Adiabatic and Superadiabatic Control of Decoherence-Free Subspaces in Collective SU(n) Systems

We examine time-dependent decoherence-free subspaces in a bad-cavity system using n-dimensional atoms. By adiabatically varying the intensity of external driving lasers, we can transfer the system from a trivial coherent spin state to a highly entangled state while remaining in the instantaneous decoherence-free subspace such that the state remains pure in the face of decoherence. These engineered states have applications in both quantum metrology and quantum information science. We further comment on the prospects of superadiabatic transfer within a decoherence-free subspace, and develop an adiabatic shortcut to quickly transfer from a state localized in "position'' to one localized in "momentum'' in a tilted lattice system.