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Four-mode squeezing in an optical fiber

Bonny L. Schumaker, Stephen H. Perlmutter, Robert M. Shelby, M. D. Levenson

Published Apr 26, 1987• 0 citations
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Abstract

It has been predicted that three- or four-wave mixing with two or more pump frequencies can produce squeezing (2N-mode squeezing) that is potentially greater than that produced by single-frequency pumping (two-mode squeezing).1,2 We demonstrated four-mode squeezing via four-wave mixing with two pump frequencies in an optical fiber.3

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Four-mode squeezing

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The four-wave-mixing interactions produced by pumping at two well-separated frequencies can couple four different radiation modes to generate a new kind of squeezed state of light. A dual-frequency homodyne detection scheme is described and is used to observe this type of nonclassical correlation. Initial experimental results in an optical fiber show a noise level 20% below the vacuum noise level for the output of the dual-frequency detector, even though the noise at each individual detector remains above the vacuum level.

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The influence of multiple four-wave mixing in optical fiber on noise propagation

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The noise properties of propagation through optical fiber are of interest in optical communications. In recent years much attention has been focused on reducing the quantum fluctuations in one of two complementary field variables below the limit associated with coherent states. Nonlinear optical processes have played a key role in the realization of such behavior. We numerically investigate the noise properties associated with competing four-wave mixing (FWM) processes in optical fiber from a classical perspective. The nonlinear interaction of two pump waves at frequencies ω1 and ω2, which produce sidebands at 2ω2–ω1 and 2ω1–ω2 by multiple FWM, is considered. By introducing known classical fluctuations at the fiber input, one can trace the evolution of the noise in the different frequency components of the FWM spectrum by generating histograms at different fiber lengths and for different input pump powers and frequency separations. Classical behavior resembling squeezing is observed under appropriate conditions.

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What's so ultra about ultrasqueezed light?

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At a previous OSA conference the author introduced the phenomenon of ultrasqueezed light, produced by three-wave and four-wave mixing in nonlinear media pumped at multiple frequencies spaced so as to produce appropriate phase-matching. Here quantitative results are given of the advantages offered by ultrasqueezing in terms of the degree of squeezing obtainable for a given total amount of input pump power. Phase-matching requirements and detection techniques are described, and resulting implications for the usefulness (enhanced squeezing vs ease of production and detection) are indicated. The results differ appreciably for three-wave and four-wave mixing. Several different experimental schemes for producing ultrasqueezed light are described using three-wave and four-wave mixing. Only one of these, four-wave mixing with two pump frequencies in an optical fiber, has been attempted experimentally; its success has been described at a previous OSA conference and is reviewed only briefly. Comparison is made between ultrasqueezed light and pulsed squeezed light, which can be viewed as a special limit of ultrasqueezing with many pump frequencies.

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The fundamental and simplest kind of squeezing (broadband squeezing) is produced by pumping a nonlinear medium at a single frequency. The observables squeezed are the electric-field quadrature phases defined relative to the pump frequency. Their measurement requires homodyning against an optical-frequency (the pump frequency) local oscillator. When the medium is pumped at several different frequencies (equally spaced), different kinds of observables exhibit squeezing. Their measurement requires further homodyning, against a radio-frequency (the pump frequency spacing) local oscillator, and, for four or more pump frequencies, against subsequent lower-frequency local oscillators. For a given total pump power, it is possible to achieve greater squeezing by distributing the pump power over several (at least three) different pump frequencies than by pumping at a single frequency. The drawback is that a more sophisticated detection scheme is required (i.e., further homodyning) to measure the maximum squeezing (less squeezing is produced in more easily measured observables, such as the electric-field quadrature phases). The required further homodyning at rf and lower frequencies is straightforward to accomplish, however, and the advantages of using lower pump powers at each optical frequency can be substantial, especially in mediums such as optical fibers, where large pump powers bring with them substantial added noise sources.

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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

