Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement

TL;DR

This paper proposes a method to detect fractional Chern insulators in cold atom systems by measuring the quantized displacement of an atomic cloud under a constant force, providing an accessible experimental signature of topological order.

Contribution

It introduces a novel detection technique for FCIs in optical lattices using cloud displacement measurements, bypassing the need for transport measurements.

Findings

Displacement of atomic cloud correlates with Hall conductivity in FCI states.

Method effective in both cylinder and square geometries.

Quantized displacement serves as a signature of topological order.

Abstract

The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields providing the required topological band structures. However, detecting their occurrence might prove difficult since transport measurements akin to those in solid state systems are challenging to perform in cold atom setups and alternatives have to be found. We show that for a $\nu= 1/2$ FCI state realized in the lowest band of a Harper-Hofstadter model of interacting bosons confined by a harmonic trapping potential, the fractionally quantized Hall conductivity $\sigma_{xy}$ can be accurately determined by the displacement of the atomic cloud under the action of a constant force which provides a suitable experimentally measurable signal for detecting the topological nature of the state. Using matrix-product state algorithms, we show that, in both cylinder and square geometries, the movement of the particle cloud in time under the application of a constant force field on top of the confining potential is proportional to $\sigma_{xy}$ for an extended range of field strengths.