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Physical Review A

Generation and detection of squeezed states of light by nondegenerate four-wave mixing in an optical fiber

M. D. Levenson, Robert M. Shelby, Alain Aspect, M. D. Reid, Daniel F. Walls

Published Sep 1, 1985• 173 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.32.1550

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Bistability, nondegenerate four-wave mixing and squeezed state generation in a single-mode fiber ring resonator

Robert M. Shelby, M. D. Levenson

In optical fibers, nonlinear dispersion due to the same third-order susceptibility as that responsible for parametric mixing significantly alters the squeezing behavior in a traveling wave geometry, giving the squeezed quadrature an intensity dependent phase and reducing the overall squeezing. Phase noise is not squeezed at all. In the case of a fiber ring resonator, the nonlinear susceptibility will also lead to dispersive optical bistability and the squeezing will be strongly dependent on pump and sideband detuning. Yurke1 has analyzed squeezing due to backward four-wave mixing in a cavity, but the pump wave did not circulate in the cavity, and bistability was not dealt with. We have developed a theory of the resonant fiber ring interferometer, where the pump wave is near resonance with an interferometer mode and the circulating power is thereby enhanced. For perfect pump resonance and for frequencies corresponding to sideband resonance, the overall enhancement of the squeezing in the output mode compared to the traveling wave case is proportional to the square of the resonator finesse. The best squeezing in the output mode is always found for this condition of sideband resonance. The phase of the minimum noise quadrature is quite sensitive to both pump and sideband detuning. This feature may provide a means for avoiding excess thermal phase noise due to guided acoustic wave Brillouin scattering in the fiber itself. At the critical points for dispersive optical bistability in such a resonator and for sideband resonance (i.e., noise frequencies which are multiples of the resonator free spectral range), perfect squeezing of the output light is predicted. This result was also obtained previously for the case of degenerate mixing in a resonant cavity by Collett and Walls.2 Our current theory does not account for the reduction in squeezing due to the loss present in such a resonator.2 Since the loss is also enhanced by a factor of the resonator finesse, this is of some concern and will limit the maximum useful finesse for quantum noise squeezing. The major source of loss is the single-mode directional coupler, which for currently available technology is of the order of a few percent.

Annual Meeting Optical Society of America•Jan 1, 1985•1 citation
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.
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.
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.
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.
In optical fibers, nonlinear dispersion due to the same third-order susceptibility as that responsible for parametric mixing significantly alters the squeezing behavior in a traveling wave geometry, giving the squeezed quadrature an intensity dependent phase and reducing the overall squeezing. Phase noise is not squeezed at all. In the case of a fiber ring resonator, the nonlinear susceptibility will also lead to dispersive optical bistability and the squeezing will be strongly dependent on pump and sideband detuning. Yurke1 has analyzed squeezing due to backward four-wave mixing in a cavity, but the pump wave did not circulate in the cavity, and bistability was not dealt with. We have developed a theory of the resonant fiber ring interferometer, where the pump wave is near resonance with an interferometer mode and the circulating power is thereby enhanced. For perfect pump resonance and for frequencies corresponding to sideband resonance, the overall enhancement of the squeezing in the output mode compared to the traveling wave case is proportional to the square of the resonator finesse. The best squeezing in the output mode is always found for this condition of sideband resonance. The phase of the minimum noise quadrature is quite sensitive to both pump and sideband detuning. This feature may provide a means for avoiding excess thermal phase noise due to guided acoustic wave Brillouin scattering in the fiber itself. At the critical points for dispersive optical bistability in such a resonator and for sideband resonance (i.e., noise frequencies which are multiples of the resonator free spectral range), perfect squeezing of the output light is predicted. This result was also obtained previously for the case of degenerate mixing in a resonant cavity by Collett and Walls.2 Our current theory does not account for the reduction in squeezing due to the loss present in such a resonator.2 Since the loss is also enhanced by a factor of the resonator finesse, this is of some concern and will limit the maximum useful finesse for quantum noise squeezing. The major source of loss is the single-mode directional coupler, which for currently available technology is of the order of a few percent.