Going beyond quantum Markovianity and back to reality: An exact master equation study

TL;DR

This paper provides an exact analytical description of non-Markovian open quantum system dynamics, revealing complex behaviors like the Mpemba effect and demonstrating pulse control's ability to manage decoherence without approximations.

Contribution

It introduces an exact master equation approach for non-Markovian dynamics, moving beyond typical Markovian approximations and exploring new phenomena like the Mpemba effect in quantum systems.

Findings

Rapid increase of steady-state excitation number with non-Markovianity

Pulse control prolongs or speeds up relaxation depending on parameters

Observation of the Mpemba effect in quantum non-Markovian dynamics

Abstract

The precise characterization of dynamics in open quantum systems often presents significant challenges, leading to the introduction of various approximations to simplify a model. One commonly used strategy involves Markovian approximations, assuming a memoryless environment. In this study, such approximations are not used and an analytical dynamical depiction of an open quantum system is provided. The system under consideration is an oscillator that is surrounded by a bath of oscillators. The resulting dynamics are characterized by a second-order complex coefficient linear differential equation, which may be either homogeneous or inhomogeneous. Moreover, distinct dynamical regions emerge, depending on certain parameter values. Notably, the steady-state average excitation number (AEN) of the system shows rapid escalation with increasing non-Markovianity, reflecting the intricacies of real-world dynamics. In cases where there is detuning between the system frequency and the environmental central frequency within a non-Markovian regime, the AEN maintains its initial value for an extended period. Furthermore, the application of pulse control can effectively protect the quantum system from decoherence effects without using approximations. The pulse control can not only prolong the relaxation time of the oscillator, but can also be used to speed up the relaxation process, depending on the specifications of the pulse. By employing a kick pulse, the Mpemba effect can be observed in the non-Markovian regime in a surprisingly super-cooling-like effect.