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arXiv:1704.05202 · Modern Physics Letters A

Specific heat and thermal entanglement in an open quantum system

Behzad Lari, HASSAN HASSANABADI

Published Mar 21, 2019• 3 citations
arXivHTMLPDF

Abstract

In this paper, the density matrix is obtained using the non-Markovian master equation method for a system consisting of two-qubit modeling with the Heisenberg XXZ chain, which involves the Dzyaloshinskii–Moriya interaction and is exposed to the bosonic baths. Also, using the proposed formula for calculating the specific heat through the density matrix of the open quantum system, the specific heat is calculated. The quantum entanglement behavior with time and coupling constant is investigated. It is observed that the specific heat at low temperatures becomes negative when the system is exposed to the environment. The time behavior of quantum entanglement for this model showed that the entanglement decreases to zero with increasing time.

DOI
10.1142/s0217732319500597

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In this paper, the density matrix is obtained using the non-Markovian master equation method for a system consisting of two-qubit modeling with the Heisenberg XXZ chain, which involves the Dzyaloshinskii–Moriya interaction and is exposed to the bosonic baths. Also, using the proposed formula for calculating the specific heat through the density matrix of the open quantum system, the specific heat is calculated. The quantum entanglement behavior with time and coupling constant is investigated. It is observed that the specific heat at low temperatures becomes negative when the system is exposed to the environment. The time behavior of quantum entanglement for this model showed that the entanglement decreases to zero with increasing time.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
The thermal entanglement is investigated in a two-qubit Heisenberg XXZ system with Dzyaloshinskii–Moriya (DM) interaction. It is shown that the entanglement can be efficiently controlled by the DM interaction parameter and coupling coefficient J z . D x (the x -component parameter of the DM interaction) has a more remarkable influence on the entanglement and the critical temperature than D z (the z -component parameter of the DM interaction). Thus, by changing the DM interaction direction, we can get a more efficient control parameter to increase the entanglement and the critical temperature.
Based on the exact non-Markovian system dynamic equation about the reduced density matrix of quantum system,which is a non-closed,unequal in time,integral-differential equation,a closed,equal in time,differential Markovian master equation was derived about the reduced density matrix of quantum system by means of Born approximation and Markov approximation.The Lindblad form of the Markovian master equation,GKS expression for the convenience of testing positivity,Bloch sphere expression for single qubit system,Kraus expression describing dissipative quantum system without specific information of environment were analyzed respectively.Four kinds of Markov approximations that can remove the non-Markovian property were compared.The post-Markovian master equation was analyzed that can meet the perfect requirements of dissipative dynamic when the Markov approximation is not suitable to the open quantum system.When energy exchange existed between the heat bath and quantum system,and the total system composed of the bath and the quantum system has a conservation of energy,the dynamic equation of open quantum system was presented when the bath does not have a constant state,and the Markovian master equation was derived by the Markov approximation.
Entanglement (EN) is a determinative correlation in designation of quantum gates and quantum memories. All quantum operations which are assembled by quantum circuits, are exposed to environment. However, quantum discord (QD) as a new key of resource for quantum information theory is in spotlight of research. Therefore, the study of EN and QD in open quantum systems seems to be important. In this Brief Report, We derived a formula for specific heat of the principle system as a part of open quantum system (in special for Jaynes-Cumming regime), and we looked for relations between entanglement and specific heat which is important for designing of the quantum memory. We also studied the dynamics of thermal EN and QD in Jaynes-Cumming regime including the Non-Markovian processes via Born-Markove approximation and obtained a regions of temperature and coupling constant between parts of systems which the entanglement of formation had a stable behavior .It seems to be useful to design the quantum gates. We observed the negative and divergence specific heat (in contradiction with third law of thermodynamics) in low temperature because the state of open system is entangle. According to obtained results, we did not find out any violence oscillation in quantum discord and because entanglement decreases with respect time, fast response to inputs is crucial for assembling quantum circuits and quantum memory.
We study two continuous variable systems (or two harmonic oscillators) and investigate their entanglement evolution under the influence of non-Markovian thermal environments. The continuous variable systems could be two modes of electromagnetic fields or two nanomechanical oscillators in the quantum domain. We use the quantum open system method to derive the non-Markovian master equations of the reduced density matrix for two different but related models of the continuous variable systems. The two models both consist of two interacting harmonic oscillators. In model A, each of the two oscillators is coupled to its own independent thermal reservoir, while in model B the two oscillators are coupled to a common reservoir. To quantify the degrees of entanglement for bipartite continuous variable systems in Gaussian states, logarithmic negativity is used. We find that the dynamics of the quantum entanglement is sensitive to the initial states, the oscillator-oscillator interaction, the oscillator-environment interaction and the coupling to a common bath or to different, independent baths.