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

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 $|G({\lambda }_i)⟩$ 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.

References in corpus (36)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantum Simulation
• Nonequilibrium dynamics of closed interacting quantum systems
• Scaling of Entanglement close to a Quantum Phase Transitions
• Dynamical suppression of decoherence in two-state quantum systems
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Decoherence from spin environments
• Gaussian Decoherence from Random Spin Environments
• Decoherence induced by interacting quantum spin baths
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Loschmidt Echo
• Environment Assisted Precision Measurement
• Universal decoherence induced by an environmental quantum phase transition
• Dynamic scaling of fronts in the quantum XX chain
• Critical dynamics of decoherence
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Relaxation in the XX quantum chain
• Disentanglement of two qubits coupled to an XY spin chain: Role of quantum phase transition
• Spin decoherence due to a randomly fluctuating spin bath
• Scaling and front dynamics in Ising quantum chains
• Scaling behaviour of the relaxation in quantum chains
• Critical quench dynamics in confined systems
• Loschmidt echo with a non-equilibrium initial state: early time scaling and enhanced decoherence
• Entangling many-body bound states with propagative modes in Bose-Hubbard systems
• The scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points
• Bang-Bang control of a qubit coupled to a quantum critical spin bath
• Work fluctuations in quantum spin chains
• Decoherence of Bell states by local interactions with a dynamic spin environment
• Decoherence induced by a dynamic spin environment (II): Disentanglement by local system-environment interactions
• Hydrodynamic description of Hard-core Bosons on a Galileo ramp
• Entangling two defects via a surrounding crystal
• Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
• Quantum reservoirs with ion chains
• The algebra of Grassmann canonical anti-commutation relations (GAR) and its applications to fermionic systems

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• Probing the out-of-equilibrium dynamics of two interacting atoms
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• Generation of concurrence between two qubits locally coupled to a one dimensional spin chain
• Dynamics of entanglement creation between two spins coupled to a chain