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CONTROL OF QUANTUM STATES BY DECOHERENCE

Luigi Accardi, K. IMAFUKU

Published Mar 1, 2006• 4 citations
Publisher

Abstract

We propose a new technique to control quantum states by exploiting the decoherence due to the coupling with environment.With this technique we can get any target state, in a stable way and in an exponentially small time, as a stationary state of a semigroup (master equation) canonically derived from a microscopic Hamiltonian model.The stationary state of the system depends (i) on the interaction with the environment; (ii) on the initial state of the environment and it "inherits" some properties of it in a sense that will be explained in sec.5 of the present paper.Moreover this is true not only for by thermal or vacuum environments but also for more general non-equilibrium environments.We prove that, by appropriately choosing this control parametes (interaction system-environment, initial environment state) one can drive the system to an arbitrary preassigned quantum state.

DOI
10.1142/9789812774491_0003

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We propose a new technique to control quantum states by exploiting the decoherence due to the coupling with environment.With this technique we can get any target state, in a stable way and in an exponentially small time, as a stationary state of a semigroup (master equation) canonically derived from a microscopic Hamiltonian model.The stationary state of the system depends (i) on the interaction with the environment; (ii) on the initial state of the environment and it "inherits" some properties of it in a sense that will be explained in sec.5 of the present paper.Moreover this is true not only for by thermal or vacuum environments but also for more general non-equilibrium environments.We prove that, by appropriately choosing this control parametes (interaction system-environment, initial environment state) one can drive the system to an arbitrary preassigned quantum state.
We investigate the conditions which can lead to the occurrence of "decoherence" (i.e., of "environment-induced superselection"), in a quantum system interacting with another, infinite quantum system (an apparatus, environment, etc.), in the context of the nonrelativistic quantum mechanics. We are particularly concerned with: a kind of interaction, its relative strength, initial state of the apparatus (environment), and compatibility of the self-Hamiltonian and the interaction Hamiltonian of the composite system, "system plus apparatus", including time dependent interactions. As necessary conditions concerning occurrence of decoherence appear the two requirements: (i) That the interaction Hamiltonian is of the separable kind , and (ii) That the complete Hamiltonian, Ĥ u satisfies commutator relation [Ĥ u ( t ), Ĥ u ( t ')] = 0 ( t and t ' arbitrary instants). Since non-separable interaction cannot produce the same, we conclude that occurrence of decoherence is neither a rule (as it is sometimes assumed in the context of the "environment theory"), nor an exceptional consequence of the dynamics of a system interacting with its environment (as it is sometimes claimed in the criticism of the environment theory). Exhaustiveness and generality of our analysis extend applicability of related results (which are independent on a particular model of (infinite) environment), at least as a qualitative test and/or quantitative estimation of the results of the calculations obtained by the use of the different methods (semiclassical methods, path-integration technique, etc.) in quantum many-particle physics.
We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalized in the diagonal basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalization is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are structurally similar to recently proposed models for consistently combining quantum and classical stochastic dynamics.
The usual paradigm of open quantum systems falls short when the environment is actually coupled to additional fields or components that drive it out of equilibrium. Here we explore the simplest such scenario, by considering a two level system coupled to a first thermal reservoir that in turn couples to a second thermal bath at a different temperature. We derive a master equation description for the system and show that, in this situation, the dynamics can be especially rich. In particular, we observe prethermalization, a transitory phenomenon in which the system initially approaches thermal equilibrium with respect to the first reservoir, but after a longer time converges to the thermal state dictated by the temperature of the second environment. Using analytical arguments and numerical simulations, we analyze the occurrence of this phenomenon, and how it depends on temperatures and coupling strengths. The phenomenology gets even richer if the system is placed between two such non-equilibrium environments. In this case, the energy current through the system may exhibit transient features and even switch direction, before the system eventually reaches a non-equilibrium steady state.
We investigate the dissipative dynamics of a generalized Lipkin-Meshkov-Glick (LMG) model coupled to a thermal environment. In this generalized model, in addition to the conventional quadratic interaction, one considers quartic interactions between spin-1/21/21/2's coupled all-to-all and evolving in presence of a transverse field. Employing the usual linear Lindblad master equation with thermally-balanced jump processes, we derive magnetisation evolution equations, and demonstrate that the corresponding stationary solution reproduces the canonical equilibrium phase diagram of the model. We then extend our analysis to a nonlinear Lindblad equation that incorporates imperfect quantum-jump processes in terms of jump-retention parameters. Here, remarkably, the system relaxes to a genuine nonequilibrium stationary state whose properties differ qualitatively from those obtained in the linear case. The jump-retention parameters provide tunable knobs that shift the phase boundaries and even modify the nature of the phase transitions with respect to the linear case. Our exact results establish a direct connection between dissipative relaxation dynamics and stationary-state behavior, while identifying controlled quantum-jump retention as a mechanism for engineering nonequilibrium phases in long-range interacting open quantum systems.
Abstract The usual paradigm of open quantum systems falls short when the environment is actually coupled to additional fields or components that drive it out of equilibrium. Here we explore the simplest such scenario, by considering a two level system coupled to a first thermal reservoir that in turn couples to a second thermal bath at a different temperature. We derive a master equation description for the system and show that, in this situation, the dynamics can be especially rich. In particular, we observe prethermalization, a transitory phenomenon in which the system initially approaches thermal equilibrium with respect to the first reservoir, but after a longer time converges to the thermal state dictated by the temperature of the second environment. Using analytical arguments and numerical simulations, we analyze the occurrence of this phenomenon, and how it depends on temperatures and coupling strengths. The phenomenology gets even richer if the system is placed between two such non-equilibrium environments. In this case, the energy current through the system may exhibit transient features and even switch direction, before the system eventually reaches a non-equilibrium steady state.