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Bulletin of the Russian Academy of Sciences Physics

Formation of entangled states in nonequilibrium quantum systems with partial coherent pumping

V. O. Martynov, Vyacheslav A. Mironov, Lev A. Smirnov

Published Jan 1, 2017• 1 citation
Publisher

Abstract

The problem of generating the entangled states of two parametrically coupled quantum oscillators at finite temperatures is considered. For coherent pumping, an analytical expression describing the behavior of logarithmic negativity is obtained using the Heisenberg–Langevin formalism. The expression also describes the attaining of a long nonzero steady-state value of logarithmic negativity. It is shown numerically that pumping noise limits the lifetime of entanglement in the system.

DOI
10.3103/s1062873817010178

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The problem of generating the entangled states of two parametrically coupled quantum oscillators at finite temperatures is considered. For coherent pumping, an analytical expression describing the behavior of logarithmic negativity is obtained using the Heisenberg–Langevin formalism. The expression also describes the attaining of a long nonzero steady-state value of logarithmic negativity. It is shown numerically that pumping noise limits the lifetime of entanglement in the system.
Abstract A study of ‘high temperature’ entangled states in a system of two parametrically coupled quantum oscillators placed into independent thermal baths is performed taking into account partially coherent parametric pump. Processes in an open system are considered based on the Heisenberg–Langevin formalism. We obtain a closed system of equations for the averaged quadratic correlation functions in quantum stochastic problem as a result of Markov processes approximation. On the basis of numerical calculations the dynamics of the logarithmic negativity, which is the measure of entanglement in the system, is investigated. It is shown that the partial coherence of the parametric pump makes the lifetime of the entangled states finite. The threshold characteristics of the formation and existence of these states are specified.
We consider a model of two qubits, which interact through a Rotating Wave Approximation (RWA) potential; while the first qubit is incoherently pumped to its excited state, the second qubit loses its excitations by contact to a zero-temperature bath. We show that purely dissipative effects (and the help of the qubit-qubit interaction) can produce entangled stationary states. The steady state entanglement is significant when the interaction constant, and the pumping and dissipation rates are of the same order of magnitude. In this toy model, the entanglement of the system exists only when the two thermal baths are on and the qubits are coupled; if we turn off either the pumping or the dissipation these correlations disappear. We calculate and compare two quantifiers of non-classical correlations: the quantum discord [3] and the entanglement of formation, in the steady state. We find an analytical form for the conditions for which the steady-state qubit-qubit entanglement attains its maximum value Css..
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The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of nonclassical steady states. Starting from a microscopic description of two oscillators individually interacting with their dissipative environments, it is found that in addition to energy relaxation, dephasing arises due to the mutual coupling. Using the negativity as an entanglement measure, it is shown that the coupling entangles the oscillators in the long-time limit. For finite temperatures, entanglement sudden death and rebirth are observed.