  Mobility edges (ME), separating Anderson-localized states from extended
states, are known to arise in the single-particle energy spectrum of certain
one-dimensional lattices with aperiodic order. Dephasing and decoherence
effects are widely acknowledged to spoil Anderson localization and to enhance
transport, suggesting that ME and localization are unlikely to be observable in
the presence of dephasing. Here it is shown that, contrary to such a wisdom, ME
can be created by pure dephasing effects in quasicrystals in which all states
are delocalized under coherent dynamics. Since the lifetimes of localized
states induced by dephasing effects can be extremely long, rather
counter-intuitively decoherence can enhance localization of excitation in the
lattice. The results are illustrated by considering photonic quantum walks in
synthetic mesh lattices.
