  We generalize the quantum optical input-output theory developed for optical
cavities to ultracold fermionic atoms confined in a trapping potential, which
forms an "atom cavity". In order to account for the Pauli exclusion principle,
quantum Langevin equations for all cavity modes are derived. The dissipative
part of these multi-mode Langevin equations includes a coupling between cavity
modes. We also derive a set of boundary conditions for the Fermi field that
relate the output fields to the input fields and the field radiated by the
cavity. Starting from a constant uniform current of fermions incident on one
side of the cavity, we use the boundary conditions to calculate the occupation
numbers and current density for the fermions that are reflected and transmitted
by the cavity.
