Ivander Felix, Anto-Sztrikacs Nicholas, Segal Dvira
Chemical Physics Theory Group, Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario, Canada M5S 3H6.
Department of Physics, 60 Saint George Street, University of Toronto, Toronto, Ontario, Canada M5S 1A7.
Phys Rev E. 2023 Jul;108(1-1):014130. doi: 10.1103/PhysRevE.108.014130.
We develop a perturbative technique for solving Markovian quantum dissipative dynamics, with the perturbation parameter being a small gap in the eigenspectrum. As an example, we apply the technique and straightforwardly obtain analytically the dynamics of a three-level system with quasidegenerate excited states, where quantum coherences persist for very long times, proportional to the inverse of the energy splitting squared. We then show how to bypass this long-lived coherent dynamics and accelerate the relaxation to thermal equilibration in a hyper-exponential manner, a Markovian quantum-assisted Mpemba-like effect. This hyperacceleration of the equilibration process manifests if the initial state is carefully prepared, such that its coherences precisely store the amount of population relaxing from the initial condition to the equilibrium state. Our analytical method for solving quantum dissipative dynamics readily provides equilibration timescales, and as such it reveals how coherent and incoherent effects interlace in the dynamics. It further advises on how to accelerate relaxation processes, which is desirable when long-lived quantum coherences stagnate dynamics.
我们开发了一种微扰技术来求解马尔可夫量子耗散动力学，微扰参数是本征谱中的一个小间隙。作为一个例子，我们应用该技术并直接解析地得到了具有准简并激发态的三能级系统的动力学，其中量子相干持续很长时间，与能量分裂平方的倒数成正比。然后我们展示了如何绕过这种长寿命的相干动力学，并以超指数方式加速弛豫到热平衡，即一种马尔可夫量子辅助的类姆潘巴效应。如果初始状态经过精心准备，使得其相干性精确地存储了从初始条件弛豫到平衡状态的粒子数，那么平衡过程的这种超加速就会显现出来。我们求解量子耗散动力学的解析方法很容易提供平衡时间尺度，因此它揭示了相干和非相干效应在动力学中是如何交织的。它还就如何加速弛豫过程提供了建议，当长寿命的量子相干使动力学停滞时，这是很有必要的。
