Thermal purification and thermal entanglement of the two-resonant-coupled-oscillator system at finite temperature

Following the spirit of thermo field dynamics, we adopt the partial trace method to explicitly derive the thermal vacuum state (TVS) for the Hamiltonian H of the two-resonant-coupled-oscillator system coupled to the thermal equilibrium environment. The TVS is a pure state in the four-dimensional ext...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 47; no. 37; pp. 375301 - 12
Main Authors Li, Heng-Mei, Xu, Xue-Xiang, Huang, Hong-Yun, Xu, Ye-Jun
Format Journal Article
LanguageEnglish
Published IOP Publishing 19.09.2014
Subjects
Dynamical systems
Dynamics
Entanglement
Functions (mathematics)
Gaussian
logarithmic negativity
Mathematical analysis
partial trace method
Purification
Quadratures
thermal field dynamics
two-resonant-coupled oscillator
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Summary:Following the spirit of thermo field dynamics, we adopt the partial trace method to explicitly derive the thermal vacuum state (TVS) for the Hamiltonian H of the two-resonant-coupled-oscillator system coupled to the thermal equilibrium environment. The TVS is a pure state in the four-dimensional extended Hilbert space. Based on the TVS, the Wigner function of this quantum system is derived conveniently. From the known Gaussian Wigner function, we obtain the covariance matrix of the quadrature component and quantify the degree of thermal entanglement for the TVS by using logarithmic negativity. It is found that entanglement takes place only at low temperature.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/47/37/375301