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Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms

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

Tatsuya Minami, Carlos O Reinhold, Joachim Burgdörfer

Published May 1, 2003• 0 citations
Publisher
DOI
10.1016/s0168-583x(03)00531-7

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We present a theoretical framework for the evolution of the internal state of a fast highly charged one-electron ion traversing an amorphous solid. We employ an open quantum system approach which incorporates the complex array of collisions with electrons and ionic cores in the solid within the framework of system-reservoir interactions. Interactions with the solid environment and the radiation field are treated on the same footing and the quantum master equation for the reduced density matrix of the electronic state of the ion is approximated by a Lindblad equation. The latter allows the solution of this multistate problem in terms of Monte Carlo sampling of quantum trajectories. Similarities and extensions to methods used in quantum optics and previously employed in ion-solid interactions are discussed. Our focus is on the transient buildup and destruction of coherences by stochastic processes. We apply our method to the study of coherence properties of the internal state of a fast Kr35+{\mathrm{Kr}}^{35+}Kr35+ ion traversing carbon foils. Simulations exhibit clear signatures of partially coherent transitions and are found to be in good agreement with experimental data.
We have developed a generalized nonunitary Lindblad equation and its quantum trajectory Monte Carlo implementation for the evolution of open quantum systems (OQSs) whose coupling to the environment features not only energy exchange but also probability flux to the environment. This generalization allows the treatment of a class of problems where the state space of the system includes bound and continuum states. We show the equivalence between the solution of the generalized Lindblad equation and the Monte Carlo average over open quantum trajectories. As a first test case we study the multilevel radiative decay of a hydrogenic ion. As a second test case we apply the theory to the time development of the internal state of fast highly charged Kr35+{\mathrm{Kr}}^{35+}Kr35+ ions traversing carbon foils with varying thickness subject to collisions and to spontaneous radiative decay. We find significantly improved agreement of the nonunitary transport theory with experimental data.
Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011)]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.