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Physical Review A

Quantum propagation: Squeezing via modulational polarization instabilities in a birefringent nonlinear medium

T. A. B. Kennedy, Stefan W. Wabnitz

Published Jul 1, 1988• 16 citations
Publisher

Abstract

We calculate the spectrum of quadrature fluctuations of orthogonal polarizations of light for a beam propagating along a birefringence axis of a dispersive transparent Kerr medium. Reshaping and tuning of the spectrum is achievable by variation of the pump power or the linear birefringence: Wide-band squeezing is predicted, and its relationship to modulational polarization instabilities discussed.

DOI
10.1103/physreva.38.563

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We calculate the spectrum of quadrature fluctuations of orthogonal polarizations of light for a beam propagating along a birefringence axis of a dispersive transparent Kerr medium. Reshaping and tuning of the spectrum is achievable by variation of the pump power or the linear birefringence: Wide-band squeezing is predicted, and its relationship to modulational polarization instabilities discussed.
We theoretically study quadrature and polarization squeezing in dispersive optical bistability through a vectorial Kerr cavity model describing a nonlinear cavity filled with an isotropic ${\ensuremath{\chi}}^{(3)}$ medium in which self-phase- and cross-phase-modulation, as well as four-wave mixing, occur. We derive expressions for the quantum fluctuations of the output field quadratures as a function of which we express the spectrum of fluctuations of the output-field Stokes parameters. We pay particular attention to study how the bifurcations affecting the non-null linearly polarized output mode squeezes the orthogonally polarized vacuum mode, and show how this produces polarization squeezing.
The influence of quantum fluctuations of the electromagnetic field on the propagation of a polarized light wave in a nonlinear dielectric is investigated. It is shown that in some cases the fluctuations couple to the optical nonlinearities of the medium and make its refractive index dependent on the polarization of the propagating wave. As a consequence, two light waves propagating in the same direction but with different polarizations will have different speeds, so there will be a Kerr-effect birefringence induced by quantum fluctuations. We consider the case of the electromagnetic field in a squeezed vacuum state, where there are regions where the mean squared electric field can be negative and the birefringence effect has the opposite sign to the Kerr effect in classical physics. We give some estimates for the magnitude of these effects, and discuss their possible observability.
Polarization squeezing [1] is attracting much attention in the last few years because of its potential applications in quantum information. We reconsider here the analysis of quantum fluctuations in dispersive optical bistability by generalizing the standard model in order to take into account fluctuations in the two orthogonal polarization components of the intracavity field, and not only in the pumped one as it is customary. In other words, we consider a relatively simple model for a vectorial Kerr cavity: The Kerr nonlinearity is the responsible for dispersive bistability, and two extra nonlinear terms, describing cross-phase modulation and four-wave mixing, couple the intense (pumped) intracavity field (with polarization parallel to that of the field injected in the cavity) with the orthogonally polarized mode. The weight of the new nonlinearities is controlled by the Maker-Terhune coefficients, which verily A + B!2 = 1 for an isotropic material, which we consider. This system exhibits a very rich variety of bifurcations [2], In this communication we describe the simplest results.
The propagation of a quasimonochromatic beam in an optical fiber may be unstable owing to phase-matched four-wave mixing. The phase matching may arise in a variety of ways, and the resulting instabilities are commonly referred to as modulational instabilities. Here I consider the cross-phase-modulational (XPM) instability arising in a high birefringence optical fiber in the normal dispersion (visible) regime when the pump is polarized at 45° to the principal axes of birefringence.1,2 Orthogonally polarized sidebands are generated along these axes. Phase matching arises from a balance between dispersion and the group velocity mismatch of the sidebands and dictates that the up-shifted sideband travels on the fast axis. The sidebands result in terahertz modulation of the pump and are interesting from the point of view of optical communications. From a quantum-statistical perspective, the quantum correlations, which develop as the sidebands are generated from quantum noise, are the focus of attention here.
We investigate the formation of the polarization-squeezed state of light in different schemes of perfect spatial overlap of quadrature-squeezed ultrashort light pulses produced by self-phase modulation effect in electronic Kerr media. The light polarization is treated in terms of four Stokes operators whose spectra of quantum fluctuations are investigated for each configuration of interest. We establish that the frequency at which the suppression of quantum fluctuations of Stokes operators is the greatest can be controlled by adjusting the linear phase difference between initial coherent pulses. The increase of the intensity of one pulse can squeeze efficiently the quantum fluctuations of Stokes operators. We study the spatial overlap of quadrature-squeezed pulses produced in an anisotropic electronic Kerr medium and show that the cross-phase modulation which occurs in addition to the self-phase one can be employed to control the fluctuation spectra of Stokes operators. The change of the nonlinear phase shift per photon for one pulse controls effectively the polarization squeezing. The spatial overlap of a coherent pulse with an interference one, produced by mixing two quadrature-squeezed pulses on a beam splitter, is analysed. It is found that squeezing is produced in three of the four Stokes operators, with the squeezing in the first two being simultaneous.
A brief review of theoretical studies of the quantum state of polarization of light exhibiting the level of fluctuations in at least one of the Stokes parameters which is below the quantum noise limit is presented. Two approaches to generation of polarization-squeezed state of light are analyzed in detail: by propagating coherent radiation in a cubic nonlinear medium and by mixing radiation of two orthogonally polarized quadrature-squeezed modes. The degree of polarization of light is discussed. Other areas of quantum polarization optics, in particular, entanglement of quantum Stokes parameters and quantum polarization tomography, are also discussed.