we demonstrate how this narrow resonance enables the dynamical creation of a large closed-channel molecular fraction superfluid, appearing in the vicinity of unitarity. Theoretically, the observed superchemistry (i.e., Bose-enhanced reactions of atoms and molecules) is found to be assisted by the formation of Cooper-like pairs of bosonic atoms that have opposite momenta. Importantly, this narrow resonance opens the possibility to explore the quantum critical point of a molecular Bose superfluid and related phenomena which would not be possible near a more typically broad Feshbach resonance.
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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.
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 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 $\ensuremath{\lambda}$, 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 $0<{a}_{\mathrm{bg}}\ensuremath{\ll}\ensuremath{\lambda}$, 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.
We create atom-molecule superpositions in a Bose-Fermi mixture of 87Rb^{87}\text{R}\text{b}87Rb and 40K^{40}\text{K}40K atoms. The superpositions are generated by ramping an applied magnetic field near an interspecies Fano-Feshbach resonance to coherently couple atom and molecule states. Rabi- and Ramsey-type experiments show oscillations in the molecule population that persist as long as $150\text{ }\ensuremath{\mu}\text{s}$ and have up to 50% contrast. The frequencies of these oscillations are magnetic-field dependent and consistent with the predicted molecule binding energy. This quantum superposition involves a molecule and a pair of free particles with different statistics (i.e., bosons and fermions) and furthers exploration of atom-molecule coherence in systems without a Bose-Einstein condensate.
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.