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Annual Meeting Optical Society of America

Theory of squeezed light generation in optical fibers

Gerard J Milburn, M. D. Reid, Daniel F. Walls, Robert M. Shelby, M. D. Levenson

Published Jan 1, 1986• 0 citations
Publisher

Abstract

We give a quantum theoretical analysis of squeezed light generation via nondegenerate four-wave mixing in an optical fiber. The medium is modeled by an ensemble of anharmonic oscillators and loss is included. We include the coupling to acoustic phonons which gives rise to guided acoustic wave Brillouin scattering (GAWBS). The GAWBS introduces random noise which destroys the squeezing at room temperatures. By cooling the fiber to temperatures ~2 K the GAWBS is substantially reduced and the observation of squeezing becomes possible. A comparison is made with the recent experimental results of Levenson et al.1, 2 A scheme to suppress the GAWBS at room temperatures using a two-frequency pump and difference detection is analyzed and the conditions in which good squeezing results are determined.

DOI
10.1364/oam.1986.tuj8

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We give a quantum theoretical analysis of squeezed light generation via nondegenerate four-wave mixing in an optical fiber. The medium is modeled by an ensemble of anharmonic oscillators and loss is included. We include the coupling to acoustic phonons which gives rise to guided acoustic wave Brillouin scattering (GAWBS). The GAWBS introduces random noise which destroys the squeezing at room temperatures. By cooling the fiber to temperatures ~2 K the GAWBS is substantially reduced and the observation of squeezing becomes possible. A comparison is made with the recent experimental results of Levenson et al.1, 2 A scheme to suppress the GAWBS at room temperatures using a two-frequency pump and difference detection is analyzed and the conditions in which good squeezing results are determined.
Thermally excited transverse phonons in glass fibers generate guided acoustic wave Brillouin scattering (GAWBS) which afflicts the propagating light with phase and polarization noise. This excess noise is a major limitation for fiber-based squeezing sources as well as for the transmission of quantum information through fibers. In order to achieve quantum states of high quality it is therefore important to reduce the harmful effect of GAWBS. The thermal nature of GAWBS naturally allows for a reduction by cooling the fiber. Alternatively, subtracting the correlated noise of two closely spaced pulses leads to a cancellation. These methods, however, are inconvenient for fiber-based squeezing sources and inapplicable in practical quantum information transmission systems.
Near-degenerate four-wave parametric mixing in an optical fiber couples fluctuations in signal and idler frequency bands in such a way that the noise at a particular optical phase is reduced while that in an orthogonal phase quadrature is amplified. We have performed experiments on this effect and explained our results in terms of a theory which incorporates a nonlinear dispersion effect. The nonlinear dispersion alters the mathematical character of the solutions and limits the effective interaction length. For relatively low frequency shifts (<100 GHz) and 100 m of fiber, the heterodyne detected optical noise can be reduced by 5 dB in the squeezed quadrature. Theory predicts that this parametric interaction should reduce the noise level below the standard quantum limit. In a realistic fiber, phase noise due to guided acoustic wave Brillouin scattering (GAWBS) dominates the quanturn noise and cannot be reduced by four-wave mixing. Narrow gaps in the GAWBS noise can be engineered into special fibers. At the frequencies of these gaps, the noise level indeed can be squeezed below the quantum limit.
Forward nondegenerate four-wave mixing in an optical-fiber ring resonator is proposed as a method to generate squeezed states of light. The nonlinear interactions are analyzed both with a self-consistent propagation-equation technique and with Fokker-Planck equations in the Glauber-Sudarshan P representation. Excellent squeezing is predicted at modest input power levels, with perfect quantum-noise squeezing at the critical points for optical bistability. A method to suppress the stimulated Brillouin effect is proposed and demonstrated experimentally, and the effects of forward spontaneous guided acoustic wave Brillouin scattering inside the resonator are analyzed. Methods are suggested for minimizing this noise under conditions where squeezing can be detected. Experimental apparatus and procedures are outlined for verifying the predictions of our theory and demonstrating squeezing of classical and quantum noise.
Nondegenerate four-wave mixing in a single-mode optical fiber is proposed as a method of squeezed state generation. An analysis of the near-degenerate mixing process for forward propagation in realistic fibers is presented along with the theory of an experimentally feasible detection strategy. The effects of the quantum nature of the optical nonlinearity and absorption are modeled by treating the fiber medium as a collection of anharmonic oscillators. Methods of suppressing undesired effects such as stimulated Brillouin scattering are presented as is a technique for providing the phase-shifted local oscillator wave necessary for the detection of squeezing. Preliminary experiments on fiber characterization and the detection of four-wave parametric fluorescence are described.
The realization of a compact squeezed-state-generation device at 1.5 µm may have potential applications in optical communication. The squeezed state has been generated in both χ(2) and χ(3) media. In χ(2) media the frequency of the squeezed vacuum is half that of the pump. Therefore frequency doubling is necessary for generating a local oscillator (LO). Such frequency doubling is not needed in χ(3) media. However, squeezing in y(3) media has not been as successful as in X(2) media, for example, in atomic vapor,1 self-focusing seriously limits the amount of squeezing, whereas in optical fibers,2 guided-acoustic-wave Brillouin-scattering (GAWBS) noise causes difficulties that can be circumvented through low- temperature cooling of the fiber or the use of soli ton pulses.