A reservoir for inverse power law decoherence of a qubit

TL;DR

This paper analytically studies a specially designed reservoir that induces inverse power law decoherence in a qubit, significantly suppressing decoherence compared to traditional exponential relaxation, with potential realizations in photonic band gap media.

Contribution

It introduces an exactly solvable model of a reservoir causing inverse power law decoherence in a qubit, advancing understanding of non-exponential decoherence dynamics.

Findings

Decoherence follows an inverse power law with exponent 3/2 over long times.

Compared to Lorentzian spectral densities, decoherence is strongly suppressed.

The reservoir design aligns with photonic band gap media for practical implementation.

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 an upper 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.