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International Journal of Modern Physics B

PHASE CHANGES IN NONLINEAR PROCESSES IN INTERACTING FOCK SPACE

Pradip Das, Arpita Ghosh

Published Feb 10, 2006• 2 citations
Publisher

Abstract

In this paper we study quantum mechanical phase distribution of some nonlinear optical phenomena in a general setting of interacting Fock space. We have investigated the optical phenomena of propagation through a nonlinear medium as in optical fiber and the process of photon absorption from a thermal beam. The input and output phase distribution have been investigated analytically in these two cases.

DOI
10.1142/s0217979206033371

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In this paper we study quantum mechanical phase distribution of some nonlinear optical phenomena in a general setting of interacting Fock space. We have investigated the optical phenomena of propagation through a nonlinear medium as in optical fiber and the process of photon absorption from a thermal beam. The input and output phase distribution have been investigated analytically in these two cases.
Quantum-mechanical phase distributions are investigated for some nonlinear optical phenomena which, at a classical level, involve only changes in the phase of the electric field. The phenomena investigated include reflection from a phase-conjugate mirror and propagation through an optical fiber. It is found that, while the peaks of the respective phase distributions exhibit the expected classical behavior, the widths of the phase distributions also undergo substantial changes. The relation between the input and the output phase distributions in the two cases mentioned above is investigated analytically as well as numerically. The results are compared with a phase distribution defined via the Wigner function.
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 nonlinear interaction of light with matter is described from a quantum-statistical point of view. The phenomena of two-photon emission and two-photon absorption including both the single- and two-mode cases and the Raman effect are discussed in detail. A master equation for the density operator of the light fields alone is derived. This operator equation is converted to a c number equation and analytic solutions are obtained for the diagonal matrix elements of the density operator in the Fock representation. No linearizing approximation is introduced. These solutions allow one to compute the moments of the photon distribution for the above nonlinear processes.
Nonlinear interaction of light with matter is described from the quantum-statistical point of view. The cases of two-photon absorption, Raman transition, sum-frequency generation, parametric amplification, and incoherent scattering are discussed. It is shown that the nonlinear optical effects depend strongly on the statistical properties of the light fields. The rate of nonlinear absorption, generation, and amplification is higher for chaotic than for coherent, and also higher for multimode than for single-mode pump fields. Measurements of the statistics of the output fields may yield information about the statistics of the input fields and the properties of the medium.
Partial table of contents: PART I: GENERAL CONCEPTS AND METHODS OF NONLINEAR OPTICS. Electromagnetic Fields. Classical Description. The Quantized Free Radiation Field. Interaction Between Radiation and Matter. Semiclassical Description of Nonlinear Optics. Statistical and Coherence Properties of the Radiation Field and Their Measurement. Nonstationary Processes. PART II: EFFECTS AND PROCESSES OF NONLINEAR OPTICS. Nonlinear One--photon Processes in Lasers. Nonlinearities in Transient One--photon Processes. Nonlinearities and Qunatum Phenomena in Transient One--photon Processes. Multiphoton Absorption and Emission. Generation of Harmonics and Sum and Difference Frequencies. Parametric Amplification and Oscillation. Stimulated Raman Scattering. Optical Bistability. APPENDIX A: Compilation of Quantum--Theoretical Definitions and Relations. General References. Index.