We propose using the dynamical invariants, also known as the Lewis–Riesenfeld invariants, to speed-up the equilibration of a driven open quantum system. This allows us to reverse engineer the time-dependent master equation that describes the dynamics of the open quantum system and systematically derive a protocol that realizes a shortcut to equilibration. The method does not require additional constraints on the timescale of the dynamics beside the Born–Markov approximation and can be generically applied to boost single particle quantum engines significantly. We demonstrate this with the damped harmonic oscillator, and show that our protocol can achieve high-fidelity control on shorter timescales than simple non-optimized protocols. We find that the system is heated during the dynamics to speed-up the equilibration, which can be considered as an analogue of the Mpemba effect in quantum control.

中文翻译：

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开放量子系统中基于动力学不变量的平衡捷径


我们建议使用动力学不变量（也称为 Lewis-Riesenfeld 不变量）来加速驱动开放量子系统的平衡。这使我们能够对描述开放量子系统动力学的时间依赖性主方程进行逆向工程，并系统地推导出实现平衡捷径的协议。除了 Born-Markov 近似之外，该方法不需要对动力学的时间尺度进行额外约束，并且可以普遍应用于显着提升单粒子量子引擎。我们用阻尼谐振子证明了这一点，并表明我们的协议可以在比简单的非优化协议更短的时间内实现高保真控制。我们发现系统在动力学过程中被加热以加速平衡，这可以被认为是量子控制中 Mpemba 效应的类似物。