A theoretical framework is briefly reviewed that treats the multiple collisions that a quantum system undergoes with particles in its environment. The dynamics is governed by the quantum Lindblad master equation for the density matrix, which can be solved using a Monte Carlo technique. Its classical limit is identified and provides an opportunity to study the role of decoherence in the quantum to classical transition. Applications are discussed related to the dynamics of ions and atoms interacting with solids and gases, and Rydberg wavepackets subject to coloured noise.
A theoretical framework is briefly reviewed that treats the multiple collisions that a quantum system undergoes with particles in its environment. The dynamics is governed by the quantum Lindblad master equation for the density matrix, which can be solved using a Monte Carlo technique. Its classical limit is identified and provides an opportunity to study the role of decoherence in the quantum to classical transition. Applications are discussed related to the dynamics of ions and atoms interacting with solids and gases, and Rydberg wavepackets subject to coloured noise.
An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..
Master equations in the Lindblad form describe evolution of open quantum systems that are completely positive and simultaneously have a semigroup property. We analyze the possibility to derive this type of master equations from an intrinsically discrete dynamics that is modelled as a sequence of collisions between a given quantum system (a qubit) with particles that form the environment. In order to illustrate our approach we analyze in detail how the process of an exponential decay and the process of decoherence can be derived from a collision-like model in which particular collisions are described by SWAP and controlled-NOT interactions, respectively.
The theoretical description of materials' properties driven out of equilibrium has important consequences in various fields such as semiconductor spintronics, nonlinear optics, and continuous and discrete quantum information science and technology. The coupling of a quantum many-body system to an external bath can dramatically modify its dynamics compared to that of closed systems; new phenomena like relaxation and decoherence appear as a consequence of the non-unitary evolution of the quantum system. In addition, electron-electron correlations must be properly accounted for in order to go beyond a simple one-electron or mean-field description of the electronic system. Here, we discuss a first-principles methodology based on the evolution of the electronic density matrix capable of treating electron-environment interactions and electron-electron correlations at the same level of description. The effect of the environment is separated into a coherent contribution, like the coupling to applied external electromagnetic fields, and an incoherent contribution, like the interaction with lattice vibrations or the thermal background of radiation. Electron-electron interactions are included using the nonequilibrium Green's function plus the generalized Kadanoff-Baym ansatz. The obtained non-Markovian coupled set of equations reduces to the ordinary Lindblad quantum master equation form in the Markovian limit.
Abstract This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation, the text begins with a survey of classical probability theory and with an introduction to the foundations of quantum mechanics, with particular emphasis on its statistical interpretation and on the formulation of generalized measurement theory through quantum operations and effects. The fundamentals of density matrix theory, quantum Markov processes, and completely positive dynamical semigroups are developed. The most important master equations used in quantum optics and condensed matter theory are derived and applied to the study of many examples. Special attention is paid to the Markovian and non-Markovian theory of environment induced decoherence, its role in the dynamical description of the measurement process, and to the experimental observation of decohering electromagnetic field states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics. The fundamentals of the treatment of non-Markovian quantum processes in open systems are developed on the basis of various mathematical techniques, such as projection superoperator methods and influence functional techniques. In addition, the book expounds the relativistic theory of quantum measurements and the density matrix theory of relativistic quantum electrodynamics.
Quantum decoherence is widely regarded as the principal dynamical mechanism through which classical behaviour emerges from quantum dynamics. This review presents a technical account of decoherence as an open-system phenomenon, emphasizing its mathematical framework, microscopic models, experimental evidence, and foundational implications. Starting from system-environment interactions and reduced density operators, we introduce completely positive trace-preserving maps and Lindblad master equations. We then discuss pure dephasing, pointer-state selection, quantum Brownian motion, spin-boson dynamics, and collisional decoherence. Experimental evidence from atom and molecular interferometry, superconducting qubits, and mesoscopic platforms is examined. Finally, the review assesses the role of decoherence in the quantum measurement problem. Decoherence explains preferred-basis selection and practical suppression of interference, but it does not independently account for the occurrence of a unique measurement outcome.
We provide an alternative derivation of a master equation formalism for open quantum systems and apply it to illustrative examples. Using this formalism, we show that generally there can be interference between non-interacting baths on a system's reduced dynamics, confirming results in Phys. Rev. A 89, 042117 (2014). However, we also find that, up to second order, such interference vanishes as long as the baths are initially statistically independent, thereby identifying a satisfiable condition for non-interference. We use a two-dimensional series expansion method to develop a master equation formalism that deals with the effects of both system-environment interaction and classical noise on a system's dynamics in a unified manner. We apply this formalism to the example of a Zeeman-splitted atom in a stochastic B-field interacting with an optical cavity and find that the atom's total decoherence rate is, up to second order, a simple sum of the decoherence rate due to the atom-cavity interaction alone and that due to the stochastic B-field alone. We also develop a formalism for the dynamics of the (marginal) probability density of open classical systems in a similar fashion as the master equation formalism for open quantum systems.