Quench Dynamics of Thermal Bose Gases Across Wide and Narrow Feshbach

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.