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IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS)

Vacuum-induced fluctuations of Manakov solitons based on a linearization approximation

Darren Rand, Ken Steiglitz, Paul R. Prucnal

Published Dec 23, 2004• 0 citations
Publisher

Abstract

We investigate analytically the vacuum-induced fluctuations in Manakov soliton propagation and collision, demonstrating the extent of wave packet spreading and phase diffusion.
DOI
10.1109/leos.2004.1363397

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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.
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.
Lattice-based quantum algorithms are developed for vector soliton collisions in the completely integrable Manakov equations, a system of coupled nonlinear Schrödinger (coupled-NLS) equations that describe the propagation of pulses in a birefringent fibre of unity cross-phase modulation factor. Under appropriate conditions the exact 2-soliton vector solutions yield inelastic soliton collisions, in agreement with the theoretical predictions of Radhakrishnan et al. (1997 Phys. Rev. E56, 2213). For linearly birefringent fibres, quasi-elastic solitary-wave collisions are obtained with emission of radiation. In a coupled integrable turbulent NLS system, soliton turbulence is found with mode intensity spectrum scaling as kappa(-6).