Hybrid squeezing of solitonic resonant radiation in photonic crystal fibers

Truong X. Tran, Fabio Biancalana

Squeezing is a fundamental quantum optical phenomenon - induced by various nonlinear optical processes - in which a special state of the electromagnetic field is generated, for which quantum noise fluctuations are reduced below the shot noise level for certain frequency ranges. Two qualitatively different kinds of squeezing are currently known to take place in optical fibers. The first is the four-wave mixing (FWM) induced quadrature squeezing, in which an intense continuous wave (CW) pump initiates a spontaneous emission of signal and idler waves from vacuum fluctuations at symmetric detunings from the pump. The noise components at the signal and idler frequencies become correlated via the fiber nonlinearity, leading to a reduction of the noise power spectrum below the shot noise level. All the waves participating to the FWM-induced squeezing are monochromatic waves. The second kind of squeezing is the so called self-phase modulation (SPM) induced squeezing, in which the spectral components of an intense short pulse in a coherent state become correlated via the SPM during propagation. We demonstrate theoretically that a third kind of squeezing is possible in optical fibers, in which the noise spectrum of the quasi-monochromatic resonant radiation (RR) emitted by optical solitons when subject to perturbations shows evidence of photon correlation and a reduction of noise below the shot-noise level.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2011•2 citations
The four-wave-mixing interactions produced by pumping at two well-separated frequencies can couple four different radiation modes to generate a new kind of squeezed state of light. A dual-frequency homodyne detection scheme is described and is used to observe this type of nonclassical correlation. Initial experimental results in an optical fiber show a noise level 20% below the vacuum noise level for the output of the dual-frequency detector, even though the noise at each individual detector remains above the vacuum level.
The noise properties of propagation through optical fiber are of interest in optical communications. In recent years much attention has been focused on reducing the quantum fluctuations in one of two complementary field variables below the limit associated with coherent states. Nonlinear optical processes have played a key role in the realization of such behavior. We numerically investigate the noise properties associated with competing four-wave mixing (FWM) processes in optical fiber from a classical perspective. The nonlinear interaction of two pump waves at frequencies ω1 and ω2, which produce sidebands at 2ω2–ω1 and 2ω1–ω2 by multiple FWM, is considered. By introducing known classical fluctuations at the fiber input, one can trace the evolution of the noise in the different frequency components of the FWM spectrum by generating histograms at different fiber lengths and for different input pump powers and frequency separations. Classical behavior resembling squeezing is observed under appropriate conditions.
At a previous OSA conference the author introduced the phenomenon of ultrasqueezed light, produced by three-wave and four-wave mixing in nonlinear media pumped at multiple frequencies spaced so as to produce appropriate phase-matching. Here quantitative results are given of the advantages offered by ultrasqueezing in terms of the degree of squeezing obtainable for a given total amount of input pump power. Phase-matching requirements and detection techniques are described, and resulting implications for the usefulness (enhanced squeezing vs ease of production and detection) are indicated. The results differ appreciably for three-wave and four-wave mixing. Several different experimental schemes for producing ultrasqueezed light are described using three-wave and four-wave mixing. Only one of these, four-wave mixing with two pump frequencies in an optical fiber, has been attempted experimentally; its success has been described at a previous OSA conference and is reviewed only briefly. Comparison is made between ultrasqueezed light and pulsed squeezed light, which can be viewed as a special limit of ultrasqueezing with many pump frequencies.
The fundamental and simplest kind of squeezing (broadband squeezing) is produced by pumping a nonlinear medium at a single frequency. The observables squeezed are the electric-field quadrature phases defined relative to the pump frequency. Their measurement requires homodyning against an optical-frequency (the pump frequency) local oscillator. When the medium is pumped at several different frequencies (equally spaced), different kinds of observables exhibit squeezing. Their measurement requires further homodyning, against a radio-frequency (the pump frequency spacing) local oscillator, and, for four or more pump frequencies, against subsequent lower-frequency local oscillators. For a given total pump power, it is possible to achieve greater squeezing by distributing the pump power over several (at least three) different pump frequencies than by pumping at a single frequency. The drawback is that a more sophisticated detection scheme is required (i.e., further homodyning) to measure the maximum squeezing (less squeezing is produced in more easily measured observables, such as the electric-field quadrature phases). The required further homodyning at rf and lower frequencies is straightforward to accomplish, however, and the advantages of using lower pump powers at each optical frequency can be substantial, especially in mediums such as optical fibers, where large pump powers bring with them substantial added noise sources.
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.
Squeezing is a fundamental quantum optical phenomenon - induced by various nonlinear optical processes - in which a special state of the electromagnetic field is generated, for which quantum noise fluctuations are reduced below the shot noise level for certain frequency ranges. Two qualitatively different kinds of squeezing are currently known to take place in optical fibers. The first is the four-wave mixing (FWM) induced quadrature squeezing, in which an intense continuous wave (CW) pump initiates a spontaneous emission of signal and idler waves from vacuum fluctuations at symmetric detunings from the pump. The noise components at the signal and idler frequencies become correlated via the fiber nonlinearity, leading to a reduction of the noise power spectrum below the shot noise level. All the waves participating to the FWM-induced squeezing are monochromatic waves. The second kind of squeezing is the so called self-phase modulation (SPM) induced squeezing, in which the spectral components of an intense short pulse in a coherent state become correlated via the SPM during propagation. We demonstrate theoretically that a third kind of squeezing is possible in optical fibers, in which the noise spectrum of the quasi-monochromatic resonant radiation (RR) emitted by optical solitons when subject to perturbations shows evidence of photon correlation and a reduction of noise below the shot-noise level.