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Journal of Modern Optics

Phase Properties of the Displaced Number State in a Kerr Medium

Bing Leng, Si-de Du, Chang-De Gong

Published Feb 1, 1995• 3 citations
Publisher

Abstract

Influences of the interaction of the displaced-number-state field with a Kerr medium on phase properties of the field are investigated. The interaction brings about the symmetrical splitting of the phase probability distribution (PPD) sometimes. Collapses and revivals have also been found in the long-time behaviours of the Hermitian, cosine and sine phase operators at high intensities. In terms of the PPD, the origin for generating these revivals has been revealed.

DOI
10.1080/09500349514550381

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•Jan 1, 1996•0 citations
Influences of the interaction of the displaced-number-state field with a Kerr medium on phase properties of the field are investigated. The interaction brings about the symmetrical splitting of the phase probability distribution (PPD) sometimes. Collapses and revivals have also been found in the long-time behaviours of the Hermitian, cosine and sine phase operators at high intensities. In terms of the PPD, the origin for generating these revivals has been revealed.
The influence of Stark shift on the phase properties when an ideal cavity is filled with a Kerr-like medium and coupling is effected through nondegenerate Raman two-photon processes is studied. This has been carried out using the Hermitian phase formalism of Pegg and Barnett. We find that the phase properties of the field reflect the collapses and revivals of the level occupation probabilities in most situations. The interaction brings about the symmetrical splitting of the phase probability distribution. A number of interesting features are found and discussed.
Using Pegg-Barnett formalism the author has studied the phase properties of displaced number states. It has been found that the phase probability distribution exhibits the same oscillations as the photon number distribution. Using the Hermitian phase operator the fluctuations of the phase of the displaced number states have been studied. The dependence of the fluctuations on the value of the reference phase have been analysed in detail. It has been found that phase of displaced number states exhibit squeezing in the high-intensity limit of the driving field. These states are approximately equivalent to phase states with precisely defined phase. It has been shown that displaced number states are not minimum uncertainty states with respect to the phase and the number operators.
Displaced and squeezed Fock states have recently been thoroughly investigated. Application of these states as the input of a Kerr nonlinear medium reveals many nonclassical effects. We solve this problem analytically and demonstrate results by numerical examples. We introduce a phase distribution for the antinormal quasidistribution ${\mathrm{\ensuremath{\varphi}}}_{\mathit{s}\mathit{c}\mathit{r}\mathit{A}}$ and show that the ``phase'' of the new states can be sharply localized at some values. This happens when revivals appear in the field. If the states are shifted by a reference wave, photon-number distributions clearly detect the structure of ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{scrA}}$. Damping of the new states is briefly discussed.