Driven-dissipative many-body pairing states for cold fermionic atoms in an optical lattice

We discuss the preparation of many-body states of cold fermionic atoms in an optical lattice via controlled dissipative processes induced by coupling the system to a reservoir. Based on a mechanism combining Pauli blocking and phase locking between adjacent sites, we construct complete sets of jump operators describing coupling to a reservoir that leads to dissipative preparation of pairing states for fermions with various symmetries in the absence of direct inter-particle interactions. We discuss the uniqueness of these states, and demonstrate it with small-scale numerical simulations. In the late time dissipative dynamics, we identify a "dissipative gap" that persists in the thermodynamic limit. This gap implies exponential convergence of all many-body observables to their steady state values. We then investigate how these pairing states can be used as a starting point for the preparation of the ground state of Fermi-Hubbard Hamiltonian via an adiabatic state preparation process also involving the parent Hamiltonian of the pairing state. We also provide a proof-of-principle example for implementing these dissipative processes and the parent Hamiltonians of the pairing states, based on Yb171 atoms in optical lattice potentials.