  Fully frustrated Josephson Junction arrays (FF-JJA's) exhibit a subtle
compound phase transition in which an Ising transition associated with discrete
broken translational symmetry and a Berezinskii-Kosterlitz-Thouless (BKT)
transition associated with quasi-long-range phase coherence occur nearly
simultaneously. In this Letter we discuss a cold atom realization of the FF-JJA
system. We demonstrate that both orders can be studied by standard
momentum-distribution-function measurements and present numerical results,
based on a successful self-consistent spin-wave approximation, that illustrate
the expected behavior of observables.
