论文标题
通过广泛的Ermakov方程的精确溶液，与交互的Bose-Einstein冷凝物的绝热捷径快捷方式
Shortcuts to adiabaticity for an interacting Bose-Einstein condensate via exact solutions of the generalized Ermakov equation
论文作者
论文摘要
通过结合变异近似和反向工程的技术，研究了对有效的一维玻色凝结物（BEC）的绝热膨胀的快捷方式。分段 - 恒定（不连续的）中间陷阱频率，类似于最佳控制理论中已知的Bang-Bang形式，源自广义Ermakov方程的精确解决方案。本文中考虑的控制方案包括短时间尺度上的假想陷阱频率，即被二次排斥的HO电位代替。考虑到BEC的内在非线性，报告了最小传输时间，激发能量（衡量与有效绝热性的偏差）以及快捷性到糖化方案的稳定性的结果。这些结果不仅可用于实现快速无摩擦冷却，还有助于解决量子速度极限和热力学的基本问题。
Shortcuts to adiabatic expansion of the effectively one-dimensional Bose-Einstein condensate (BEC) loaded in the harmonic-oscillator (HO) trap is investigated by combining techniques of the variational approximation and inverse engineering. Piecewise-constant (discontinuous) intermediate trap frequencies, similar to the known bang-bang forms in the optimal-control theory, are derived from an exact solution of a generalized Ermakov equation. Control schemes considered in the paper include imaginary trap frequencies at short time scales, i.e., the HO potential replaced by the quadratic repulsive one. Taking into regard the BEC's intrinsic nonlinearity, results are reported for the minimal transfer time, excitation energy (which measures deviation from the effective adiabaticity), and stability for the shortcut-to-adiabaticity protocols. These results are not only useful for the realization of fast frictionless cooling, but also help to address fundamental problems of the quantum speed limit and thermodynamics.
