Simulation and measurement of the fractional particle number in one-dimensional optical lattices

TL;DR

This paper proposes a method to simulate and measure fractional particle numbers in a one-dimensional optical lattice system using ultracold fermions, Berry curvature, and particle transport, avoiding the need for a spatial domain wall.

Contribution

It introduces a novel scheme to emulate fractional particle numbers via momentum-time space Berry curvature and provides practical experimental setups for realization.

Findings

Simulation of fractional particle number in momentum-time space.

Proposed experimental setups for optical lattice realization.

Methods for measuring particle transport through Wannier center shifts.

Abstract

We propose a scheme to mimic and directly measure the fractional particle number in a generalized Su-Schrieffer-Heeger model with ultracold fermions in one-dimensional optical lattices. We show that the fractional particle number in this model can be simulated in the momentum-time parameter space in terms of Berry curvature without a spatial domain wall. In this simulation, a hopping modulation is adiabatically tuned to form a kink-type configuration and the induced current plays the role of an analogous soliton distributing in the time domain, such that the mimicked fractional particle number is expressed by the particle transport. Two feasible experimental setups of optical lattices for realizing the required Su-Schrieffer-Heeger Hamiltonian with tunable parameters and time-varying hopping modulation are presented. We also show practical methods for measuring the particle transport in the proposed cold atom systems by numerically calculating the shift of the Wannier center and the center of mass of an atomic cloud.