  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.
