We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

中文翻译：

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玻色-爱因斯坦凝聚物的周期性和准周期性驱动动力学

我们研究了在Bogoliubov框架内周期性地或准周期性地调节散射长度时，玻色-爱因斯坦凝聚体的量子动力学。对于周期性驱动的情况，我们考虑调制为方波或正弦波的两种协议。在两个协议中，对于每个固定动量，都有加热阶段和非加热阶段，以及它们之间的相位边界。这两个阶段的区别在于受激粒子的数量是否呈指数增长。对于准周期驱动的情况，我们再次考虑两种协议：方波准周期，其中几乎所有参数都产生了与斐波纳契型准晶体类似的激励。和正弦波准周期，其中非加热阶段存在一个有限的量度参数范围。