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AIP conference proceedings

Nonequilibrium thermal entanglement for simple spin chains

Ilya Sinayskiy, N. Pumulo, Francesco Petruccione

Published Jan 1, 2012• 0 citations
Publisher

Abstract

The dynamics of a chain of two and three spins coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the quantum master equation in the Born-Markov approximation for the reduced density matrix of the chain is constructed. It is shown that for long times the reduced density matrix converges to the nonequilibrium steady-state. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.

DOI
10.1063/1.4746065

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The dynamics of a chain of two and three spins coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the quantum master equation in the Born-Markov approximation for the reduced density matrix of the chain is constructed. It is shown that for long times the reduced density matrix converges to the nonequilibrium steady-state. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.
The dynamics of simple qubit systems in a chain configuration coupled at both ends to separate bosonic baths at different temperatures is studied. An exact analytical solution of the master equation in the Born-Markov approximation for the reduced density matrix of the qubit system is constructed. The unique non-equilibrium stationary state for the long time behavior of the reduced density matrix in obtained. Dynamical and steady state properties of the concurrence between the first and the last spin are studied.
The dynamics of a simple spin chain (two spins) coupled to bosonic baths at different temperatures is studied. The analytical solution for the reduced density matrix of the system is found. The dynamics and temperature dependence of spin-spin entanglement is analyzed. It is shown that the system converges to a steady state. If the energy levels of the two spins are different, the steady-state concurrence assumes its maximum at unequal bath temperatures. It is found that a difference in local energy levels can make the steady-state entanglement more stable against high temperatures.
The study is focused on the thermal entanglement of spin chains. Chains consisting of two and three qubits are considered. These chains are considered open because they are coupled to bosonic baths at different temperatures. The baths represent the environment. The dynamics of these open systems are examined as are the effects of different parameters - such as bath temperature - on the entanglement of the spins. The measure of entanglement used in these cases is the concurrence. Comparisons are made between a model that assumes a strong spinspin interaction and one that assumes a weak one. In all these cases, analytical solutions for the system dynamics are presented. It is found that at large times, all systems converge to a state that depends only on bath temperature. It is also found that increases in bath temperatures diminish the entanglement between spins and that at high enough temperatures the entanglement vanishes altogether. The time and temperature dependence of the entanglement is different for the two models that are studied.
Making use of the master equation and effective Hamiltonian approach, we investigate the steady-state entanglement in a three-qubit XXXXXX model. Both symmetric and nonsymmetric qubit-qubit couplings are considered. The system (the three qubits) is coupled to two bosonic baths at different temperatures. We calculate the steady state by the effective Hamiltonian approach and discuss the dependence of the steady-state entanglement on the temperatures and couplings. The results show that for symmetric qubit-qubit couplings, the entanglements between the nearest neighbors are equal, independent of the temperatures of the two baths. The maximum of the entanglement arrives at TL=TR{T}_{L}={T}_{R}TL​=TR​. For nonsymmetric qubit-qubit couplings, however, the situation is totally different. The baths at different temperatures would benefit the entanglement and the entanglements between the nearest neighbors are no longer equal. By examining the probability distribution of each eigenstate in the steady state, we present an explanation for these observations. These results suggest that the steady entanglement can be controlled by the temperature of the two baths.