Mathew R, Tiesinga E
Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA.
Phys Rev A (Coll Park). 2017 Jul;96(1). doi: 10.1103/PhysRevA.96.013604. Epub 2017 Jul 5.
Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA), focus on the role of motion near separatrices, and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as (1/ln ), where is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady-state value is a damped oscillation. The damping is Gaussian in time with a time scale of [(ln )]. We also give the quantitative dependence of the steady-state value and the damping time on the system parameters. Our results are confirmed with numerical TWA simulations.
孤立量子系统中的猝灭目前是一个深入研究的课题。在这里，我们考虑在经典平均场极限下可积且在系统参数猝灭后变得动力学不稳定的量子少模系统。具体而言，我们研究了双阱势中的玻色 - 爱因斯坦凝聚体（BEC）以及限制在单个空间模式下的反铁磁自旋BEC。我们在截断维格纳近似（TWA）下研究猝灭后的时间动力学，关注分界线附近运动的作用，并发现由于相空间混合系统弛豫到稳态。以作用 - 角形式和摆为例，我们推导了可观测量期望值的时间演化及其长时间极限的一般解析表达式。我们发现长时间期望值与其经典值的偏差按(1/ln )缩放，其中 是凝聚体中的原子数。此外，可观测量弛豫到其稳态值是一种阻尼振荡。阻尼在时间上是高斯型的，时间尺度为[(ln )]。我们还给出了稳态值和阻尼时间对系统参数的定量依赖关系。我们的结果通过数值TWA模拟得到了证实。
