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

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.

33 pages, 7 figures. Typos corrected

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Weakly bound dimers of fermionic atoms
• Anyons and the quantum Hall effect - a pedagogical review
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Hybrid Topological Quantum Computation with Majorana Fermions: A Cold Atom Setup

Cited by in corpus (11)

• Topological Heat Transport and Symmetry-Protected Boson Currents
• Majoranas in Noisy Kitaev Wires
• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
• Unveiling Signatures of Topological Phases in Open Kitaev Chains and Ladders
• Quantum memories with zero-energy Majorana modes and experimental constraints
• Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing
• Anderson localization of Cooper pairs and Majorana fermions in an ultracold atomic Fermi gas with synthetic spin-orbit coupling
• Universal long-time behavior of stochastically driven interacting quantum systems
• Stability of the boundary zero modes in one-dimensional topological superconductors
• Effects of dynamical noises on Majorana bound states
• Memory-Critical Dynamical Buildup of Phonon-Dressed Majorana Fermions