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Spatial Entanglement in Thermal Equilibrium

Dagomir Kaszlikowski, Marcin Wieśniak, Frederic H. Willenboordse

Published Jan 13, 2006• 0 citations
OpenAlex

Abstract

We investigate the existence of spatial entanglement in a system of two-dimensional spinless bosons in thermal equilibrium that are trapped in either a one-dimensional infinite square well potential or a harmonic oscillator potential. Using the partial transposition criterion we show that entanglement exists only in a certain range of temperatures, and we observe that for both potentials there is a non-zero critical temperature for which the highest amount of spatial entanglement is obtained. It is furthermore proved that this must happen for an arbitrary one-dimensional potential.

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We investigate the existence of spatial entanglement in a system of two-dimensional spinless bosons in thermal equilibrium that are trapped in either a one-dimensional infinite square well potential or a harmonic oscillator potential. Using the partial transposition criterion we show that entanglement exists only in a certain range of temperatures, and we observe that for both potentials there is a non-zero critical temperature for which the highest amount of spatial entanglement is obtained. It is furthermore proved that this must happen for an arbitrary one-dimensional potential.
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We study the entanglement of a two-qubit one-dimensional XYZ Heisenberg chain in thermal equilibrium at temperature T. We obtain an analytical expression for the concurrence of this system in terms of the parameters of the Hamiltonian and T. We show that depending on the relation among the coupling constants, it is possible to increase the amount of entanglement of the system by increasing its anisotropy. We also show numerically that for all sets of the coupling constants entanglement is a monotonically decreasing function of the temperature T, proving that we must have at least an external magnetic field in the z-direction to obtain a behavior where entanglement increases with T.
We outline an interferometric scheme for the detection of bimode and multimode spatial entanglement of finite-temperature interacting Bose gases. Whether entanglement is present in the gas depends on the existence of the single-particle reduced density matrix between different regions of space. We apply the scheme to the problem of a harmonically trapped repulsive boson pair and show that while entanglement is rapidly decreasing with temperature, a significant amount remains for all interaction strengths at zero temperature. Thus, by tuning the interaction parameter, the distribution of entanglement between many spatial modes can be modified.