We propose an optical ring interferometer to observe environment-induced spatial decoherence of massive objects. The object is held in a harmonic trap and scatters light between degenerate modes of a ring cavity. The output signal of the interferometer permits to monitor the spatial width of the object's wave function. It shows oscillations that arise from coherences between energy eigenstates and that reveal the difference between pure spatial decoherence and that coinciding with energy transfer and heating. Our method is designed to work with a wide variety of masses, ranging from the atomic scale to nano-fabricated structures. We give a thorough discussion of its experimental feasibility.
According to the eigenstate thermalization ansatz, matrices representing generic few body observables take on a specific form when displayed in the eigenbasis of a chaotic Hamiltonian. We examine the effect of environmental induced decoherence on the dynamics of observables that conform with said eigenstate thermalization ansatz. The obtained result refers to a description of the dynamics in terms of an integro-differential equation of motion of the Nakajima-Zwanzig form. We find that environmental decoherence is equivalent to an exponential damping of the respective memory kernel. This statem…
We introduce the quantitative measures characterizing the rates of decoherence and thermalization of quantum systems. We study the time evolution of these measures in the case of a quantum harmonic oscillator whose relaxation is described in the framework of the standard master equation, for various initial states (coherent, `cat', squeezed and number). We establish the conditions under which the true decoherence measure can be approximated by the linear entropy $1-{Tr}\hatρ^2$. We show that at low temperatures and for highly excited initial states the decoherence process consists of three dis…
We study the decoherence and thermalization dynamics of a nanoscale system coupled nonperturbatively to a fully quantum-mechanical bath. The system is prepared out of equilibrium in a pure state of the complete system. We propose a random matrix model and show analytically that there are two robust temporal regimes in the approach of the system to equilibrium --- an initial Gaussian decay followed by an exponential tail, consistent with numerical results on small interacting lattices [S. Genway, A.F. Ho and D.K.K. Lee, Phys. Rev. Lett. 105, 260402 (2010)]. Furthermore, the system decays toward…
We present a rigorous analysis of the phenomenon of decoherence for general N-level systems coupled to reservoirs of free massless bosonic fields. We apply our general results to the specific case of the qubit. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.
We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced density matrix to a fully decoherent state, and furthermore the diagonal elements of the reduced density matrix approach those expected for the system in the canonical ensemble. We show one exception to the normal case is if the spin system cannot exchange energy with the spin bath. Our demonstrati…
We study measures of decoherence and thermalization of a quantum system $S$ in the presence of a quantum environment (bath) $E$. The entirety $S$$+$$E$ is prepared in a canonical thermal state at a finite temperature, that is the entirety is in a steady state. Both our numerical results and theoretical predictions show that measures of the decoherence and the thermalization of $S$ are generally finite, even in the thermodynamic limit, when the entirety $S$$+$$E$ is at finite temperature. Notably, applying perturbation theory with respect to the system-environment coupling strength, we find tha…
We present a rigorous analysis of the phenomenon of decoherence for general $N-$level systems coupled to reservoirs. The latter are described by free massless bosonic fields. We apply our general results to the specific cases of the qubit and the quantum register. We compare our results with the explicitly solvable case of systems whose interaction with the environment does not allow for energy exchange (non-demolition, or energy conserving interactions). We suggest a new approach which applies to a wide variety of systems which are not explicitly solvable.
In this review, we discuss the decoherence and thermalization of a quantum spin system interacting with a spin bath environment, by numerically solving the time-dependent Schrödinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density mat…
We study measures of decoherence and thermalization of a quantum system $S$ in the presence of a quantum environment (bath) $E$. The whole system is prepared in a canonical thermal state at a finite temperature. Applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider the uncoupled system to predict decoherence and thermalization measures of $S$. This decoupling allows closed form expressions for perturbative expansions for the measures of deco…
Choosing a specific way of dividing a closed system into parts is a starting point for the decoherence program and for the quantum thermalization program. It is shown that one can always chose such way of partitioning that decoherence-assisted classicality does not emerge and thermalization does not occur. Implications of this result are discussed.
