Parity states in the one-atom maser

An experiment to determine the parity of the photon field of one privileged mode in a high-Q resonator is proposed. Even parity indicates that the photon number equals zero, two, four or any other even integer; likewise, odd parity states are mixtures of states with any odd number of photons. The parity measurement can be performed while the resonator is pumped as in standard one-atom maser operation. The time dependence of the parity expectation value is studied theoretically, and we suggest its experimental verification, which would serve as a test of the standard models describing both the relaxation of the cavity field toward thermal equilibrium and the pumping process. The connection between parity expectation values and Wigner's phase space function is recalled; the central value of the Wigner function equals twice the mean parity and it is, therefore, a measurable quantity.