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Abstract
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spins coupled in a spin environment and subjected, simultaneously, to an external
magnetic field changing with time t as an exponential function B1 − e−λt . We
want to determine whether interaction among central spins with an external magnetic
field as well as preparation of bath in an appropriate spin coherent state, |βbath, is
shown to affect the decoherence process in a qualitatively significant manner.We show
that the dynamics of the entanglement depends on the initial state of the central spins
as well as the bath, the coupling constants and the strength of a magnetic field, B, λ.
Compared with some cases already discussed in the literature as magnetic fields of
periodic sin(λt) and cos(λt) functions, we can see that a magnetic field of exponential
function e−λt plays a very crucial role in the entanglement generation between the
two-spin qubits and its protection. To do this, we use an operator technique of the
Holstein–Primakoff transformation, and the dynamics of the reduced density matrix
of two coupled spin qubits is obtained in both finite and infinite numbers of bath spins.
We also derive the concurrence measure to quantify the entanglement of the reduced
density matrix of the two coupled central spins and look for conditions that provide
information on whether this becomes robust against decoherence. It has been shown
that the entanglement distribution can be both amplified, stabilized and protected with B, λ and β. These results motivate developments toward the implementation or
simulation of the purely theoretical model employing exponential fields.
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