Sufficient conditions for adiabaticity in open quantum systems

TL;DR

This paper establishes simple, general sufficient conditions for the validity of the adiabatic approximation in open quantum systems, extending the concept beyond closed systems and applying it to quantum thermodynamics and quantum control.

Contribution

It introduces the first comprehensive set of conditions for adiabaticity in open quantum systems, applicable to arbitrary initial states and evolving under local master equations.

Findings

Adiabatic approximation is compatible with thermal equilibrium in open systems.

Conditions effectively evaluate adiabaticity in quantum control scenarios.

Results extend adiabatic theory to realistic, dissipative quantum environments.

Abstract

The adiabatic approximation exhibits wide applicability in quantum mechanics, providing a simple approach for nontransitional dynamics in quantum systems governed by slowly varying time-dependent Hamiltonians. However, the standard adiabatic theorem is specifically derived for closed quantum systems. In a realistic open system scenario, the inevitable system-reservoir interaction must be taken into account, which strongly impacts the generalization of the adiabatic behavior. In this paper, we introduce sufficient conditions for the adiabatic approximation in open quantum systems. These conditions are simple yet general, providing a suitable instrument to investigate adiabaticity for arbitrary initial mixed states evolving under time local master equations. We first illustrate our results by showing that the adiabatic approximation for open systems is compatible with the description of quantum thermodynamics at thermal equilibrium, where irreversible entropy production is vanishing. We also apply our sufficient conditions as a tool in quantum control, evaluating the adiabatic behavior for the Hamiltonians of both the Deutsch algorithm and the Landau-Zener model under decoherence.