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Physical Review A

Generation of squeezed states of light with a fiber-optic ring interferometer

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

Published Jun 1, 1986• 62 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.33.4008

Related papers

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

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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.

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Bistability and other effects in a nonlinear fiber-optic ring resonator

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Dispersive optical bistability with a threshold cw input power of approximately 10 mW has been observed in a single-mode fiber-optic ring resonator. Light is coupled in and out of the resonator by a single-mode-fiber variable directional coupler. A fiber-optic Faraday isolator is incorporated into the ring, thus increasing the threshold for stimulated Brillouin oscillation by a factor of 100 and permitting other weaker nonlinear effects such as bistability to be observed. Phase-sensitive amplification and deamplification (squeezing) of classical time-stationary noise is demonstrated and shown to be in agreement with the theory of squeezed-state generation in such a nonlinear fiber ring resonator. Light scattering by elastic eigenmodes of the fiber (guided-acoustic-wave Brillouin scattering, GAWBS) adds noise to light circulating in the resonator and obscures the observation of squeezed quantum fluctuations. The properties of this GAWBS scattering are investigated and compared with theory.

Journal of the Optical Society of America B•Feb 1, 1988•31 citations

Theory of squeezed light generation in optical fibers

Gerard J Milburn, M. D. Reid, Daniel F. Walls +2 more

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.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations

Squeezing of classical and quantum noise in an optical fiber

M. D. Levenson, Robert M. Shelby

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.

Annual Meeting Optical Society of America•Jan 1, 1985•0 citations

Quadrature-squeezed light generation with a fiber ring reflector

Masakazu Mori, Norihiko Nishizawa, Toshio Goto

Hie generation and detection of quadrature squeezed states of light with a fiber ring reflector is reviewed. A 0.85µm polarization maintaining (PM) fiber is used as the nonlinear medium, and it is pumped by a 1.064µm mode-locked Nd:YAG laser. By the optical Kerr effect in the PM fiber, the input 1.064 mm light is squeezed. The combination of the smaller core diameter and the shorter source wavelength is effective in obtaining a higher peak power density, and consequently, a larger squeezing parameter at a low pump power. The squeezed vacuum is generated by combining the 50m long PM fiber ring with a 1:1 PM fiber coupler, and is detected by a balanced homodyne detector. The squeezed light noise is measured at 200kHz, and a squeezing parameter of 3.7dB is obtained at the input peak power of 5W. A simple calculation model based on the wave optics is used to estimate the squeezing parameter as a function of the input peak power. The calculated results agree well with the experimental ones. The squeezing in PM fibers is limited by the polarized guided acoustic wave Brillouin scattering (GAWBS), which is the phase noise originated from thermally induced fluctuations in the refractive index of the fiber. To avoid the noise due to GAWBS, a shorter PM fiber is preferable.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 2, 1998•0 citations
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.
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.
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.
Dispersive optical bistability with a threshold cw input power of approximately 10 mW has been observed in a single-mode fiber-optic ring resonator. Light is coupled in and out of the resonator by a single-mode-fiber variable directional coupler. A fiber-optic Faraday isolator is incorporated into the ring, thus increasing the threshold for stimulated Brillouin oscillation by a factor of 100 and permitting other weaker nonlinear effects such as bistability to be observed. Phase-sensitive amplification and deamplification (squeezing) of classical time-stationary noise is demonstrated and shown to be in agreement with the theory of squeezed-state generation in such a nonlinear fiber ring resonator. Light scattering by elastic eigenmodes of the fiber (guided-acoustic-wave Brillouin scattering, GAWBS) adds noise to light circulating in the resonator and obscures the observation of squeezed quantum fluctuations. The properties of this GAWBS scattering are investigated and compared with theory.
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.
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.
Hie generation and detection of quadrature squeezed states of light with a fiber ring reflector is reviewed. A 0.85µm polarization maintaining (PM) fiber is used as the nonlinear medium, and it is pumped by a 1.064µm mode-locked Nd:YAG laser. By the optical Kerr effect in the PM fiber, the input 1.064 mm light is squeezed. The combination of the smaller core diameter and the shorter source wavelength is effective in obtaining a higher peak power density, and consequently, a larger squeezing parameter at a low pump power. The squeezed vacuum is generated by combining the 50m long PM fiber ring with a 1:1 PM fiber coupler, and is detected by a balanced homodyne detector. The squeezed light noise is measured at 200kHz, and a squeezing parameter of 3.7dB is obtained at the input peak power of 5W. A simple calculation model based on the wave optics is used to estimate the squeezing parameter as a function of the input peak power. The calculated results agree well with the experimental ones. The squeezing in PM fibers is limited by the polarized guided acoustic wave Brillouin scattering (GAWBS), which is the phase noise originated from thermally induced fluctuations in the refractive index of the fiber. To avoid the noise due to GAWBS, a shorter PM fiber is preferable.