Higher-order parity states of the quantum electromagnetic field

We construct higher-order parity observables for a single mode of the quantum electromagnetic field from harmonics of the ordinary parity observable cos(πnˆ). Higher-order parity states arise when the quantum-optical Hilbert space is projected into specific groupings of photon number. Optical systems with cross-Kerr nonlinearities can produce such parity states. Here, we generalize the dispersive micromaser cavity QED formalism of C.C. Gerry [Phys. Rev. A 53 (1996) 3818] to demonstrate that these states are also produced in systems governed by atom-field interactions.