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

• Published in: arXiv.org
• Main Authors: Wendenbaum, Pierre, Taketani, Bruno G, Karevski, Dragi
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.09.2014
• Subjects: Chain entanglement; Chains; Covariance matrix; Dynamics; Ising model; Physics - Quantum Physics; Quenching; Spin dynamics; Tensors; Time dependence
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1409.0317

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.