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Journal of Modern Optics

Quasi-photon Phase States

Ravinder Nath, Pradumn Kumar

Published Feb 1, 1991• 19 citations
Publisher

Abstract

We introduce quasi-photon phase states of radiation in the single mode, and study the fluctuations in the measured phase operators. We also show that these states exhibit bunching, unlike coherent states which show no bunching.
DOI
10.1080/09500349114550291

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The concept of photon antibunching as a manifestation of nonclassical character in single-mode radiation is extended to two-mode radiation. A simple criterion for the existence of nonclassical effects in two-mode radiation is established. It implies that the intermode photon bunching, rather than antibunching, can play a key role in rendering two-mode radiation nonclassical. The two-mode squeezed vacuum states are used as simple examples to illustrate the essential point of the criterion. The criterion is then used to study the nonclassical properties of two types of two-mode squeezed states. A state generated by applying the squeeze operator to the two-mode vacuum first, followed by the displacement operator, is called a two-mode coherent squeezed state. If the order of the two operators is reversed, a two-mode squeezed coherent state is obtained. It is found that the latter has a much stronger tendency to become a nonclassical state than the former, assuming that the parameters involved are all the same. A measure of nonclassical depth of radiation is adopted. It is found that, according to this measure, the effect of squeezing in making two-mode coherent squeezed states nonclassical is not monotonic. Such phenomena do not occur in squeezed coherent states.
The phase operator for a two-mode photon system is defined in terms of the relative-number states, and its property is investigated in detail. The phase operator thus defined has a unitary exponential form. It is shown that the average value and fluctuation of the phase operator, where one mode is in some physical state, such as a coherent or a squeezed state, and the other is in a vacuum state, are equivalent to those obtained by means of the Pegg–Barnett phase operator for a single-mode photon. The average value and fluctuation of the phase operator are calculated for coherent and squeezed states of a two-mode photon system.
The initially prepared coherent state coupled to a third-order nonlinear medium is responsible for stimulated Raman and spontaneous Raman processes. By exploiting the analytical solutions of field operators for various modes, we investigate the quantum statistical properties for pure and two modes of the input coherent light responsible for stimulated Raman and spontaneous Raman processes. For spontaneous Raman processes the photons are unbunched for the pure and two-mode cases. By a suitable choice of phase, we obtain the bunching and antibunching of photons for stimulated Raman processes.