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

Optics Letters

Raman-noise limit on squeezing in continuous-wave four-wave mixing

Jeffrey H. Shapiro, Luc Boivin

Published Apr 15, 1995• 18 citations
Publisher

Abstract

The continuous-time quantum theory of self-phase modulation (SPM) in lossless, dispersionless, single-mode fiber requires a nonzero response time, to capture the classical SPM limit properly, and an accompanying Raman noise, to ensure commutator preservation. The continuous-wave, four-wave mixing limit of this theory is shown to harbor a Raman-noise limit on fiber-based squeezed-state generation.

DOI
10.1364/ol.20.000925

Related papers

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

Quantum propagation in a Kerr medium: lossless, dispersionless fiber

Lance G. Joneckis, Jeffrey H. Shapiro

Intense light beams propagating in a lossless, dispersionless, single-mode optical fiber are subject to the Kerr effect, i.e., to the intensity-dependent refractive index of the fiber’s fused-silica core. Classically, Kerr-effect-induced self-phase modulation (SPM) can be used for spectral broadening of a picosecond pulse for grating-pair pulse compression down to femtosecond duration. Quantum mechanically, Kerr-effect-induced four-wave mixing (FWM) has been used to produce squeezed-state light. We present a quantum propagation theory for a lossless, dispersionless fiber with the Kerr nonlinearity. The theory includes classical SPM and quantum FWM within their regions of validity. It introduces a material time constant for the Kerr interaction, limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any input field, to develop a coarse-grained time multitemporal mode field analysis. Explicit expressions are obtained for the first and the second output-field moments when the fiber’s input field is in an arbitrary Gaussian state. These results are used to obtain homodyne-detection noise spectra, which are employed, in turn, to seek experimentally accessible manifestations of the Kerr time constant.

Journal of the Optical Society of America B•Jun 1, 1993•45 citations

Quantum propagation in single mode fiber

Lance G. Joneckis, Jeffrey H. Shapiro

This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.

Quantum Electronics and Laser Science Conference•May 2, 1993•1 citation

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

Characterizing the noise output by a fiber-based entangled photon source

Atiyya A. Davis, Brian T. Kirby, Thomas A. Searles +1 more

By simultaneously measuring individual and coincidence counts of two single photon detectors connected to a fiber-based entangled photon source and fitting the results with a theoretical model of the photon generation rates, we determine the average number of polarization-entangled photon pairs generated by four-wave mixing and the average number of noise photons generated by Raman scattering and self-phase modulation of the pump as a function of power. In contrast to previous efforts to characterize fiber-based entangled photon sources, this method does not require additional coherence-based measurements to distinguish SPM photons from FWM and Raman-scattered photons.

Quantum Communications and Quantum Imaging•Oct 3, 2023•0 citations

“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
The continuous-time quantum theory of self-phase modulation (SPM) in lossless, dispersionless, single-mode fiber requires a nonzero response time, to capture the classical SPM limit properly, and an accompanying Raman noise, to ensure commutator preservation. The continuous-wave, four-wave mixing limit of this theory is shown to harbor a Raman-noise limit on fiber-based squeezed-state generation.
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.
Intense light beams propagating in a lossless, dispersionless, single-mode optical fiber are subject to the Kerr effect, i.e., to the intensity-dependent refractive index of the fiber’s fused-silica core. Classically, Kerr-effect-induced self-phase modulation (SPM) can be used for spectral broadening of a picosecond pulse for grating-pair pulse compression down to femtosecond duration. Quantum mechanically, Kerr-effect-induced four-wave mixing (FWM) has been used to produce squeezed-state light. We present a quantum propagation theory for a lossless, dispersionless fiber with the Kerr nonlinearity. The theory includes classical SPM and quantum FWM within their regions of validity. It introduces a material time constant for the Kerr interaction, limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any input field, to develop a coarse-grained time multitemporal mode field analysis. Explicit expressions are obtained for the first and the second output-field moments when the fiber’s input field is in an arbitrary Gaussian state. These results are used to obtain homodyne-detection noise spectra, which are employed, in turn, to seek experimentally accessible manifestations of the Kerr time constant.
This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.
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.
By simultaneously measuring individual and coincidence counts of two single photon detectors connected to a fiber-based entangled photon source and fitting the results with a theoretical model of the photon generation rates, we determine the average number of polarization-entangled photon pairs generated by four-wave mixing and the average number of noise photons generated by Raman scattering and self-phase modulation of the pump as a function of power. In contrast to previous efforts to characterize fiber-based entangled photon sources, this method does not require additional coherence-based measurements to distinguish SPM photons from FWM and Raman-scattered photons.
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.