  The realization of the quantum anomalous Hall (QAH) effect without magnetic
doping attracts intensive interest since magnetically doped topological
insulators usually possess inhomogeneity of ferromagnetic order. Here, we
propose a different strategy to realize intriguing QAH states arising from the
interplay of light and non-magnetic disorder in two-dimensional topologically
trivial systems. By combining the Born approximation and Floquet theory, we
show that a time-reversal invariant disorder-induced topological insulator,
known as the topological Anderson insulator (TAI), would evolve into a
time-reversal broken TAI and then into a QAH insulator by shining circularly
polarized light. We utilize spin and charge Hall conductivities, which can be
measured in experiments directly, to distinguish these three different
topological phases. This work not only offers an exciting opportunity to
realize the high-temperature QAH effect without magnetic orders, but also is
important for applications of topological states to spintronics.
