  We study the effective approximation for a nonlocal stochastic Schrodinger
equation with a rapidly oscillating, periodically time-dependent potential. We
use the natural diffusive scaling of heterogeneous system and study the limit
behaviour as the scaling parameter tends to 0. This is motivated by data
assimilations with non-Gaussian uncertainties. The nonlocal operator in this
stochastic partial differential equation is the generator of a non-Gaussian
Levy-type process (i.e., a class of anomalous diffusion processes), with
non-integrable jump kernel. With help of a two-scale convergence technique, we
establish effective approximation for this nonlocal stochastic partial
differential equation. More precisely, we show that a nonlocal stochastic
Schrodinger equation has a nonlocal effective equation. We show that it
approximates the orginal stochastic Schr\"{o}dinger equation weakly in a
Sobolev-type space and strongly in $L^2$ space. In particular, this effective
approximattion holds when the nonlocal operator is the fractional Laplacian.
