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We generalize the quantum optical input-output theory developed for opticalcavities to ultracold fermionic atoms confined in a trapping potential, whichforms an "atom cavity". In order to account for the Pauli exclusion principle,quantum Langevin equations for all cavity modes are derived. The dissipativepart of these multi-mode Langevin equations includes a coupling between cavitymodes. We also derive a set of boundary conditions for the Fermi field thatrelate the output fields to the input fields and the field radiated by thecavity. Starting from a constant uniform current of fermions incident on oneside of the cavity, we use the boundary conditions to calculate the occupationnumbers and current density for the fermions that are reflected and transmittedby the cavity

Input-output theory for fermions in an atom cavity