Russian Microelectronics

Quantum Entanglement in Two-Spin Systems in Multiple Pulse NMR Spin Locking with Dephasing Relaxation

G. A. Bochkin, Alexander Ivanovich Zenchuk, E. I. Kuznetsova, A. V. Fedorova, Edward B. Fel’dman

Published Dec 1, 2025• 1 citation

Abstract

Abstract Quantum entanglement in two-spin systems in multiple pulse NMR spin locking with dephasing relaxation is studied on the basis of the Lindblad equation. An exact solution for the density matrix of the system for any initial temperature is found. The dependence of the concurrence (which determines quantum entanglement) on the dephasing relaxation rate and the parameters of the multiple pulse sequence is investigated. For different rates of dephasing relaxation, the critical temperature at which entanglement arises is found.

DOI: 10.1134/s1063739725601109

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Russian Microelectronics

Quantum Entanglement in Two-Spin Systems in Multiple Pulse NMR Spin Locking with Dephasing Relaxation

G. A. Bochkin, Alexander Ivanovich Zenchuk, E. I. Kuznetsova, A. V. Fedorova, Edward B. Fel’dman

Published Dec 1, 2025• 1 citation

Publisher

Abstract

DOI: 10.1134/s1063739725601109

Related papers

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\varphi

-pulses with the same time delay

2\tau

between successive pulses. For times

t \sim {{T}_{2}}

(

{{T}_{2}} \approx \omega _{{{\text{loc}}}}^{{ - 1}}

{{\omega }_{{{\text{loc}}}}}

is determined by the dipole–dipole interaction), quasi-equilibrium with a structure depending on the relation between the pulsed field

{{\omega }_{1}} = \varphi {\text{/}}2\tau

and

{{\omega }_{{{\text{loc}}}}}

is established in the system. For

{{\omega }_{1}} \lessapprox {{\omega }_{{{\text{loc}}}}}

, a one-temperature quasi-equilibrium state arises, while a quasi-equilibrium with the dipole and Zeeman temperatures appears for

{{\omega }_{1}} \gg {{\omega }_{{{\text{loc}}}}}

. The temperature dependence of entanglement is investigated for

{{\omega }_{1}} \lessapprox {{\omega }_{{{\text{loc}}}}}

. For

{{\omega }_{1}} \gg {{\omega }_{{{\text{loc}}}}}

, the further evolution of the system is determined by the Provotorov equations and leads to the equalization of the dipole and Zeeman temperatures. It is shown that the entanglement is absent in this case.