论文标题
在时间依赖性陷阱中标尺不变的量子系统的非绝热能量波动
Nonadiabatic energy fluctuations of scale-invariant quantum systems in a time-dependent trap
论文作者
论文摘要
我们考虑了在时间依赖的谐波陷阱中多体系统的非绝热能量波动。在存在比例不变的情况下，动力学变得相似，并且可以根据哈密顿量第二矩的初始期望值，方形位置和挤压操作员的初始期望值找到非绝热的能量波动。非绝热特征是根据控制原子云的大小的缩放因子来表达的，该云的大小可以从飞行时间图像中提取。我们将此确切的关系应用于许多示例：单粒子谐波振荡器，一维Calogero-Sutherland模型，描述了具有逆方相互作用的玻色子，其中包括非相互作用的Bose Gas和Tonks-Girdardeau气体作为极限情况，以及单一的Fermi Gas。我们为各种膨胀方案说明了这些结果，涉及陷阱频率的突然淬火，线性坡道和绝热性快捷方式。我们的结果为驱动量子流体中非绝热能量波动的实验研究铺平了道路。
We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms of the initial expectation values of the second moments of the Hamiltonian, square position, and squeezing operators. Nonadiabatic features are expressed in terms of the scaling factor governing the size of the atomic cloud, which can be extracted from time-of-flight images. We apply this exact relation to a number of examples: the single-particle harmonic oscillator, the one-dimensional Calogero-Sutherland model, describing bosons with inverse-square interactions that includes the non-interacting Bose gas and the Tonks-Girdardeau gas as limiting cases, and the unitary Fermi gas. We illustrate these results for various expansion protocols involving sudden quenches of the trap frequency, linear ramps and shortcuts to adiabaticity. Our results pave the way to the experimental study of nonadiabatic energy fluctuations in driven quantum fluids.
