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.

• Received 23 July 2019
• Accepted 28 January 2020

DOI:https://doi.org/10.1103/PhysRevA.101.023825