Master Equation and Control of an Open Quantum System with Leakage

TL;DR

This paper derives an exact master equation for open quantum systems with leakage, enabling effective control of decoherence and leakage through pulse techniques, with practical applications demonstrated on harmonic oscillators.

Contribution

It introduces a trace-nonpreserving master equation for subspace leakage, providing a new framework for analyzing and controlling leakage in open quantum systems.

Findings

Leakage can be effectively suppressed by pulse control techniques.

A one-dimensional master equation suffices for quantum state storage problems.

The approach accurately models leakage and decoherence in harmonic oscillators.

Abstract

Given a multilevel system coupled to a bath, we use a Feshbach P,Q partitioning technique to derive an exact trace-nonpreserving master equation for a subspace $\mathcal{S}_{i}$ of the system. The resultant equation properly treats the leakage effect from $\mathcal{S}_{i}$ into the remainder of the system space. Focusing on a second-order approximation, we show that a one-dimensional master equation is sufficient to study problems of quantum state storage and is a good approximation, or exact, for several analytical models. It allows a natural definition of a leakage function and its control, and provides a general approach to study and control decoherence and leakage. Numerical calculations on an harmonic oscillator coupled to a room temperature harmonic bath show that the leakage can be suppressed by the pulse control technique without requiring ideal pulses.