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Communications in Theoretical Physics

Quantum Squeezing of Dark Solitons in Optical Fibers

Gholamreza Honarasa, Mohsen Hatami, Mohammad Kazem Tavassoly

Published Aug 1, 2011• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/56/2/23

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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.
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.
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.
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.
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.
Solitons on fibers are ideal for all optical switching operations.1 Squeezed solitons promise to provide improved measurement capabilities.2 The self-induced transparency (SIT) in CdS has been proposed as a particularly convenient means of squeezing.3 For this reason it is important to understand the quantization problem of solitons. Several authors have attacked the problem in the case of the nonlinear Schrodinger equation (NSE) both numerically4 and analytically.5 A particularly simple approach to quantization can be worked out in the limit of a linearized approximation. Since all switching and squeezing operations employ pulses with many photons (n > 10), the linearization is always legitimate.