Majorana Zero Modes in Synthetic Dimensions

Abstract

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.

Anyons in multichannel Kondo systems

“…This includes spin liquids 4, [14][15][16][17][18] , topological superconductivity and symmetry protected phases, 19 as well as topological phases nanowires [20][21][22] and artificially engineered low-dimensional structures. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] The gap that protects these topological systems has been understood as compulsory for the existence of anyons. Indeed, in the 2D scenarios described above, anyons exist as dynamical excitations over an isolated ground multiplet.…”