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arXiv:2407.18873 · Physical Review Research

Absence of gapless Majorana edge modes in few-leg bosonic flux ladders

Felix A. Palm, Cécile Repellin, Nathan Goldman, Fabian Grusdt

Published Jan 6, 2025• 1 citation
arXivHTMLPDF

Abstract

The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions are topologically ordered non-Abelian phases of matter, such as certain fractional quantum Hall states. Quantum simulators provide unprecedented controllability and versatility to investigate such states, and developing experimentally feasible schemes to realize and identify them is of immediate relevance. Motivated by recent experiments, we consider bosons on coupled chains, subjected to a magnetic flux and experiencing Hubbard repulsion. At magnetic filling factor ν = 1 , similar systems on cylinders have been found to host the non-Abelian Moore-Read Pfaffian state in the bulk. Here, we address the question of whether more realistic few-leg ladders can host this exotic state and its chiral Majorana edge states. To this end, we perform extensive density-matrix renormalization-group simulations and determine the central charge of the ground state. While we do not find any evidence of gapless Majorana edge modes in systems of up to six legs, exact diagonalization of small systems reveals evidence for the Pfaffian state in the entanglement structure. By systematically varying the number of legs and monitoring the appearance and disappearance of this signal, our work highlights the importance of finite-size effects for the realization of exotic states in experimentally realistic systems.

DOI
10.1103/physrevresearch.7.l012001

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Recent experimental advances in the field of cold atoms led to the development of novel techniques for producing synthetic dimensions and synthetic magnetic fields, thus greatly expanding the utility of cold atomic systems for exploring exotic states of matter. In this paper we investigate the possibility of using experimentally tunable interactions in such systems to mimic the physics of Majorana chains, currently a subject of intense research. Crucially to our proposal, the interactions, which are local in space, appear non-local in the synthetic dimension. We use this fact to induce coupling between counter-propagating edge modes in the quantum Hall regime. For the case of attractive interactions in a system composed of two tunneling-coupled chains, we find a gapless quasi-topological phase with a doubly-degenerate ground state. While the total number of particles in the system is kept fixed, this phase is characterized by strong fluctuations of the pair number in each chain. Each ground state is characterized by the parity of the total particle number in each chain, similar to Majorana wires. However, in our system this degeneracy persists for periodic boundary conditions. For open boundary conditions there is a small splitting of this degeneracy due to the single-particle hopping at the edges. We show how subjecting the system to additional synthetic flux or asymmetric potentials on the two chains can be used to control this nonlocal qubit. We propose experimental probes for testing the nonlocal nature of such a qubit and measuring its state.
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