  We discuss the possibility of phase-conjugation of an atomic Fermi field via
nonlinear wave mixing in an ultracold gas. It is shown that for a beam of
fermions incident on an atomic phase-conjugate mirror, a time reversed backward
propagating fermionic beam is generated similar to the case in nonlinear
optics. By adopting an operational definition of the phase, we show that it is
possible to infer the presence of the phase-conjugate field by the loss of the
interference pattern in an atomic interferometer.
