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We develop a theory to describe the dynamics of a driven-dissipativemany-body Fermi system, to pursue our proposal to realize exotic quantum statesbased on reservoir engineering. Our idea is to design the shape of a Fermisurface so as to have multiple Fermi edges, by properly attaching multiplereservoirs with different chemical potentials to a fermionic system. Theseemerged edges give rise to additional scattering channels that can destabilizethe system into unconventional states, which is exemplified in this work byconsidering a driven-dissipative attractively interacting Fermi gas. Byformulating a quantum kinetic equation using the Nambu-Keldysh Green's functiontechnique, we explore nonequilibrium steady states in this system and assesstheir stability. We find that, in addition to the BCS-type isotropic pairingstate, a Fulde-Ferrell-type anisotropic superfluid state being accompanied byCooper pairs with non-zero center-of-mass momentum exists as a stable solution,even in the absence of a magnetic Zeeman field. Our result implies a greatpotential of realizing quantum matter beyond the equilibrium paradigm, byengineering the shape and topology of Fermi surfaces in both electronic andatomic systems.

physical review. a/physical review, a

Proposed Fermi-surface reservoir-engineering and application to  realizing unconventional Fermi superfluids in a driven-dissipative  non-equilibrium Fermi gas