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

Quantum propagation in a Kerr medium: lossless, dispersionless fiber

Lance G. Joneckis, Jeffrey H. Shapiro

Published Jun 1, 1993• 45 citations
Publisher

Abstract

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.

DOI
10.1364/josab.10.001102

Related papers

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

Classical and quantum noise transformations generated by a Kerr nonlinearity

Lance G. Joneckis, Jeffrey H. Shapiro

The Ken nonlinearity is the source of important phenomena in both classical and quantum optics. Previously we had shown that a material dependent time constant plays a pivotal role in the quantum noise transformations produced by the Kerr nonlinearity.1 In that work, we presented the classical and quantum noise correlations for propagation of an initially phase-insensitive beam through a lossless, dispersionless, Kerr medium. In the present paper, we extend the earlier work to an arbitrary Gaussian input state. Central to both developments is the inclusion of a coarse grained time constant, τ q , which models the non-instantaneous nature of the Kerr nonlinearity. Output spectra based on Gaussian as well as other types of input spectra are presented. Also predicted is a quantum recurrence length, equal to an interaction length which yields a 2π nonlinear phase shift for an energy density of the 1 photon/cτ q m. The possibility of experimental verification of this theory is also discussed.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

Spectral correlations of ultrashort pulses in optical fibers

Friedrich König, Gerd Leuchs, M. W. Hamilton

Sources of quantum correlated light beams will find important applications in quantum communication. Such beams might be generated by Kerr effect induced four wave mixing in fibers where the nonlinear optical pulse evolution is an important issue. The resulting effect of self-phase modulation is used to broaden the spectra of ultrashort pulses in many laser applications.

Novel Lasers and Devices - Basic Aspects•Jan 1, 1999•0 citations

Squeezing of optical solitons

Robert M. Shelby, M. Rosenbluh

Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary, distortion-free propagation requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2

Quantum Electronics and Laser Science Conference•May 12, 1991•0 citations

Squeezed solitons: quantum and thermal noise effects

Robert M. Shelby, M. Rosenbluh, P. D. Drummond +1 more

Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary distortion-free propagation only requires the proper choice of pulse width and shape for a given pulse energy. However, quantum fluctuations do not undergo stationary propagation but rather evolve due to dispersion and self-phase modulation. As a soliton pulse propagates, zero-point or vacuum noise associated with the pulse evolves into squeezed noise. Vacuum fluctuations are responsible for the fundamental detector noise floor known as the shot noise limit. Reduction of the noise in the detection of squeezed soliton pulses has achieved a noise level 34% below this limit. In optical fibers, thermal fluctuation of the refractive index limit the noise reduction that can be achieved by adding phase fluctuations in excess of the vacuum noise. At low frequencies thermal noise originates from local structural dynamics of fused silica which produces a 1/f power spectrum and from guided acoustic wage Brillouin scattering which modulates the refractive index at frequencies characteristic of the fiber structure. The bandwidth of these fluctuations is ~2 GHz; and for soliton pulses with spectral bandwidth much >2 GHz, we have shown that this noise can be made insignificant. For very short pulses, however, noise from Raman scattering must be considered. Recent calculations incorporating this noise mechanism are compared with experiment.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

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

Jeffrey H. Shapiro, Luc Boivin

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.

Optics Letters•Apr 15, 1995•18 citations
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.
The Ken nonlinearity is the source of important phenomena in both classical and quantum optics. Previously we had shown that a material dependent time constant plays a pivotal role in the quantum noise transformations produced by the Kerr nonlinearity.1 In that work, we presented the classical and quantum noise correlations for propagation of an initially phase-insensitive beam through a lossless, dispersionless, Kerr medium. In the present paper, we extend the earlier work to an arbitrary Gaussian input state. Central to both developments is the inclusion of a coarse grained time constant, τ q , which models the non-instantaneous nature of the Kerr nonlinearity. Output spectra based on Gaussian as well as other types of input spectra are presented. Also predicted is a quantum recurrence length, equal to an interaction length which yields a 2π nonlinear phase shift for an energy density of the 1 photon/cτ q m. The possibility of experimental verification of this theory is also discussed.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary, distortion-free propagation requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary distortion-free propagation only requires the proper choice of pulse width and shape for a given pulse energy. However, quantum fluctuations do not undergo stationary propagation but rather evolve due to dispersion and self-phase modulation. As a soliton pulse propagates, zero-point or vacuum noise associated with the pulse evolves into squeezed noise. Vacuum fluctuations are responsible for the fundamental detector noise floor known as the shot noise limit. Reduction of the noise in the detection of squeezed soliton pulses has achieved a noise level 34% below this limit. In optical fibers, thermal fluctuation of the refractive index limit the noise reduction that can be achieved by adding phase fluctuations in excess of the vacuum noise. At low frequencies thermal noise originates from local structural dynamics of fused silica which produces a 1/f power spectrum and from guided acoustic wage Brillouin scattering which modulates the refractive index at frequencies characteristic of the fiber structure. The bandwidth of these fluctuations is ~2 GHz; and for soliton pulses with spectral bandwidth much >2 GHz, we have shown that this noise can be made insignificant. For very short pulses, however, noise from Raman scattering must be considered. Recent calculations incorporating this noise mechanism are compared with experiment.