Detecting fractional Chern insulators in optical lattices through quantized displacement

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 high controllability of optical lattices and the engineering of topological band structures with the help of synthetic gauge fields. However, their detection might prove difficult since transport measurements akin to those in solid state systems are challenging to perform in cold atom setups. We show that for a ν=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 σ_xy can be accurately determined by the displacement of the atomic cloud under the action of a constant force. This provides an experimentally realistic measurable signal to detect the topological nature of the state. Using matrix-product state algorithms, we demonstrate 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 σ_xy and determine the suitable range of field strengths.