© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Annual Meeting Optical Society of America

Quantum diffusion in soliton position measurements

P. D. Drummond, Y. Yamamoto

Published Jan 1, 1991• 0 citations

Abstract

The usual view of a soliton in an optical fiber is that it obeys the classical Maxwell equations, and propagates unchanged down a lossless fiber. Of course, it is well known that an optical amplifier introduces noise in position. It is less well known that even a perfectly lossless fiber, without an amplifier, is unable to support the classical invariant solution. Instead, all solitons experience quantum noise in position and phase, and this noise increases with propagation distance. Experimenters at IBM laboratories have recently observed the first quantum effects in solitons. These experiments focussed on quadrature squeezing, and were able to detect the large increase in phase-quadrature noise that is predicted quantum-mechanically. In this paper we treat the effects of pulse-position noise, and indicate how this noise source can limit information transmission using solitons. While these effects are small in currently proposed communication systems, they place a fundamental limit on future enhancements of soliton communications using pulse-position modulation. Of most scientific interest is the macroscopic nature of the quantum fluctuations, which can alter the location of a huge number of cooperatively positioned photons, and possible implications for QND momentum measurements.

DOI: 10.1364/oam.1991.pd18

Related papers

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

Quantum noise and thermal noise in optical soliton propagation

Robert M. Shelby, E. H. Whittaker, P. D. Drummond +2 more

Classical optical solitons propagate in optical fibers without temporal or spectral distortion as a result of a balance between phase shifts due to group velocity dispersion and those due to nonlinear self-phase modulation. This balance is achieved by the proper choice of pulse shape and duration for a given pulse energy. The quantum fluctuations associated with a coherent soliton do not undergo stationary propagation, however, and a number of effects are predicted, including the evolution of vacuum noise associated with the input coherent pulse into squeezed fluctuations and the temporal spreading of the soliton pulse because of dispersion acting on quantum fluctuations of the pulse frequency.

Quantum Electronics and Laser Science Conference•May 10, 1992•0 citations

Quantum fluctuations of optical solitons in fibers

Demin Yao

Quantum fluctuations of optical solitons in fibers are discussed on the basis of the exact quantum states in the frame of the quantum nonlinear Schr\"odinger equation. Position and momentum fluctuations as well as quadrature phase fluctuations are calculated, and explicit results are expressed in terms of the intrinsic quantum parameters. Soliton wave-packet spreading and phase-diffusion phenomena are clearly demonstrated, and the corresponding squeezing effects are analyzed. In particular, soliton amplitude squeezing is investigated in an experimental setup of a Mach-Zehnder interferometer containing an optical fiber. Coherent states for quantum solitons are discussed with attention given to their dynamical preservability. Compared with previous linearized approaches, the present study may provide a more fundamental treatment to quantum fluctuations of solitons.

Physical Review A•Dec 1, 1995•14 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

Reduction of quantum noise in soliton propagation by phase-sensitive amplification

Ivan Deutsch, Izo I. Abram

We study the possibility of employing phase-sensitive parametric amplifiers to compensate for losses incurred by solitons propagating in optical fibers. As phase-sensitive amplification is free from the excess spontaneous noise associated with laser amplifiers, the only quantum noise source in such a system arises from the fiber losses. In addition, under phase-sensitive amplification, fluctuations in the soliton frequency are squeezed to one half of the vacuum level, thus producing a negligible contribution to the fluctuations in the soliton arrival time. This greatly reduces the Gordon–Haus jitter of the solitons. The performance of the phase-sensitive amplifier is compared with that of alternative noise-reduction schemes employing phase-insensitive amplifiers and spectral filters as well as with the limits on long-distance data transmission imposed by quantum mechanics.

