Application of stochastic processes for some effects in quantum optics

Lue Bouten

Philipp Strasberg

Abstract Processes at the nanoscale happen far away from the thermodynamic limit, far from equilibrium and are dominated by fluctuations and, perhaps, even quantum effects. This book establishes a consistent thermodynamic framework for such processes by combining tools from non-equilibrium statistical mechanics and the theory of open quantum systems. The book is accessible for graduate students and of interest to all researchers striving for a deeper understanding of the laws of thermodynamics beyond their traditional realm of applicability. It puts most emphasis on the microscopic derivation and understanding of key principles and concepts as well as their interrelation. The topics covered in this book include (quantum) stochastic processes, (quantum) master equations, local detailed balance, classical stochastic thermodynamics, (quantum) fluctuation theorems, strong coupling and non non-Markovian effects, thermodynamic uncertainty relations, operational approaches, Maxwell's demon and time-reversal symmetry, among other topics. Furthermore, the book treats a few applications in detail to illustrate the general theory and its potential for practical applications. These are single-molecule pulling experiments, quantum transport and thermoelectric effects in quantum dots, the micromaser and related set-ups in quantum optics.

B. Shore

A. A. Villaeys, Alex Boeglin, S. H. Lin

Stochastic theories have been used for a long time to describe relaxation as well as line-shape functions. Since the pioneering work of Kubo, these theories have gained considerable interest in the application to optical processes. While previous theories focused on stochastic descriptions of the relaxation, our emphasis is on the dynamics induced by stochastic interactions in a system undergoing relaxation and dephasing processes, including pure dephasing. All the theories based either on the Hilbert-space representation, or on the Liouvillian-space representation, but requiring spectral decomposition methods, are unable to describe these effects simultaneously. In this paper, the implications of the statistical properties of the stochastic variables on the dynamics are elucidated, and the general time evolution of a stochastic N-level system is established in the particular Markovian or weakly colored noise cases.

Heinz‐Peter Breuer, Francesco Petruccione

Abstract This chapter deals with a presentation of continuous measurement theory on the basis of the microscopic equations of quantum electrodynamics. The emphasis lies on the derivation of the quantum operations and the corresponding stochastic processes for various detection schemes directly from the Hamiltonian, which describes the interaction of the matter degrees of freedom with the quantized electromagnetic field. The chapter treats many examples and applications to atomic physics and quantum optics, such as dark state resonances and laser cooling of atoms. This example illustrates the interplay between incoherent processes and quantum interference effects which leads to the emergence of Lévy-type distributions for the atomic waiting time. Finally, dissipative phenomena in the dynamics of open quantum systems in strong driving fields are studied, for which appropriate master equations and stochastic wave function methods can be derived by employing a representation in terms of Floquet states.

C. Gerlach, F.‐J. Schütte, R. Tiebel