Path integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative system

TL;DR

This paper introduces a numerical path-integral method for accurately modeling the combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems, applicable to quantum dots and phonon interactions.

Contribution

It develops a general, numerically exact path-integral approach that incorporates both microscopic environmental couplings and Markovian processes in quantum dissipative systems.

Findings

Successfully modeled quantum dot dynamics with phonon coupling and radiative decay.

Extended the path-integral method to include cavity photon losses.

Demonstrated the approach's effectiveness in realistic quantum systems.

Abstract

We present a numerical path-integral iteration scheme for the low dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modelled pure-dephasing type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.