We study the decoherence and thermalization of an Unruh-DeWitt detector linearly coupled to the free massless scalar field in flat spacetime of arbitrary dimensions ($d\geq 2$). The initial state of the detector is chosen to be a pure state consisting of a linear superposition of ground and excited states, and we calculate the time evolution of reduced density matrix of the detector. Using perturbation method, we analytically derive the transition rate of the detector (the rate of change of the diagonal elements in the density matrix) and the decoherence rate (the rate of change of the off-dia…
Despite the fact that a system created in relativistic heavy ion collisions is an isolated quantum system, which cannot increase its entropy in the course of unitary quantum evolution, hydrodynamical analysis of experimental data seems to indicate that the matter formed in the collisions is thermalized very quickly. Based on common consideration of hydrodynamics as an effective theory in the domain of slow- and long-length modes, we discuss the physical mechanisms responsible for the decoherence and emergence of the hydrodynamic behavior in such collisions, and demonstrate how such physical me…
We examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a two-level approximation for a system, intermolecular interactions are introduced by a mean-field theory, and interaction between a system and an environment is modeled by a continuous measurement of a population difference between the two chiral states. The resultant equations are explored for various parameters, with emphasis on the combined effects of the initial conditi…
The intention of this work is twofold, first to present a most simple system capable of simulating the intrinsic bosonic Josephson effect with photons, and second to study various outcomes deriving from inherent or external decoherence. A qubit induces an effective coupling between two externally pumped cavity modes. Without cavity losses and in the dispersive regime, intrinsic Josephson oscillations of photons between the two modes occurs. In this case, contrary to regular Markovian decoherence, the qubit purity shows a Gaussian decay and recurrence of its coherence. Due to intrinsic non-line…
Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review analyzes the basic approaches to describing the phenomena of equilibration, thermalization, and decoherence in finite quantum systems. Isolated, nonisolated, and quasi-isolated quantum systems are considered. The relations between equilibration, decoherence, and the existence of time arrow are emphasized. The possibility for the occurrence of rare events, p…
We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part. We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N^2, while that one induced by the energy exchange interaction is of the order N only. Moreover, the diag…
An approach, differing from two commonly used methods (the stochastic \SE \ and the master equation \cite {Schlosshauer,BieleA}) but entrenched in the traditional density matrix formalism, is developed in a semi-classical setting, so as to go from the solutions of the time dependent \SE to decohering and thermalized states. This is achieved by utilizing the time-ergodicity, rather than the sampling- (or ensemble-) ergodicity, of physical systems. We introduce the formalism through a study of the Rabi model (a two level system coupled to an oscillator) and show that our semi-classical version e…
Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室）；Physics Department, Washington University in St. Louis（华盛顿大学圣路易斯分校物理系）；LPTMC, CNRS-UMR 7600, Sorbonne Université（索邦大学CNRS-UMR 7600理论统计物理中心）
We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperat…
We study the role of the system-bath coupling for the generalized canonical thermalization [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein et al., Phys. Rev. Lett. 96, 050403(2006)] that reduces almost all the pure states of the "universe" [formed by a system S plus its surrounding heat bath $B$] to a canonical equilibrium state of S. We present an exactly solvable, but universal model for this kinematic thermalization with an explicit consideration about the energy shell deformation due to the interaction between S and B. By calculating the state numbers of the "universe" and…
We study the out-of-equilibrium dynamics of bosonic atoms in a 1D optical lattice, after the ground-state is excited by a single spontaneous emission event, i.e. after an absorption and re-emission of a lattice photon. This is an important fundamental source of decoherence for current experiments, and understanding the resulting dynamics and changes in the many-body state is important for controlling heating in quantum simulators. Previously it was found that in the superfluid regime, simple observables relax to values that can be described by a thermal distribution on experimental time-scales…
We study the thermalization of an ensemble of $N$ elementary, arbitrarily-complex, quantum systems, mutually noninteracting but coupled as electric or magnetic dipoles to a blackbody radiation. The elementary systems can be all the same or belong to different species, distinguishable or indistinguishable, located at fixed positions or having translational degrees of freedom. Even if the energy spectra of the constituent systems are nondegenerate, as we suppose, the ensemble unavoidably presents degeneracies of the energy levels and/or of the energy gaps. We show that, due to these degeneracies…
