Persistent current by a static non-Hermitian ratchet

We propose a scheme to generate a persistent current in driven-dissipative systems which can be described by the generalized Gross-Pitaevskii (GP) equation. Our proposal consists of fabricating a rachet-potential shape of the loss-rate profile, which simultaneously breaks the time-reversal symmetry and the parity-inversion symmetry. Unlike existing schemes to generate a current using a rachet potential in Hermitian systems, no dynamic drive is needed. The basic physics of our scheme is discussed by a simple discrete driven-dissipative GP model, and the results are also verified by a realistic continuous model. Furthermore, we demonstrate the experimental feasibility of our scheme to generate the persistent current in exciton-polariton condensates in a semiconductor microcavity.