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

Abstract

We study the decoherence of a coupled quantum system consisting of a central spin and its correlated environment described by a general XY spin-chain model. We make it clear that the evolution of the coherence factor sensitively depends on the initial states of the environment spinchain. Specially, the dynamical evolution of the coherence factor of the central spin is numerically and analytically investigated in both weak and strong coupling cases for different initial states including thermal equilibrium state. In both weak and strong coupling regimes, the decay of the coherence factor can be approximated by a Gaussian and in the strong coupling regime the coherence factor oscillate rapidly under a Gaussian envelope. The width of the Gaussian decay (envelope) has been studied in details and we explained the origin of the so-called universal regime.

Orthogonality catastrophe and quantum speed limit for spin chain at finite temperature

“… after exactly calculations is therefore formulated as coincides with the analytical results derived in Ref. 27 , and for large spin system Eq. ( 17 ) scales linearly with N .…”

Energy Variance in Decoherence*

“…Here 𝛽 is the variance of the commutator Hamiltonian between different effective environmental Hamiltonians. We also show that the time scale of the Gaussian envelope [8,9,11,13,15,16] in the strong coupling regime is also determined by variance of certain Hamiltonian. In the above-mentioned cases, the speeds of the decoherence are all related to the variances of certain Hamiltonian in the initial state (i.e., the energy variance).…”

“…[6,7] In fact, speed enhancing near the QCP of the environment is a finite size phenomenon which requires the initial state of the environment being ground state of one of the effective environmental Hamiltonians. [9] Hence, the special behavior near the QCP indeed originates from the initial state of the environment, but not the environmental Hamiltonian. In Fig.…”

“…The settings for Hamiltonian and parameters is same as that in Ref. [9], where the environmental Hamiltonian and the interaction Hamiltonian read…”

“…All the solid lines are drawn numerically from exact analytical expression of LE. [9] The green and blue dashed lines are drawn with Eq. ( 11) with the variances calculated from Eq.…”