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Physics Letters A

Phase fluctuations of coherent light coupled to a nonlinear medium of inversion symmetry

Anirban Pathak, Swapan Mandal

Published Aug 1, 2000• 18 citations
Publisher
DOI
10.1016/s0375-9601(00)00446-1

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The quantum statistical properties of a single mode of the radiation field, prepared in the coherent state, interacting with a nonlinear medium of inversion symmetry are studied with the help of the usual two photon correlation function for zero time delay. We report the photon antibunching and sub-Poissonian photon statistics in addition to the usual photon bunching and the super-Poissonian photon statistics for an input vacuum field. The manipulation of the phase of input coherent light gives rise to the well known self induced transparency. The possible physical explanations for these events are presented.

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An analytical approach is adopted for the calculation of squeezed property of coherent light interacting with a nonlinear medium of inversion symmetry. A medium is called inversion symmetric if the potential energy remains invariant under parity transformation. Thus the even order susceptibilities would vanish for the medium and the leading contribution to the nolinear polarization due to the medium is the third order susceptibility. Therefore interaction Hamitonian of the single mode light field with the medium is proportional to the fourth power of the annihilation operator plus creation operator. This means is to take care all the non conserving energy terms for the calculation of the squeezing property of coherent light passing through the nonlinear medium of inversion symmetry. For a single mode light, two dimensionless quadrature operators are defined which are proportional to the usual position and momentum operators respectively. Using the Heisenberg operator equation of motion, the differential equation of the quadrature operators and the approximate solutions to the equations are got. Then the quantum fluctuations of the two quadratures are calculated. The result shows that the squeezing property of the two quadrature operators is controllable through changing the following parameters: coupling constant, mean photon number, light field frequency, and interaction time.
The interaction of coherent light with a nonlinear medium is modeled here by a general quantum anharmonic oscillator. The model is not exactly solvable in a closed analytical form. But we need operator solutions of the equations of motion corresponding to these models in order to study the quantum fluctuations of coherent light in nonlinear media. In the present work we derive approximate operator solutions. From these solutions we observe that there exists an apparent discrepancy between the solutions obtained by different techniques. We compare different solutions and conclude that all correct solutions are equivalent and the apparent discrepancy is due to the use of different ordering of the operators. We use these solutions to investigate the possibilities of observing different optical phenomena in a nonlinear dielectric medium. To be precise, we have studied quantum phase fluctuations of coherent light in a third order inversion symmetric nonlinear medium. Fluctuations in phase space quadrature for the same system are studied and the possibility of generating squeezed state is reported. Fluctuations in photon number are studied and the nonclassical phenomenon of antibunching is predicted. We have generalized the results obtained for third order nonlinear medium and have studied the interaction of an intense laser beam with a general (m-1)-th order nonlinear medium. Aharanov Anandan nonadiabatic geometric phase is also discussed in the context of (m-1)-th order nonlinear medium.
The quantum statistical properties of a single mode of the radiation field, prepared in the coherent state, interacting with a nonlinear medium of inversion symmetry are studied with the help of the usual two photon correlation function for zero time delay. We report the photon antibunching and sub-Poissonian photon statistics in addition to the usual photon bunching and the super-Poissonian photon statistics for an input vacuum field. The manipulation of the phase of input coherent light gives rise to the well known self induced transparency. The possible physical explanations for these events are presented.