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arXiv:1005.2886

Entanglement between states of single quadrupole nuclear spin

G. B. Furman, V. Meerovich, Vladimir Sokolovsky

Published May 17, 2010• 0 citations
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Abstract

We study entanglement between quantum states of multi level spin system of a single particle considering a nucleus with spin 3/2 in both the internal electric field gradient and the external magnetic field. It was shown that entanglement is achieved by applying a magnetic field to a single particle at low temperature (~ 5 mK). In this temperature range, the numerical calculation revealed the coincidence between magnetization and concurrence. As a result, the magnetization can be used as an entanglement witness for such systems.

DOI
10.48550/arxiv.1005.2886

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We study entanglement between quantum states of multi level spin system of a single particle considering a nucleus with spin 3/2 in both the internal electric field gradient and the external magnetic field. It was shown that entanglement is achieved by applying a magnetic field to a single particle at low temperature (~ 5 mK). In this temperature range, the numerical calculation revealed the coincidence between magnetization and concurrence. As a result, the magnetization can be used as an entanglement witness for such systems.
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We investigate the evolution of entanglement in multiple-quantum (MQ) NMR experiments in crystals with pairs of close nuclear 1/2-spins. The initial thermodynamic equilibrium state of the system in a strong external magnetic field evolves under the nonsecular part of the dipolar Hamiltonian. As a result, MQ coherences of the zeroth and plus/minus second orders appear. A simple condition for the emergence of entanglement is obtained. We show that the measure of the spin-pair entanglement—concurrence—coincides qualitatively with the intensity of MQ coherences of the plus/minus second order and, hence, the entanglement can be studied with MQ NMR methods. We introduce an entanglement witness using MQ NMR coherences of the plus/minus second order.
The entanglement at zero-temperature is studied in a two-qubit XZ spin-1/2 chain model in an external magnetic field which is applied in the z direction. We have obtained an analytical relation for the effect of the external magnetic field on the concurrence. It is shown that the ground state of the system depends on the strength of exchange coupling. We have shown that the analytical relation of the concurrence is independent of Jz. It is shown that for Jz >0 the concurrence is depended on the critical value of the external magnetic field and it is changed at the critical external magnetic field. Also we have shown that for h hc, the concurrence decreases by increasing the external magnetic field. For Jz <0, the concurrence decreases by increasing the external magnetic field.
Entanglement is studied in an open alternating chain of nuclear spins s = 1/2 with spin-spin couplings in an external magnetic field under the thermodynamic equilibrium conditions. A reduced density matrix has been calculated for an arbitrarily chosen spin pair. The entanglement of the spin pair has been estimated according to the Wootters criterion. The temperature at which an entangled state appears in a chosen pair has been determined. It has been shown that the numerical characteristics of the entanglement are oscillating functions of the position of the spin pair in the chain.
Quantum thermal entanglement of two next nearest-neighbor qubits in a four-qubit isotropic Heisenberg XY model consisting of spin 1/2 and spin S in a homogeneous external magnetic field B was investigated by concurrence measure of entanglement.The results show that the external magnetic field can induce the thermal entanglement of two next nearest-neighbor qubits.The amplitude of thermal entanglement is dependent on the spin S,temperature T and homogeneous external magnetic field B.As a result,it is feasible to control thermal entanglement by adjusting the value of external magnetic field B.When S is sufficiently large,the threshold temperature above which there is no thermal entanglement may also be very high.The feature can be used in high-temperature entanglement of condensed matter systems and it will be useful in the research of quantum information in solid systems.