Journal of the Optical Society of America B•Nov 1, 1994•48 citations

Phase-noise scaling in quantum soliton propagation

Robert M. Shelby, P. D. Drummond, S. J. Carter

We treat the scaling of thermal phase-noise effects and quantum fluctuations for solitons in optical fibers. The central result is that the size of the thermal noise relative to quantum noise is reduced in proportion to the soliton duration for solitons whose duration is less than the thermal correlation times, suggesting that squeezed quantum solitons should be realizable in optical fibers. The physical basis for this effect is largely the fact that squeezing, which is nonlinear, occurs more rapidly for shorter pulses.

Physical Review A•Sep 1, 1990•45 citations

The usual view of a soliton in an optical fiber is that it obeys the classical Maxwell equations, and propagates unchanged down a lossless fiber. Of course, it is well known that an optical amplifier introduces noise in position. It is less well known that even a perfectly lossless fiber, without an amplifier, is unable to support the classical invariant solution. Instead, all solitons experience quantum noise in position and phase, and this noise increases with propagation distance. Experimenters at IBM laboratories have recently observed the first quantum effects in solitons. These experiments focussed on quadrature squeezing, and were able to detect the large increase in phase-quadrature noise that is predicted quantum-mechanically. In this paper we treat the effects of pulse-position noise, and indicate how this noise source can limit information transmission using solitons. While these effects are small in currently proposed communication systems, they place a fundamental limit on future enhancements of soliton communications using pulse-position modulation. Of most scientific interest is the macroscopic nature of the quantum fluctuations, which can alter the location of a huge number of cooperatively positioned photons, and possible implications for QND momentum measurements.

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.

Classical optical solitons propagate in optical fibers without temporal or spectral distortion as a result of a balance between phase shifts due to group velocity dispersion and those due to nonlinear self-phase modulation. This balance is achieved by the proper choice of pulse shape and duration for a given pulse energy. The quantum fluctuations associated with a coherent soliton do not undergo stationary propagation, however, and a number of effects are predicted, including the evolution of vacuum noise associated with the input coherent pulse into squeezed fluctuations and the temporal spreading of the soliton pulse because of dispersion acting on quantum fluctuations of the pulse frequency.

Quantum fluctuations of optical solitons in fibers are discussed on the basis of the exact quantum states in the frame of the quantum nonlinear Schr\"odinger equation. Position and momentum fluctuations as well as quadrature phase fluctuations are calculated, and explicit results are expressed in terms of the intrinsic quantum parameters. Soliton wave-packet spreading and phase-diffusion phenomena are clearly demonstrated, and the corresponding squeezing effects are analyzed. In particular, soliton amplitude squeezing is investigated in an experimental setup of a Mach-Zehnder interferometer containing an optical fiber. Coherent states for quantum solitons are discussed with attention given to their dynamical preservability. Compared with previous linearized approaches, the present study may provide a more fundamental treatment to quantum fluctuations of solitons.

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

We study the possibility of employing phase-sensitive parametric amplifiers to compensate for losses incurred by solitons propagating in optical fibers. As phase-sensitive amplification is free from the excess spontaneous noise associated with laser amplifiers, the only quantum noise source in such a system arises from the fiber losses. In addition, under phase-sensitive amplification, fluctuations in the soliton frequency are squeezed to one half of the vacuum level, thus producing a negligible contribution to the fluctuations in the soliton arrival time. This greatly reduces the Gordon–Haus jitter of the solitons. The performance of the phase-sensitive amplifier is compared with that of alternative noise-reduction schemes employing phase-insensitive amplifiers and spectral filters as well as with the limits on long-distance data transmission imposed by quantum mechanics.

We treat the scaling of thermal phase-noise effects and quantum fluctuations for solitons in optical fibers. The central result is that the size of the thermal noise relative to quantum noise is reduced in proportion to the soliton duration for solitons whose duration is less than the thermal correlation times, suggesting that squeezed quantum solitons should be realizable in optical fibers. The physical basis for this effect is largely the fact that squeezing, which is nonlinear, occurs more rapidly for shorter pulses.