Phonon-induced decoherence of the two-level quantum subsystem due to relaxation and dephasing processes

TL;DR

This paper theoretically investigates phonon-induced decoherence in a double-well quantum system, distinguishing between dephasing and relaxation processes depending on the potential symmetry, with implications for quantum information processing.

Contribution

It provides explicit solutions for the reduced density matrix beyond the Markovian approximation, clarifying the dominant decoherence mechanisms in asymmetric and symmetric potentials.

Findings

Decoherence is mainly due to dephasing in asymmetric potentials.

Relaxation processes dominate decoherence in symmetric potentials.

Different temporal evolutions of electron states are observed depending on potential symmetry.

Abstract

Phonon-related decoherence effects in a quantum double-well two-level subsystem coupled to a solid are studied theoretically by the example of deformation phonons. Expressions for the reduced density matrix at T=0 are derived beyond the Markovian approximation by means of explicit solution of the non-stationary Schrodinger equation for the interacting electron-phonon system at the initial stage of its evolution. It is shown that as long as the difference between the energies of the electron in the left and the right well greatly exceeds the energy of the electron tunneling between the minima of the double-well potential, decoherence is primarily due to dephasing processes. This case corresponds to a strongly asymmetric potential and spatially separated eigenfunctions localized in the vicinity of one or another potential minimum. In the opposite case of the symmetric potential, the decoherence stems from the relaxation processes, which may be either "resonant" (at relatively long times) or "nonresonant" (at short times), giving rise to qualitatively different temporal evolution of the electron state. The results obtained are discussed in the context of quantum information processing based on the quantum bits encoded in electron charge degrees of freedom.