Numerical time propagation of quantum systems in radiation fields

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 Schrödinger 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.

arXiv comment23 pages, 11 figures

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• Entanglement properties of Floquet Chern insulators
• Ultrafast control of spin-orbital separation probed with time-resolved RIXS
• Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators
• Efficient Magnus-type integrators for solar energy conversion in Hubbard models
• Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap based quantum simulator
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• Energy and particle currents in a driven integrable system
• Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology
• Anomalous behavior of control pulses in presence of noise with singular autocorrelation