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.

Entanglement dephasing dynamics driven by a bath of spins

“…But for the pure state bath, we see 0.4 entanglement generation measured by concurrence in an early stage due to the initial relaxation of the environment into its steady state. Such an initial generation of entanglement is also observed in the Holstein-Primakoff boson case [23,25].…”

“…spin-boson model [20,21] and (iii) Qubits (or harmonic oscillators) coupled to a bath of spins-1/2, i.e. spin bath model [22][23][24][25][26][27][28][29][30][31][32][33]. It is shown that open system dynamics can be significantly modified by environmental configurations.…”

“…Our strategy is to directly solve the models without any approximations that may lead to the conversion of bath spins into the effective HolsteinPrimakoff bosons or Schwinger bosons (e.g., see [23,25]). The purpose of this paper is to find important features induced from the spin environment that are not seen in the boson case.…”

Rabi oscillations, decoherence, and disentanglement in a qubit–spin-bath system

“…Exceptions include Refs. [31,32], where the authors considered the spin-flip * These two authors equally contributed to the work. † hrabitz@princeton.edu XX-type qubit-bath coupling but with a spin bath having homogeneous self-interactions, and Ref.…”

“…A more realistic type of environment takes the form of quantum interacting spin chains [3,[30][31][32][33][34][35], where the decay of the qubit's coherence is found to be related to the critical properties of the spin environments. Most prior work making use of such an environment considered qubit-spin bath coupling of the Ising form, which is spin conserving.…”