Decoherence of a quantum system coupled to an XY spin chain: Role of the initial state of the spin chain

We study the decoherence of a coupled quantum system consisting of a central spin and its correlated environment described by a general XYXY spin-chain model. We make it clear that the evolution of the coherence factor sensitively depends on the initial state of the environment spin-chain. Specially, the dynamical evolution of the coherence factor of the central spin is numerically and analytically investigated in both weak and strong coupling cases with initial state set as the ground state of the initial Hamiltonian HE(λi) at time t=0t=0 which may be different from the evolving Hamiltonian HE(λe) for time tt>> 0, as well as set as the thermal equilibrium state. In both weak and strong coupling cases, we show that the evolution of the coherence factor with initial state being the ground state of the initial Hamiltonian can be approximated by a Gaussian. Particularly, in the strong coupling regime the coherence factor oscillates rapidly under a Gaussian envelope. The width of the Gaussian decay (envelope) is presented in detail.