Non-unitary master equation for the internal state of ions traversing solids

We present a new method describing the time development of the internal state of fast highly charged ions subject to collisions and to spontaneous radiative decay during transport through solids. Our method describes both the build-up of coherences and the decoherence of the open quantum system due to the interaction with its environment. The dynamics of the reduced density matrix is governed by a Lindblad master equation that can be solved by Monte Carlo sampling techniques. In practice, the standard Lindblad equation can be of limited value because it describes strictly unitary time transformations of the reduced density matrix. We have developed a generalized non-unitary Lindblad form (and its Monte Carlo implementation) for the evolution in finite subspaces in which the coupling to the complement is taken into account. We use the radiative decay of a free hydrogenic atom in vacuum as a simple test case. We present an application for Kr35+ ions traversing carbon foils with varying thickness and compare our results with experiments.