Numerical time propagation of quantum systems in radiation fields

TL;DR

This paper introduces an efficient numerical method using commutator-free exponential propagators for solving time-dependent quantum system equations, demonstrated on a driven dissipative Dicke model.

Contribution

It presents an optimized fourth order propagator that improves computational efficiency for large quantum systems with time-dependent Hamiltonians.

Findings

The new propagator outperforms Runge-Kutta methods in efficiency.

Effective simulation of driven dissipative quantum systems.

Accurate calculation of steady states and emission spectra.

Abstract

Atoms, molecules or excitonic quasiparticles, for which excitations are induced by external radiation fields and energy is dissipated through radiative decay, are examples of driven open quantum systems. We explain the use of commutator-free exponential time-propagators for the numerical solution of the associated Schr\"odinger or master equations with a time-dependent Hamilton operator. These time-propagators are based on the Magnus series but avoid the computation of commutators, which makes them suitable for the efficient propagation of systems with a large number of degrees of freedom. We present an optimized fourth order propagator and demonstrate its efficiency in comparison to the direct Runge-Kutta computation. As an illustrative example we consider the parametrically driven dissipative Dicke model, for which we calculate the periodic steady state and the optical emission spectrum.