Optical pumping through the Liouvillian skin effect

Abstract: The Liouvillian skin effect describes the boundary affinity of Liouvillian eignemodes that originates from the intrinsic non-Hermiticity of the Liouvillian superoperators. Dynamically, it manifests as directional flow in the transient dynamics, and the accumulation of population near open boundaries at long times. Intriguingly, similar dynamic phenomena exist in the well-known process of optical pumping, where the system is driven into a desired state (or a dark-state subspace) through the interplay of dissipation and optical drive. In this work, we show that typical optical pumping processes can indeed be understood in terms of the Liouvillian skin effect. By studying the Liouvillian spectra under different boundary conditions, we reveal that the Liouvillian spectra of the driven-dissipative pumping process sensitively depend on the boundary conditions in the state space, a signature that lies at the origin of the Liouvillian skin effect. Such a connection provides insights and practical means for designing efficient optical-pumping schemes through engineering Liouvillian gaps under the open-boundary condition. Based on these understandings, we show that the efficiency of a typical side-band cooling scheme for trapped ions can be dramatically enhanced by introducing counterintuitive dissipative channels. Our results provide a useful perspective for optical pumping, with interesting implications for state preparation and cooling.