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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Self-modulation of pulses in Kerr medium and limits of the single-mode approximation

Dmitri A. Kouznetsov, Eduardo García Gómez

Published Jul 19, 1999• 0 citations
Publisher

Abstract

Any nonlinear interaction, in principle, can produce non-classical state. The Kerr nonlinearity seems to be the simplest one. Since papers [1-3], it seemed that as the squeezed states, as the Schriidinger cat ones can be produced by the self-modulation. The squeezing was really observed [ 3] in such a scheme. As for cats, Ref. {4,5] mention the large distance of propagation and linear absorption as factors which make the experimental realization unlike. Note that neither the large distance of propagation nor the linear absorption are fundamental reasons why the Schrödinger cat cannot be obtained by such a manner.

DOI
10.1117/12.354790

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Any nonlinear interaction, in principle, can produce non-classical state. The Kerr nonlinearity seems to be the simplest one. Since papers [1-3], it seemed that as the squeezed states, as the Schriidinger cat ones can be produced by the self-modulation. The squeezing was really observed [ 3] in such a scheme. As for cats, Ref. {4,5] mention the large distance of propagation and linear absorption as factors which make the experimental realization unlike. Note that neither the large distance of propagation nor the linear absorption are fundamental reasons why the Schrödinger cat cannot be obtained by such a manner.
Programmable control and production of quantum light states with required non-classical properties are theoretically demonstrated using the cross-Kerr modulation induced between nonlinearly coupled signal and ancillary quantum field modes. By varying the squeezing and displacement parameters of input modes, it is possible to obtain different types of non-classical field states at the output. High-number Fock states, Schrödinger cat states, and cubic phase states are shown to be almost perfectly produced. The proposed approach gives rise to a tunable method for the synthesis of a wide class of non-classical states of quantum fields critical for quantum computation and quantum information technology.
There has been a lot of interest recently in what are referred to as Schrodinger cat states. No precise formulation of the concepts of Schrodinger cat states and classical distinguishability appears to exist. This paper aims to explore these concepts. A number of illustrative examples are presented, including a perturbed harmonic oscillator admitting coherent states with time-dependent amplitude modulation. One can convert the results on harmonic oscillators to single-mode optical systems in the standard manner. It would be interesting to see an experimental realization of these amplitude-modulated coherent states.
Quantum theory of self-phase and cross-phase modulation of ultrashort light pulses in the Kerr medium is developed, taking into account the response time of an electronic nonlinearity. The corresponding algebra of time-dependent Bose operators is elaborated. It is established that the spectral region of the pulse where the quadrature fluctuation level is lower than the shot-noise one depends on the value of the nonlinear phase shift, the intensity of another pulse and the relaxation time of the nonlinearity. It is shown that the frequency of the pulse spectrum at which the suppression of fluctuations is maximum can be controlled by adjusting the other pulse intensity.
The consistent quantum theory of self-phase modulation (SPM) and cross-phase modulation (XPM) for ultrashort light pulses (USP) in medium with electronic Kerr-nonlinearity are developed. The approach makes use of momentum operator of electrical field which takes account of the inertial behaviour of the nonlinearity. The spectrum of quantum fluctuations of squeezed-quadrature component as a function of response time of nonlinearity and values of nonlinear phase shifts due to the SPM and XPM effects, is investigated.
Self-induced transparency in a resonant two-level system creates a 2\ensuremath{\pi}-soliton pulse, which produces large optical nonlinearities with a very fast response time and an extremely small loss. The self-phase modulation of a 2\ensuremath{\pi} soliton and the mutual-phase modulation by the collision of two 2\ensuremath{\pi} solitons in the excitonic range of the spectrum in CdS can achieve the effective ${\ensuremath{\chi}}^{(3)}$ coefficient of ${10}^{\mathrm{\ensuremath{-}}6}$ to ${10}^{\mathrm{\ensuremath{-}}4.5}$ esu for a pulse duration of 1 to 3 ps. The quantum theory of 2\ensuremath{\pi} solitons predicts this new nonlinear process can realize squeezed states and quantum nondemolition measurement 20 dB below the standard quantum limit.