Non-Markovian reduced dynamics and entanglement evolution of two coupled spins in a quantum spin environment

TL;DR

This paper presents an exact analysis of the non-Markovian dynamics and entanglement evolution of two coupled spins in a quantum spin environment, revealing how initial states, temperature, coupling, and detuning influence entanglement.

Contribution

It introduces a novel operator technique that simplifies the analysis of strongly coupled spin systems and derives exact dynamics and entanglement measures.

Findings

Entanglement dynamics depend on initial states and system parameters.

Detuning significantly affects entanglement generation.

The operator technique is applicable to strongly coupled systems.

Abstract

The exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.