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Physical Review A

Definition and construction of the quantum soliton states in optical fibers

Duan Lu-ming, Guo Guang-Can

Published Jul 1, 1995• 7 citations
Publisher

Abstract

An explicit and reasonable definition of the quantum soliton states in optical fibers is given. Based on this definition we construct the quantum soliton states from the exact solution of the quantum nonlinear Schr"odinger equation. The dispersion effect of the quantum soliton is also exactly analyzed.
DOI
10.1103/physreva.52.874

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Comment on ‘‘Definition and construction of the quantum soliton states in optical fibers’’

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It is pointed out that the claim of Duan and Guo [Phys. Rev. A 52, 874 (1995)] based on a reasonable definition of the quantum soliton states in optical fibers, that the superposition of momentum eigenstates with the Gaussian weight function makes the fluctuation of the position operator reduce to the minimum, is not correct. \textcopyright{} 1996 The American Physical Society.

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In the preceding paper [paper I of a two-part study; Lai and Haus, Phys. Rev. A 40, 844 (1989)] we have used the time-dependent Hartree approximation to solve the quantum nonlinear Schr\"odinger equation. In the present paper, the eigenstates of the Hamiltonian are constructed exactly by Bethe's ansatz method and are superimposed to construct exact soliton states. Both fundamental and higher-order soliton states are constructed and their mean fields are calculated. The quantum effects of soliton propagation and soliton collisions are studied in the framework of this construction. It is shown that a soliton experiences dispersion as well as phase spreading. The magnitude of this dispersion is estimated and is shown to be very small when the average photon number of the soliton is much larger than unity. The phase and position shifts due to a collision and the uncertainty of these shifts are also calculated.
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.
The dynamics of a quantum soliton propagating in nonlinear optical fibers is analyzed in the second-quantized picture in a fully canonical way. The quantum nonlinear Schr\"odinger equation with equal-time commutation relations for the field operators is solved using the formalism developed by Haus and Lai [J. Opt. Soc. Am. B 7,7,7, 386 (1990)]. The canonical approach is compared with the treatment of Haus and Lai based on phenomenological equal-space commutation relations. The two theories are shown to provide similar outcomes of a homodyne measurement. This result justifies the use of equal-space commutation relations in quantum studies of soliton propagation.