Reservoir for inverse-power-law decoherence of a qubit

Abstract

The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a continuous distribution of bosons, characterized by a special form of the spectral density, is evaluated analytically. The special reservoir is designed to induce anomalous decoherence, resulting in an inverse power-law relaxation, of power $3/2$, over an evaluated long time scale. If compared to the exponential-like relaxation obtained from the original Jaynes-Cummings model for Lorentzian-type spectral density functions, decoherence is strongly suppressed. The special reservoir exhibits a band-edge frequency coinciding with the qubit transition frequency. Known theoretical models of photonic band-gap media suitable for the realization of the designed reservoir are proposed.