Phase properties of a damped anharmonic oscillator

Phase properties of a damped anharmonic oscillator are studied within the Hermitian phase formalism of Pegg and Barnett. Exact analytical formulas for the phase distribution function, the expectation value and variance of the phase operator, and the expectation value and variance of the cosine of the phase operator are obtained assuming the zero-temperature reservoir and a coherent initial state of the system. It is shown that quantum periodicity in the evolution of phase quantities is destroyed by damping. The effect of damping on the formation of discrete superpositions of coherent states is discussed. A comparison is made between different phase approaches.