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Physical Review A

Dissipative effects on squeezed light generated in systems governed by the nonlinear Schrödinger equation

Mary J. Potasek, Bernard Yurke

Published Aug 1, 1988• 21 citations
Publisher

Abstract

Dissipation is expected to have detrimental effects on squeezed light. An analytical expression for dissipation in systems governed by the nonlinear Schr\"odinger equation is presented. As an example, parameters for an optical fiber were used to evaluate the squeezed-state spectrum. In addition, a scheme for detecting high-frequency components of the squeezed parameter is given.

DOI
10.1103/physreva.38.1335

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•May 8, 1994•4 citations
Dissipation is expected to have detrimental effects on squeezed light. An analytical expression for dissipation in systems governed by the nonlinear Schr"odinger equation is presented. As an example, parameters for an optical fiber were used to evaluate the squeezed-state spectrum. In addition, a scheme for detecting high-frequency components of the squeezed parameter is given.
A quantum description of the spatial behavior of a field that satisfies a spatial nonlinear Schrödinger equation (e.g., a single-mode field in a nonlinear planar waveguide) is studied with the assumption that quantum effects are small. An analytical expression for dissipation in systems governed by the spatial nonlinear Schrödinger equation is presented. Dissipation is found to have detrimental effects on the behavior of quantum phenomena such as quantum noise, squeezing, and bunching. A detecting scheme for the spatial frequency components of the nonclassical properties is also given.
Squeezed light, in which the quantum noise in one amplitude component is reduced below the vacuum level, has been generated using parametric processes. The starting point described here is the nonlinear Schrodinger equation which models light propagating through optical fibers. When such a dispersive nonlinear medium with a third-order susceptibility is pumped with an optical beam, squeezing can result. It is found that the degree of squeezing oscillates as a function of fiber length in the normal dispersion regime, whereas in the anomalous dispersion regime, it grows exponentially with fiber length. Examination of squeezing near the fiber’s zero dispersion wavelength shows that odd-order dispersive terms have no effect on squeezing. However, small values of higher-order even terms have significant effects on squeezing. In practice, high-frequency components of the squeezing spectrum are difficult to obtain. However, it is shown that a cross-correlation technique may be used to explore the frequency dependence of the squeezing spectrum.
A first-order perturbation calculation is performed on a generalized nonlinear Schr\"odinger equation in order to investigate the degree of squeezing that can be obtained for a medium described by such a field theory. Expressions for the amount of squeezing in the normal and anomalous dispersion regimes are obtained. In particular, it is found that the amount of squeezing is greater in the anomalous dispersion region than in the normal dispersion region. By keeping fourth-order derivatives in the field, the squeezing when the pump is located at the zero-dispersion wavelength is also investigated.
Generation of light with nonclassical properties, such as squeezed light, has gathered a lot of attention because of possible uses in such areas as quantum state engineering, quantum imaging, continuous variable quantum computing, and detection of gravitational waves. Squeezed light is generally produced by transporting light through a nonlinear medium. One such media is Kerr-nonlinear optical fibres. We aim to find the parameters for a fibre polarization squeezing setup by studying the dependencies of quantum noise suppression on the duration of the pulse and the input power. This is performed by modeling the light field propagation using the split-step Fourier method to numerically solve the stochastic nonlinear Schrödinger equation obtained by using the Wigner representation. This equation includes such physical effects as damping, quantum loss noise, dispersion, Kerr and Raman nonlinearities, and stochastic Raman noise.
The aim of this work is to study how losses modify quantum effects in a system governed by the spatial nonlinear Schrodinger equation. Quantum effects in space, such as quantum noise, squeezing, and bunching, have been studied in a lossless case.1 We will consider the propagation of a field through a planar nonlinear waveguide,2,3 where confinement is provided in one transverse dimension (y direction) by a linear refractive index and in the orthogonal dimension (x direction) by the intensity dependence of the refractive index.1,4 Attenuation is given to the spatial distribution in the x-z plane. In this work we want to extend the dissipation approach described in Ref. 5 to a system governed by the spatiai-nonlinear Sclirodinger equation (SNLS). We use a quantum-field description1 in which the spatial variable of propagation z plays the role of the time in the standard quantum theory, and we apply it to the case of a strong plane wave that can be described as a classical field propagating through a nonlinear waveguide in the z direction.4 By using both paraxial and slowly-varying-envelope approximations, the propagation of the field in a planar waveguide is described by the NLS.1