谐振子中的Floquet两体问题

Floquet two-body problem in a harmonic trap

由于近期在光诱导的Feshbach共振等实验技术上的发展,具有含时相互作用的量子气体的动力学问题引起了学界广泛的兴趣.人们已经在这一类超冷原子系统中观察到了一系列诸如Farady图案和玻色焰火等新颖的动力学行为.研究了具有周期性调节相互作用强度的谐振子势阱中的两原子动力学问题.虽然Hamilton量的时间依赖性,使系统的能量不再是一个守恒量,但仍然可以利用随时间周期变化的Hamilton量的Floquet理论定义其准能量.推导出了两体问题准能量的精确方程.通过数值求解这些方程,揭示了两体准能谱在不同驱动参数或频率下展现出的各种新颖的动力学行为.

The dynamics of quantum gases with time-varying interactions have attracted research interests owing to recent advances in experimental techniques such as optical Feshbach resonance.A range of novel dynamic behaviors including the Farady pattern and Bose fireworks have been observed in these systems.In this research,the dynamic problem of two harmonically trapped atoms with periodically modulating interaction strength is investigated.Because of the Hamiltonian time dependence,the system energy is an unconserved quantity.However,we may continue to utilize the Floquet theory for the time-periodic Hamiltonian and define its quasi-energy.The exact equations for the quasi-energies of the two-body problem are derived.Upon numerically solving these equations,we identify that the two-body quasi-energy spectrum exhibits various novel behaviors for different driven parameters or frequencies.