Generation of concurrence between two qubits locally coupled to a one dimensional spin chain

Abstract

We consider a generalized central spin model, consisting of two central qubits and an environmental spin chain (with periodic boundary condition) to which these central qubits are locally and weakly connected either at the same site or at two different sites separated by a distance $d$. Our purpose is to study the subsequent temporal generation of entanglement, quantified by concurrence, when initially the qubits are in an unentangled state. In the equilibrium situation, we show that the concurrence survives for a larger value of $d$ when the environmental spin chain is critical. Importantly, a common feature observed both in the equilibrium and the non-equilibrium situations while the latter is created by a sudden but global change of the environmental transverse field, is that the two qubits become maximally entangled for the critical quenching. Following a non-equilibrium evolution of the spin chain, our study for $d\ne 0$, indicates that there exists a threshold time above which concurrence attains a finite value. Additionally, we show that the number of independent decohering channels (DCs) is determined by $d$ as well as the local difference of the transverse field of the two underlying Hamiltonians governing the time evolution. The qualitatively similar behavior displayed by the concurrence for critical and off-critical quenches, as reported here, is characterized by analyzing the non-equilibrium evolution of these channels. The concurrence is maximum when the decoherence factor or the echo associated with the most rapidly DC decays to zero; on the contrary, the condition when the concurrence vanishes is determined non-trivially by the associated decay of one of the intermediate DCs. Analyzing the reduced density of a single qubit, we also explain the observation that the dephasing rate is always slower than the unentanglement rate.

11 pages and 11 figures

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Cited by in corpus (5)

• Phase transitions and thermal entanglement of the distorted Ising-Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders
• Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain
• Entanglement generation and scaling from noisy quenches across a quantum critical point
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• Generation of concurrence in a generalized central spin model with a three-spin interacting environment