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We theoretically propose an idea based on reservoir engineering to processthe structure of a Fermi edge to split into multiple Fermi edges, so as to besuitable for the state which we want to realize. When one appropriately tunesthe chemical-potential difference between two reservoirs being coupled with thesystem, the system is shown to be in the non-equilibrium steady state with themomentum distribution having a two-edge structure. We argue that these edgesplay similar roles to two Fermi surfaces, which can be designed to realizeexotic quantum many-body states. To demonstrate this, we consider a modeldriven-dissipative two-component Fermi gas with an attractive interaction as aparadigmatic example and show that it exhibits an unconventional Fermisuperfluid. While the superfluid order parameter of this state has the sameform as that in the Fulde-Ferrell state discussed in metallic superconductivityunder an external magnetic field, the former non-equilibrium pairing state isnot accompanied by any spin imbalance. Our proposed reservoir engineering toprocess the Fermi momentum distribution would provide further possibilities ofmany-body quantum phenomena beyond the thermal equilibrium case.

Proposed Fermi-surface reservoir-engineering and application to realizing unconventional Fermi superfluids