Graphical representation of squeezed-state variances

Donita Cohen, Y. Ben-Aryeh, A. Mann

R. Tanaś, Adam Miranowicz, S. Kielich

The problem of squeezing and its graphical representations in the anharmonic oscillator model is considered. Explicit formulas for squeezing, principal squeezing, and the quasiprobability distribution (QPD) function are given and illustrated graphically. Approximate analytical formulas for the variances, extremal variances, and QPD are obtained for the case of small nonlinearities and large numbers of photons. The possibility of almost perfect squeezing in the model is demonstrated and its graphical representations in the form of variance lemniscates and QPD contours are plotted. For large numbers of photons the crescent shape of the QPD contours is hardly visible and quite regular ellipses are obtained.

Skylar Turner, Brian R. La Cour

Ts. Gantsog, R. Tanaś

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.

G. S. Agarwal, R. Simon

Hai-Woong Lee

A representation is introduced in which a state of a radiation field is characterized by a function of a parameter which can be any arbitrary number. This functional representation of a field state offers a convenient means of classifying squeezed states and calculating their variances. Some new squeezed states are found from an analysis based on this representation.