Decoherence of Bell states by local interactions with a suddenly quenched spin environment

TL;DR

This paper investigates how two qubits initially entangled in a Bell state become disentangled over time due to local interactions with a suddenly quenched transverse field spin chain environment, analyzing the dynamics through concurrence and Loschmidt echo.

Contribution

It provides a detailed numerical and analytical study of qubit disentanglement dynamics post-quench, highlighting the impact of environment criticality and quench parameters.

Findings

Disentanglement depends on qubit distance and bath properties.

Critical initial environment enhances decoherence effects.

Analytical relations between concurrence and Loschmidt echo are established.

Abstract

We study the dynamics of disentanglement of two qubits initially prepared in a Bell state and coupled at different sites to an Ising transverse field spin chain (ITF) playing the role of a dynamic spin environment. The initial state of the whole system is prepared into a tensor product state $\rho_{Bell}\otimes \rho_{chain}$ where the state of the chain is taken to be given by the ground state $|G(\lambda_i)\rangle$ of the ITF Hamiltonian $H_E(\lambda_i)$ with an initial field $\lambda_i$. At time $t=0^+$, the strength of the transverse field is suddenly quenched to a new value $\lambda_f$ and the whole system (chain $+$ qubits) undergoes a unitary dynamics generated by the total Hamiltonian $H_{Tot}=H_E(\lambda_f) + H_I$ where $H_I$ describes a local interaction between the qubits and the spin chain. The resulting dynamics leads to a disentanglement of the qubits, which is described through the Wooter's Concurrence, due to there interaction with the non-equilibrium environment. The concurrence is related to the Loschmidt echo which in turn is expressed in terms of the time-dependent covariance matrix associated to the ITF. This permits a precise numerical and analytical analysis of the disentanglement dynamics of the qubits as a function of their distance, bath properties and quench amplitude. In particular we emphasize the special role played by a critical initial environment.