Quench Dynamics of Thermal Bose Gases Across Wide and Narrow Feshbach

TL;DR

This paper investigates the quench dynamics of thermal Bose gases near different Feshbach resonances using virial expansion, revealing how bound states influence oscillations in long-time behavior across various resonance types.

Contribution

It provides a detailed analysis of quench dynamics near wide, narrow, and intermediate Feshbach resonances, highlighting the role of shallow bound states and background scattering length in oscillation phenomena.

Findings

Long-time oscillations occur near wide Feshbach resonance with finite positive scattering length.

Oscillations vanish when scattering length is quenched to infinity or negative.

Presence of oscillations depends on background scattering length and resonance type.

Abstract

Using high-temperature virial expansion, we study the quench dynamics of the thermal Bose gases near a wide, narrow, and intermediate Feshbach resonance. Our results show that the shallow bound state near Feshbach resonance leads to interesting phenomena. Near the wide Feshbach resonance, the long-time $\hat{n}_{\bf k}$ oscillates when the scattering length $a_{s}$ is quenched from zero to large but with finite positive values. The oscillation frequency $\omega=E_{\rm b}/\hbar$ with $E_{\rm b}$ being the binding energy. When $a_{s}$ is quenched to infinity or negative value, the oscillation vanishes. Near the narrow Feshbach resonance, the interaction should be characterized by a two-channel model. When the background scattering length $a_{\rm bg}\gtrsim\lambda$, there is an oscillation in the long-time dynamics, and the frequency is determined by the energy of the shallow bound state in the open channel. When $a_{\rm bg}<0$ or $0<a_{\rm bg}\ll\lambda$, there is no shallow bound state in the open channel, hence no long-time oscillation. We check our conclusion using some realistic systems, and the results are consistent with our conclusion.