  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.
