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 theory of a second-order soliton based on a linearization approximation

Chen‐Pang Yeang

Published Aug 1, 1999• 7 citations
Publisher

Abstract

A linearized perturbation quantum theory of second-order soliton propagation is developed. The theory shows that the quantum fluctuations of photon number, phase, momentum, and position at an arbitrary propagation distance are linear combinations of these fluctuations at zero distance. The evolutions of second-order soliton quantum fluctuations are evaluated and compared with the quantum-fluctuation evolutions of a fundamental soliton. Based on this theory, the squeezing effect of a second-order soliton is studied. It is shown that, like a fundamental soliton, a second-order soliton also exhibits squeezing along propagation when a proper combination of the number and phase operators is detected.

DOI
10.1364/josab.16.001269

Related papers

Quantum theory of soliton squeezing: a linearized approach

H. A. Haus, Yinchieh Lai

A linearized quantum theory of soliton squeezing and detection is presented. The linearization reduces the quantum problem to a classical one. The classical formulation provides physical insight. It is shown that a quantized soliton exhibits uncertainties in photon number and phase, position (time), and momentum (frequency). Detectors for the measurement of all four operators are discussed. The squeezing of the soliton in the fiber is analyzed. An optimal homodyne detector for detection of the squeezing is presented that suppresses the noise associated with the continuum and the uncertainties in position and momentum.

Journal of the Optical Society of America B•Mar 1, 1990•253 citations

Perturbation theory of quantum solitons:?continuum evolution and optimum squeezing by spectral filtering

Dmitry Levandovsky, Michael Vasilyev, Prem Kumar

We study the quantum-noise properties of spectrally filtered solitons in optical fibers. Perturbation theory, including a quantum description of the continuum, is used to derive a complete analytical expression for the second-order correlator of the amplitude quadrature. This correlator is subsequently used to optimize the frequency response of the filter numerically in order to achieve the minimum photon-number noise. For propagation distances up to three soliton periods, the length at which the best noise reduction occurs, a square filter is found to be approximately optimum. For longer distances, more-complicated filter shapes are predicted for the best noise reduction.

Optics Letters•Jan 1, 1999•49 citations

Quantum theory of Manakov solitons

Darren Rand, Ken Steiglitz, Paul R. Prucnal

A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schr\"odinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.

Physical Review A•May 11, 2005•21 citations

Quantum theory of self-induced transparency solitons: A linearization approach

Yinchieh Lai, H. A. Haus

Linearization of the self-induced transparency equations reduces the problem to a single linear integro-differential equation for the perturbation field of a soliton. The adjoint system is introduced to establish orthogonality relations that lead to the relations between the perturbed field and perturbed scattering data. The commutation relations of the perturbation field provide the quantization rules for the perturbed ``scattering data.'' The quantized solitons are described by operators for photon number, phase, momentum, and position. The evolution and detection of these fluctuations are studied. The contribution of the continuum part can be suppressed by suitable detection schemes.

Physical Review A•Sep 1, 1990•35 citations

Quantum theory of soliton propagation: a unified approach based on the linearization approximation

Yinchieh Lai

Based on the linearization approximation, a unified approach to the quantum effects of soliton propagation is developed. The new formulation provides a clearer picture. The real and imaginary parts of the perturbation field are expanded in different basis sets. Orthogonality relations are used to project out the soliton parameters. The new formulation also provides a general numerical approach to the calculation of detection noise. Numerical analyses of fiber ring gyros that use squeezed solitons are presented.

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

Quantum Squeezing of Dark Solitons in Optical Fibers

Gholamreza Honarasa, Mohsen Hatami, Mohammad Kazem Tavassoly

The quantum theory of dark soliton propagation in fibers is studied based on the linearization approximation. Then the uncertainties in photon number, phase, position (time) and momentum of quantized dark solitons are calculated. Finally, the squeezing of the dark soliton is investigated by using homodyne detection and compared with bright soliton case.

Communications in Theoretical Physics•Aug 1, 2011•6 citations
A linearized perturbation quantum theory of second-order soliton propagation is developed. The theory shows that the quantum fluctuations of photon number, phase, momentum, and position at an arbitrary propagation distance are linear combinations of these fluctuations at zero distance. The evolutions of second-order soliton quantum fluctuations are evaluated and compared with the quantum-fluctuation evolutions of a fundamental soliton. Based on this theory, the squeezing effect of a second-order soliton is studied. It is shown that, like a fundamental soliton, a second-order soliton also exhibits squeezing along propagation when a proper combination of the number and phase operators is detected.
A linearized quantum theory of soliton squeezing and detection is presented. The linearization reduces the quantum problem to a classical one. The classical formulation provides physical insight. It is shown that a quantized soliton exhibits uncertainties in photon number and phase, position (time), and momentum (frequency). Detectors for the measurement of all four operators are discussed. The squeezing of the soliton in the fiber is analyzed. An optimal homodyne detector for detection of the squeezing is presented that suppresses the noise associated with the continuum and the uncertainties in position and momentum.
We study the quantum-noise properties of spectrally filtered solitons in optical fibers. Perturbation theory, including a quantum description of the continuum, is used to derive a complete analytical expression for the second-order correlator of the amplitude quadrature. This correlator is subsequently used to optimize the frequency response of the filter numerically in order to achieve the minimum photon-number noise. For propagation distances up to three soliton periods, the length at which the best noise reduction occurs, a square filter is found to be approximately optimum. For longer distances, more-complicated filter shapes are predicted for the best noise reduction.
A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schr\"odinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.
Linearization of the self-induced transparency equations reduces the problem to a single linear integro-differential equation for the perturbation field of a soliton. The adjoint system is introduced to establish orthogonality relations that lead to the relations between the perturbed field and perturbed scattering data. The commutation relations of the perturbation field provide the quantization rules for the perturbed ``scattering data.'' The quantized solitons are described by operators for photon number, phase, momentum, and position. The evolution and detection of these fluctuations are studied. The contribution of the continuum part can be suppressed by suitable detection schemes.
Based on the linearization approximation, a unified approach to the quantum effects of soliton propagation is developed. The new formulation provides a clearer picture. The real and imaginary parts of the perturbation field are expanded in different basis sets. Orthogonality relations are used to project out the soliton parameters. The new formulation also provides a general numerical approach to the calculation of detection noise. Numerical analyses of fiber ring gyros that use squeezed solitons are presented.