Conduction electrons and the decoherence of solid state qubits

TL;DR

This paper models how conduction electrons influence the decoherence of solid state qubits, deriving master equations and analyzing the impact of bath-mediated interactions on decoherence times.

Contribution

It introduces a theoretical framework for understanding impurity electron dynamics and bath-mediated interactions in solid state qubits.

Findings

RKKY interaction causes energy shifts when inter-qubit distance is small.

Decoherence times are significantly affected by bath-mediated interactions.

The impact of the bath interaction decreases as the inter-qubit distance increases.

Abstract

We study the dynamics of impurity bound electrons interacting with a bath of conduction band electrons in a semiconductor. Only the exchange interaction is considered. We derive master equations for the density matrices of single and two qubit systems under the usual Born and Markov approximations. The bath mediated RKKY interaction in the two qubit case arises naturally. It leads to an energy shift significant only when the ratio ($R_{T}$) of the inter-qubit distance to the thermal deBroglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact on the decoherence times; the effect decreases monotonically with $R_{T}$.