  The non-Hermitian skin effect (NHSE), featured by the collapse of bulk-band
eigenstates into the localized boundary modes of the systems, is one of most
striking properties in the fields of non-Hermitian physics. Unique physical
phenomena related to the NHSE have attracted a lot of interest, however, their
experimental realizations usually require nonreciprocal hopping, which faces a
great challenge in ultracold-atom systems. In this work, we propose to realize
the NHSE in a 1D optical lattice by periodically-driven ultracold atoms in the
presence of staggered atomic loss. By studying the effective Floquet
Hamiltonian in the high-frequency approximation, we reveal the underlying
mechanism for the periodic-driving-induced the NHSE. We found that the robust
NHSE can be tuned by driving phase, which is manifested by the dynamical
localization. Most remarkably, we uncover the periodic-driving-induced critical
skin effect for two coupled chains with different driving phases, accompanied
by the appearance of size-dependent topological in-gap modes. Our studies
provide a feasible way for observing the NHSE and exploring corresponding
unique physical phenomena due to the interplay of non-Hermiticity and many-body
statistics in ultracold-atom systems.
