Dynamics of two qubits in a spin-bath of Quantum anisotropic Heisenberg XY coupling type

TL;DR

This paper investigates the time evolution of two qubits interacting with a quantum Heisenberg XY spin-bath, revealing how anisotropy, temperature, and initial states influence entanglement and fidelity dynamics.

Contribution

It introduces a novel numerical polynomial scheme for calculating the dynamics of two qubits in an XY spin-bath, highlighting the effects of anisotropy and initial conditions.

Findings

Higher anisotropic parameter increases the likelihood of maintaining initial qubit states.

Increasing temperature and coupling strength weaken the subsystem's coherence.

Concurrence revival does not necessarily indicate state restoration.

Abstract

The dynamics of two 1/2-spin qubits under the influence of a quantum Heisenberg XY type spin-bath is studied. After the Holstein-Primakoff transformation, a novel numerical polynomial scheme is used to give the time-evolution calculation of the center qubits initially prepared in a product state or a Bell state. Then the concurrence of the two qubits, the $z$-component moment of either of the subsystem spins and the fidelity of the subsystem are shown, which exhibit sensitive dependence on the anisotropic parameter, the temperature, the coupling strength and the initial state. It is found that (i) the larger the anisotropic parameter $\gamma$, the bigger the probability of maintaining the initial state of the two qubits; (ii) with increasing temperature $T$, the bath plays a more strong destroy effect on the dynamics of the subsystem, so does the interaction $g_0$ between the subsystem and the bath; (iii) the time evolution of the subsystem is dependent on the initial state. The revival of the concurrence does not always means the restore of the state. Further, the dynamical properties of the subsystem should be judged by the combination of concurrence and fidelity.