Exact recurrence of a qubit immersed in a homogeneous N-qubit environment

Abstract

A central qubit immersed in a homogeneous N-qubit environment with a diagonal Hamiltonian is considered. Exact recurrence implies that the dynamical evolution of the state of the central qubit can return exactly to its initial state. An exact recurrence can occur when the condition of commensurate parameters ω and g is satisfied. Here, ω is the strength of the self-Hamiltonian of the central qubit while g is the strength of the interaction coupling into the qubit environment. Commensurability of ω and g yields to a periodic decoherence factor. The period of the decoherence factor is also the recurrence time of the central qubit. At the onset of recurrence, there is also a revival of initial coherence. Moreover, the recurrence time oscillates between odd and even number of qubit environment.