Beau Mathieu, Del Campo Adolfo
Department of Physics, University of Massachusetts, Boston, MA 02125, USA.
Donostia International Physics Center, E-20018 San Sebastián, Spain.
Entropy (Basel). 2020 Apr 30;22(5):515. doi: 10.3390/e22050515.
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.
我们考虑处于随时间变化的谐振子势阱中的多体系统的非绝热能量涨落。在存在标度不变性的情况下，动力学变得自相似，并且非绝热能量涨落可以根据哈密顿量、平方位置和压缩算符的二阶矩的初始期望值来确定。非绝热特征通过控制原子云大小的标度因子来表示，该标度因子可从飞行时间图像中提取。我们将这个精确关系应用于多个例子：单粒子谐振子、一维卡洛杰罗 - 萨瑟兰模型，该模型描述具有平方反比相互作用的玻色子，其中包括非相互作用玻色气体和汤克斯 - 吉拉尔代奥气体作为极限情况，以及幺正费米气体。我们针对涉及阱频率突然猝灭、线性斜坡和绝热捷径的各种膨胀协议说明了这些结果。我们的结果为驱动量子流体中非绝热能量涨落的实验研究铺平了道路。
