Effective operator formalism for open quantum systems

TL;DR

This paper introduces an effective operator formalism for open quantum systems that simplifies the dynamics to ground states using perturbation theory and adiabatic elimination, enabling easier analysis and control.

Contribution

It develops a new formalism that derives effective master equations with simplified operators for ground-state dynamics in open quantum systems.

Findings

Effective equations involve a single Hamiltonian and Lindblad operator per decay process.

Derived simple expressions for effective operators applicable to various systems.

Demonstrated the formalism with examples including dissipative state preparation.

Abstract

We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method with the hitherto existing concepts for effective interactions and present physical examples for the application of our formalism, including dissipative state preparation by engineered decay processes.