Quantum jumps and entropy production

The irreversible motion of an open quantum system can be represented through an ensemble of state vectors following a stochastic dynamics with piecewise deterministic paths. It is shown that this representation leads to a natural definition of the rate of quantum entropy production. The entropy production rate is expressed in terms of the von Neumann entropy and of the numbers of quantum jumps corresponding to the various decay channels of the open system. The proof of the positivity and of the convexity of the entropy production rate is given. Monte Carlo simulations of the stochastic dynamics of a driven qubit and of a $\Lambda$-configuration involving a dark state are performed in order to illustrate the general theory.Comment: 7 pages, 2 figure

The non-Markovian quantum behavior of open systems: An exact Monte Carlo method employing stochastic product states

It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo wave function method that enables the stochastic treatment of the full non-Markovian behavior of open quantum systems. Numerical simulations are carried out which demonstrate that the method is applicable to open systems strongly coupled to a bosonic reservoir, as well as to the interaction with a spin bath. Full details of the simulation algorithms are given, together with an investigation of the dynamics of fluctuations. Several potential generalizations of the method are outlined.Comment: 14 pages, 5 figure

Quantum Semi-Markov Processes

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow the treatment of a variety of physical systems, as is illustrated by means of various examples and applications, including quantum optical systems and models of quantum transport.Comment: 4 pages, revtex, no figures, to appear in Phys. Rev. Let

Revealing correlations between a system and an inaccessible environment

How can we detect that our local, controllable quantum system is correlated with some other inaccessible environmental system? The local detection method developed in recent years allows to realize a dynamical witness for correlations without requiring knowledge of or access to the environment that is correlated with the local accessible quantum system. Here, we provide a brief summary of the theoretical method and recent experimental studies with single photons and trapped ions coupled to increasingly complex environments.Comment: 12 pages, 3 figure

Structure of completely positive quantum master equations with memory kernel

Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is demonstrated to yield quantum master equations with memory kernels which allow the formulation of explicit conditions for the complete positivity of the corresponding quantum dynamical maps, thus leading to important insights into the structural characterization of the non-Markovian quantum dynamics of open systems. Explicit examples are analyzed in detail.Comment: 13 pages, revtex, 2 figure

Concepts and methods in the theory of open quantum systems

The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting from the appropriate characterization of the quantum statistical ensembles naturally arising in the description of open quantum systems, the corresponding dynamical evolution equations are derived for the Markovian as well as for the non-Markovian case.Comment: 15 pages, 7 figures, conference proceedings, to be published in: Irreversible Quantum Dynamics, Lecture Notes in Physics, F. Benatti and R. Floreanini (Eds