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 soliton propagation: a unified approach based on the linearization approximation

Yinchieh Lai

Published Mar 1, 1993• 45 citations
Publisher

Abstract

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.

DOI
10.1364/josab.10.000475

Related papers

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

Yinchieh Lai

A quantum treatment of soliton squeezing based on the linearization approximation has been carried out numerically.2 are recast more naturally. The new formulation also provides a general approach to calculation of detection noise. With the projection interpretation of homodyne detection, the squeezing ratio can be easily calculated by applying the propagation operator to the characteristic function of homodyne detection instead of the perturbation field operator. All the results in Ref. 1 also can be reproduced naturally. Finally, numerical analysis of fiber ring gyros using squeezed solitons and analysis of modelocked lasers are presented.

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

General quantum theory of nonlinear optical-pulse propagation

Yinchieh Lai, Shinn-Sheng Yu

Based on the linearization approximation and the conservation of commutation brackets, a general, self-consistent scheme is developed to quantize nonlinear optical-pulse propagation problems. A general computation procedure is developed to calculate the quantum uncertainties of the inner product between any given function and the (perturbed) field operator. As an illustration, a self-consistent quantum theory of the self-Raman effect in optical fibers is presented. The influence of the self-Raman effect on soliton squeezing is examined.

Physical Review A•Jan 1, 1995•64 citations

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

Chen‐Pang Yeang

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.

Journal of the Optical Society of America B•Aug 1, 1999•7 citations

Quantum theory of soliton propagation in an optical fiber using the Hartree approximation

Ewan M. Wright

The quantum theory of pulse propagation in a nonlinear optical fiber is presented using the time-dependent Hartree approximation. This formulation clarifies the connections between the quantum theory of soliton propagation and single-mode theories that have been used to describe the effects of self-phase modulation. An approximate solution is obtained for coherent-state soliton pulses that gives excellent agreement with numerical calculations for the quadrature phase amplitudes of the field. These amplitudes are found to undergo a series of collapses and revivals with propagation; the first collapse is related to the appearance of interference fringes in the field Q function.

Physical Review A•Apr 1, 1991•58 citations

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

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
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.
A quantum treatment of soliton squeezing based on the linearization approximation has been carried out numerically.2 are recast more naturally. The new formulation also provides a general approach to calculation of detection noise. With the projection interpretation of homodyne detection, the squeezing ratio can be easily calculated by applying the propagation operator to the characteristic function of homodyne detection instead of the perturbation field operator. All the results in Ref. 1 also can be reproduced naturally. Finally, numerical analysis of fiber ring gyros using squeezed solitons and analysis of modelocked lasers are presented.
Based on the linearization approximation and the conservation of commutation brackets, a general, self-consistent scheme is developed to quantize nonlinear optical-pulse propagation problems. A general computation procedure is developed to calculate the quantum uncertainties of the inner product between any given function and the (perturbed) field operator. As an illustration, a self-consistent quantum theory of the self-Raman effect in optical fibers is presented. The influence of the self-Raman effect on soliton squeezing is examined.
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.
The quantum theory of pulse propagation in a nonlinear optical fiber is presented using the time-dependent Hartree approximation. This formulation clarifies the connections between the quantum theory of soliton propagation and single-mode theories that have been used to describe the effects of self-phase modulation. An approximate solution is obtained for coherent-state soliton pulses that gives excellent agreement with numerical calculations for the quadrature phase amplitudes of the field. These amplitudes are found to undergo a series of collapses and revivals with propagation; the first collapse is related to the appearance of interference fringes in the field Q function.
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.
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.