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

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.

9 pages (two-coulumn), 6 figures. To appear in Phys. Rev. B

References in corpus (4)

• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Exact quantum jump approach to open systems in Bosonic and spin baths
• One-spin quantum logic gates from exchange interactions and a global magnetic field
• 1/N-expansion for the Dicke model and the decoherence program

Cited by in corpus (18)

• Entanglement invariant for the double Jaynes-Cummings model
• Non-Markovian dynamics of a qubit coupled to an Ising spin bath
• Suppression of decoherence in a generalization of the spin-bath model
• High-capacity and high-power collective charging with spin chargers
• Decoherence by a spin thermal bath: Role of the spin-spin interactions and initial state of the bath
• Dynamics of two qubits in a spin-bath of Quantum anisotropic Heisenberg XY coupling type
• Influence of an external magnetic field on the decoherence of a central spin coupled to an antiferromagnetic environment
• Controllable dynamics of two separate qubits in Bell states
• Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems
• Qubit Entanglement Dephasing Dynamics Driven by a Bath of Spins
• Loss-of-entanglement prediction of a controlled-PHASE gate in the framework of steepest-entropy-ascent quantum thermodynamics
• Exact dynamics of the homogeneous two-qubit $XXZ$ central spin model with the spin bath prepared in superpositions of symmetric Dicke states
• Excitation spectra of a quantum ring embedded in a photon cavity
• Dynamics of a driven spin coupled to an antiferromagnetic spin bath
• Collapse and revival structure of information backflow for a central spin coupled to a finite spin bath
• Measurement-induced nuclear spin polarization
• Dephasing effects on quantum correlations and teleportation in presence of state dependent bath
• General recipe for immediate entanglement death-birth transitions via Bell states: environmental Heisenberg exchange as an example