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 optical lattices with synthetic gauge fields has recently come within experimental reach. 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 consider a ν = 1/2 FCI state realized in the lowest band of a Harper-Hofstadter model of hardcore bosons in a harmonic trapping potential. We demonstrate the stability of the topological state for a wide range of confining strengths by density matrix renormalization group simulations. Using matrix-product state algorithms, we study the time evolution when applying an effective electric field for the particles on top of the harmonic confinement. The movement of the particle cloud allows an accurate determination of the fractionally quantized Hall conductivity which provides an experimentally measurable signal to detect the topological nature of the state. Below a critical field strength, the particle displacement shows oscillations around the quantized value which abate as the field strength decreases.