  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.
