Adiabatic preparation of a number-conserving atomic Majorana phase

TL;DR

This paper proposes an adiabatic protocol to prepare a topological Majorana phase in ultracold atoms, using a symmetry-breaking flux to open a bulk gap, supported by theoretical analysis and numerical simulations.

Contribution

It introduces a novel flux-based method to adiabatically generate Majorana edge states in a number-conserving atomic system, with analytical and numerical validation.

Findings

The protocol achieves optimal linear ramp times with system size.

The flux term is essential for opening a bulk gap in the model.

Numerical MPS simulations support the theoretical predictions.

Abstract

We construct a protocol to adiabatically prepare the ground state of a widely discussed number-conserving model Hamiltonian for ultracold atoms in optical lattices that supports Majorana edge states. In particular, we introduce a symmetry breaking mass term that amounts to threading a commensurate (artificial) magnetic flux through the plaquettes of the considered two-leg ladder which opens a constant bulk gap. This enables the preparation of the topological Majorana phase from a trivial Mott insulator state with optimal asymptotic scaling of the ramp time in system size, which is linear owing to the critical nature of the target state. Using constructive bosonization techniques that account for both finite size effects and global fermion number conservation, we are able to fully explain with theory the somewhat counterintuitive necessity of the aforementioned commensurate flux for a controlled bulk gap. Our analytical predictions are corroborated and quantified by unbiased numerical matrix product states (MPS) simulations. Directly building up on previous experimental work, the crucial flux-term of the proposed protocol is feasible with state-of-the-art experimental techniques in atomic quantum simulators.