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Physical Review A

Squeezed-light generation in a medium governed by the nonlinear Schrödinger equation

Mary J. Potasek, Bernard Yurke

Published May 1, 1987• 57 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.35.3974

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Physical Review A•Aug 1, 1988•21 citations
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.
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.
The theory of quantum effects in nonlinear dielectric media is developed. The nonlinear dielectric media is influenced by an external pumping field. The diagonalization of the Hamiltonian of a quantized field is obtained by the canonical Bogoliubov transformations. The transformations allow us to obtain the general expressions for the number of created photons and for the degree of squeezing. In the case of a plane pumping wave, for example, the results are calculated by using the zero order of the secular perturbation theory, with small parameters characterizing the medium nonlinearity. The Heisenberg equations of motion are obtained for non-stationary case and a commonly used Hamiltonian is derived from the first principles of quantum electrodynamics.
We develop a quantum theory of propagation in dispersive nonlinear media from the foundations of a correctly quantized field theory. Quantum fluctuations are handled by coherent-state expansions of localized field states. A stochastic nonlinear Schrödinger equation in the field variables is obtained for media with an intensity-dependent refractive index. This predicts squeezing for a continuous-wave input, over a wide bandwidth with anomalous dispersion, and over a gradually reducing bandwidth with normal dispersion. The equation is easily modified to include thermal-noise sources as well. For solitons, fluctuations are reduced over the soliton bandwidth. This leads to quantum solitons that have quadrature fluctuations less than the level of vacuum fluctuations. The complementary quadrature has a correspondingly increased fluctuation level.