  The form of the eigenstates of an atom coupled to a cavity mode displaying a
three dimensional periodic profile are obtained. It is shown that the quantized
motion leads to degenerate states where the atomic degrees of freedom are
masked, that is, upon detection of one component of this composite system the
others remain in an entangled state. When the system is extended to include
drive and dissipation it is found to undergo a dissipative quantum phase
transition at a critical drive amplitude. Unlike other phase transitions
reported in the literature, the degeneracy prepares the system in a
superposition of incompatible states upon detection of the electromagnetic
field. Probing the field hints at an order above the transition point that, due
to state masking, allows for atomic coherence to survive at long times.
