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Journal of Modern Optics

Stabilized magnetic spin dimer entanglement using a genetic algorithm

Jin Wang

Published Nov 13, 2021• 2 citations
Publisher

Abstract

Genetic algorithm optimized time varying magnetic field functions for stabilizing and maximizing entanglement in a decoherence-free Heisenberg spin dimer are presented. The oscillation in entanglement in a decoherence free magnetic spin dimer is presented. The effect on the coherence and population terms in the density matrix due to the time-varying magnetic field functions is discussed and viewed using two dimensional time varying plots of entanglement and three-dimensional Bloch sphere diagrams. This work shows that it is possible to remove the natural oscillatory nature of decoherence free entanglement and maximize entanglement using time varying transient magnetic field stabilizing functions.

DOI
10.1080/09500340.2021.1998840

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Genetic algorithm optimized time varying magnetic field functions for stabilizing and maximizing entanglement in a decoherence-free Heisenberg spin dimer are presented. The oscillation in entanglement in a decoherence free magnetic spin dimer is presented. The effect on the coherence and population terms in the density matrix due to the time-varying magnetic field functions is discussed and viewed using two dimensional time varying plots of entanglement and three-dimensional Bloch sphere diagrams. This work shows that it is possible to remove the natural oscillatory nature of decoherence free entanglement and maximize entanglement using time varying transient magnetic field stabilizing functions.
A method for stabilizing oscillations and maximizing entanglement in a decoherence free Heisenberg spin dimer using a time varying magnetic field is presented. Unentangled and fully entangled initial states are investigated. A stabilizing magnetic field intensity function was found for both initial states. These time varying magnetic field intensity functions are different from each other, implying that the magnetic intensity variation needed to stabilize the system depends on the initial state. The time varying magnetic field functions were found using simulated annealing optimization. This work proves that it is possible to remove the oscillatory nature of entanglement and maximize entanglement in decoherence free systems.
This work proposes a method for stabilizing entanglement in Heisenberg spin dimers by optimizing time-varying magnetic fields. Unlike traditional approaches that rely on static configurations, the method adapts the magnetic field in real-time using simulated annealing, addressing oscillatory degradation of entanglement. This dynamic control approach aims to extend coherence times and improve the stability of high-concurrence states, offering a potentially more robust solution for quantum communication and computation. The approach complements existing findings by focusing on the longevity and coherence of entanglement, rather than its generation or distribution, providing an alternative to conventional fixed-field methods and contributing to the ongoing efforts to enhance entanglement stability in quantum systems.
The transitory and steady-state entanglement of a two-qubit XY Heisenberg magnetic spin system immersed in an external magnetic field are analyzed in terms of the entanglement measure of concurrence. The dependence of the system entanglement on coupling strength, decay rate, and applied magnetic field is numerically simulated for two distinct models of system evolution involving decoherence to the environment. An applied magnetic field was found to consistently reduce the system entropy. The external magnetic field increases entanglement for small strength, and if too strong, it reduces the entanglement. The maximum entanglement is formed from a balance of external magnetic field and the decay rate. The transitory level of entanglement in the system is found to oscillate with a frequency that is proportional to the magnetic field strength before reaching steady-state entanglement. It was found that collective decay produces more entanglement than individual decay.
We investigate the nonlocal advantage of quantum coherence (NAQC) and entanglement for two spins coupled via the Heisenberg interaction and under the intrinsic decoherence. Solutions of this decoherence model for the initial spin-1/2 and spin-1 maximally entangled states are obtained, based on which we calculate the NAQC and entanglement. In the weak region of magnetic field, the NAQC behaves as a damped oscillation with the time evolves, while the entanglement decays exponentially (behaves as a damped oscillation) for the spin-1/2 (spin-1) case. Moreover, the decay of both the NAQC and entanglement can be suppressed significantly by tuning the magnetic field and anisotropy of the spin interaction to some decoherence-rate-determined optimal values.
Abstract This work considers the spin-1/2 Heisenberg dimer, the mixed spin-(1/2,1) Heisenberg dimer and their quantum entanglement, particularly, the dependence of the entanglement on the system characteristics and the external magnetic field. The quantum entanglement in this work is determined using two different methods, namely ‘Negativity’ and ‘Concurrence’. The dependence of the corresponding quantities on spins Landé g-factors, system anisotropy constants and exchange constant is discussed.
An exactly solvable model for the decoherence of one and two-qubit states interacting with a spin bath, in the presence of a time-dependent magnetic field is studied. The magnetic field is static along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction and oscillatory in the transverse plane. The transition probability and Rabi oscillations between the spin states of a single qubit is shown to depend on the size of bath, the distribution of qubit-bath couplings, and the initial bath polarization. In contrast to the fast Gaussian decay for short times, the polarization of the qubit shows an oscillatory power-law decay for long times. The loss of entanglement for the maximally entangled two-qubit states can be controlled by tuning the frequency of the rotating field. The decay rates of entanglement and purity for all the Bell states are the same when the qubits are noninteracting, and different when they are interacting.