Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Optical-fiber media for squeezed-state generation

Gerard J Milburn, M. D. Levenson, Robert M. Shelby, Stephen H. Perlmutter, Ralph G. DeVoe, Daniel F. Walls

Published Oct 1, 1987• 78 citations
Publisher

Abstract

The Kerr nonlinearity characteristic of optical fibers produces squeezed states of light by a mechanism that differs from conventional four-wave mixing. The noise sources characteristic of such a medium also have a unique character. We present a unified picture of these interactions for both traveling-wave and cavity geometries. Results of experiments on squeezing in optical fibers and fiber ring resonators are discussed and compared with the theory.

DOI
10.1364/josab.4.001476

Related papers

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

Robert M. Shelby, M. D. Levenson, Daniel F. Walls +2 more

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.

Physical Review A•Jun 1, 1986•62 citations

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 +2 more

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.

Physical Review A•Sep 1, 1985•173 citations

Current status of squeezed light generation

Daniel F. Walls, M. D. Reid

We review current theoretical and experimental work on squeezed light generation.1 Quantum treatments of four-wave mixing using a two-level atomic model and an anharmonic oscillator model of the medium are presented.2 The results are compared with experiments on four-wave mixing in atomic sodium3 and optical fibers.4 Methods to suppress spontaneous emission noise are discussed.

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

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

“SQUEEZING” OF CLASSICAL AMPLITUDE AND PHASE FLUCTUATIONS BY NON-DEGENERATE FOUR WAVE MIXING IN AN OPTICAL FIBER

M. D. Levenson, Robert M. Shelby, Stephen H. Perlmutter

Parametric interactions such as four wave mixing have been predicted to produce states of the radiation field where the quantum fluctuations in one phase quadrature are less than those of a coherent state.1 These “squeezed states” have proved remarkably difficult to generate and detect, not least because of the presence of additional classical noise in many laser sources and parametric devices. We have now demonstrated the reduction of classical fluctuations by means of four wave mixing in an optical fiber under conditions very similar to those needed to demonstrate squeezed state generation. This success reinforces the plausibility of related quantum noise experiments, and has implications for fiber optic communications.

Conference on Lasers and Electro-Optics•Jan 1, 1985•0 citations

Squeezed states in optical cavities: A spontaneous-emission-noise limit

R. E. Slusher, Leo W. Hollberg, Bernard Yurke +2 more

Squeezed states of light have been predicted to be generated by four-wave mixing in cavity configurations. Any noise fields in the cavity can degrade or modify these squeezed states. An experiment using a Na atomic beam as the nonlinear mixing medium shows that spontaneous emission from the excited atoms results in a broadband frequency spectrum of noise in the cavity used for squeezing. The limits this noise places on the observed amount of squeezing and possible techniques for avoiding this noise source are discussed.

Physical Review A•May 1, 1985•59 citations
The Kerr nonlinearity characteristic of optical fibers produces squeezed states of light by a mechanism that differs from conventional four-wave mixing. The noise sources characteristic of such a medium also have a unique character. We present a unified picture of these interactions for both traveling-wave and cavity geometries. Results of experiments on squeezing in optical fibers and fiber ring resonators are discussed and compared with the theory.
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.
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.
Parametric interactions such as four wave mixing have been predicted to produce states of the radiation field where the quantum fluctuations in one phase quadrature are less than those of a coherent state.1 These “squeezed states” have proved remarkably difficult to generate and detect, not least because of the presence of additional classical noise in many laser sources and parametric devices. We have now demonstrated the reduction of classical fluctuations by means of four wave mixing in an optical fiber under conditions very similar to those needed to demonstrate squeezed state generation. This success reinforces the plausibility of related quantum noise experiments, and has implications for fiber optic communications.
Squeezed states of light have been predicted to be generated by four-wave mixing in cavity configurations. Any noise fields in the cavity can degrade or modify these squeezed states. An experiment using a Na atomic beam as the nonlinear mixing medium shows that spontaneous emission from the excited atoms results in a broadband frequency spectrum of noise in the cavity used for squeezing. The limits this noise places on the observed amount of squeezing and possible techniques for avoiding this noise source are discussed.