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Optics Communications

An exact calculation of the expectation values of phase operators in squeezed states

Hong-Yi Fan, Haider R. Zaidi

Published Sep 1, 1988• 44 citations
Publisher
DOI
10.1016/0030-4018(88)90140-x

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A new set of phase operators for the electromagnetic field has been defined by an extension of squeezed-state theory. In several cases these operators have similar or the same properties as the previously defined (Susskind–Glogower) operators. However, the new operators also have unique properties of their own. The expectation values of the phase operators have been found for a squeezed state and been shown to reduce to the expected classical values in the limit of small amounts of squeezing and large field excitation.
The phase properties of the self-squeezed states generated during the evolution of the anharmonic oscillator are discussed from the point of view of the new phase formalism of Pegg and Barnett. The phase distribution, the expectation values and the variances of the Hermitian phase operator are obtained and their evolution illustrated graphically. The mean values for the phase cosine and sine functions as well as their variances are also calculated. The results are compared to the Susskind-Glogower formalism results and the results based on the measured phase concept. The relation between squeezing and the phase properties of the field is discussed briefly.
It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.