Quantum trajectory Monte Carlo method describing the coherent dynamics of highly charged ions

Abstract

We present a theoretical framework for studying dynamics of open quantum systems. Our formalism gives a systematic path from Hamiltonians constructed by first principles to a Monte Carlo algorithm. Our Monte Carlo calculation can treat the build-up and time evolution of coherences. We employ a reduced density matrix approach in which the total system is divided into a system of interest and its environment. An equation of motion for the reduced density matrix is written in the Lindblad form using an additional approximation to the Born–Markov approximation. The Lindblad form allows the solution of this multi-state problem in terms of Monte Carlo sampling of quantum trajectories. The Monte Carlo method is advantageous in terms of computer storage compared to direct solutions of the equation of motion. We apply our method to discuss coherence properties of the internal state of a Kr35+ ion subject to spontaneous radiative decay. Simulations exhibit clear signatures of coherent transitions.