A time dependent Markovian master equation for adiabatic systems and its application to the Cooper pair pumping

TL;DR

This paper derives a time-dependent Markovian master equation for adiabatic, periodically driven dissipative quantum systems using Floquet theory, highlighting its application to Cooper pair pumping and the limitations of the secular approximation.

Contribution

It introduces a novel time-dependent master equation that explicitly accounts for Hamiltonian time dependence, improving accuracy in modeling adiabatic quantum systems.

Findings

The derived master equation accurately models the quantum state evolution.

The secular approximation fails to predict the pumped charge accurately.

Non-Lindblad equations beyond the rotating wave approximation are necessary for charge calculations.

Abstract

For adiabatically and periodically manipulated dissipative quantum systems we derive, using Floquet theory, a simple Markovian master equation. Contrary to some previous works we explicitly take into account the time dependence of the Hamiltonian and, therefore, obtain a master equation with a time-dependent dissipative part. We illustrate our theory with two examples and compare our results with the previously proposed master equations. In particular, we consider the problem of Cooper pair pumping and demonstrate the inadequacy of the secular (rotating wave) approximation when calculating the pumped charge. The secular approximation producing a master equation of the Lindblad type approximates well the quantum state (density matrix) of the system, while to determine the pumped charge a non-Lindblad master equation beyond the rotating wave approximation is necessary.