Dynamical invariant based shortcut to equilibration in open quantum systems

TL;DR

This paper introduces a method using dynamical invariants to accelerate the equilibration process in open quantum systems, enabling faster control of quantum states without additional timescale constraints.

Contribution

It develops a systematic protocol leveraging Lewis-Riesenfeld invariants to shortcut equilibration in open quantum systems, demonstrated on a damped harmonic oscillator.

Findings

Achieves high-fidelity control in shorter timescales

Demonstrates a quantum analogue of the Mpemba effect

Provides a general approach applicable to quantum engines

Abstract

We propose using the dynamical invariant also known as the Lewis-Riesenfeld invariant, 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 it with the damped harmonic oscillator, and show that our protocol can achieve a high-fidelity control in 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.