Effects of Gapless Bosonic Fluctuations on Majorana Fermions in Atomic Wire Coupled to a Molecular Reservoir

TL;DR

This paper investigates how quantum and thermal fluctuations affect Majorana edge states in a topological atomic wire coupled to a superfluid reservoir, revealing their exponential decay dependence on wire length and temperature-dependent decoherence times.

Contribution

It provides a detailed analysis of fluctuation effects on Majorana states, showing their impact on stability and coherence in mesoscopic systems at finite temperatures.

Findings

Coupling between Majorana states remains exponentially decaying with wire length at finite temperatures.

Thermal fluctuations influence the preexponential factor, increasing with temperature and wire length.

Thermalization time exceeds typical operational timescales, allowing quantum operations before decoherence.

Abstract

We discuss the effects of quantum and thermal fluctuations on the Majorana edge states in a topological atomic wire coupled to a superfluid molecular gas with gapless excitations. We find that the coupling between the Majorana edge states remains exponentially decaying with the length of the wire, even at finite temperatures smaller than the energy gap for bulk excitations in the wire. This exponential dependence is controlled solely by the localization length of the Majorana states. The fluctuations, on the other hand, provide the dominant contribution to the preexponential factor, which increases with temperature and the length of the wire. More important is that thermal fluctuations give rise to a decay of an initial correlation between Majorana edge states to its stationary value after some thermalization time. This stationary value is sensitive to the temperature and to the length of the wire, and, although vanishing in the thermodynamic limit, can still be feasible in a mesoscopic system at sufficiently low temperatures. The thermalization time, on the other hand, is found to be much larger than the typical time scales in the wire, and is sufficient for quantum operations with Majorana fermions before the temperature-induced decoherence sets in.