Quench Dynamics of Thermal Bose Gases Across Wide and Narrow Feshbach

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 ${\widehat{n}}_{\mathbf{k}}$ oscillates when the scattering length $a_s$ is quenched from zero to large but with finite positive values. The oscillation frequency $\omega =E_{\mathrm{b}}\mathrm{/}\mathrm{\hslash }$ with $E_{\mathrm{b}}$ 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 $a_{\mathrm{b}\mathrm{g}}\gtrsim \lambda$, 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 $a_{\mathrm{b}\mathrm{g}}<0$ or $0<a_{\mathrm{b}\mathrm{g}}\ll \lambda$, 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.