Quantum dynamics of double-qubits in a spin star lattice with an XY interaction

摘要

The dynamics of two coupled spins-1/2 interacting with a spin-bath via thequantum Heisenberg XY coupling is studied. The pair of central spins served asa quantum open subsystem are initially prepared in two types of states: theproduct states and the Bell states. The bath, which consists of $N$ (in thethermodynamic limit $N\to\infty$) mutually coupled spins-1/2, is in a thermalstate at the beginning. By the Holstein-Primakoff transformation, the model canbe treated effectively as two spin qubits embedded in a single mode cavity. Thetime-evolution of the purity, z-component summation and the concurrence of thecentral spins can be determined by a Laguerre polynomial scheme. It is foundthat (i) at a low temperature, the uncoupled subsystem in a product state canbe entangled due to the interaction with bath, which is tested by thePeres-Horodecki separability; however, at a high temperature, the bath producesa stronger destroy effect on the purity and entanglement of the subsystem; (ii)when the coupling strength between the two central spins is large, they areprotected strongly against the bath; (iii) when the interaction between thesubsystem and the bath is strong, the collapse of the two spin qubits fromtheir initial entangled state is fast.