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Quantum Electronics and Laser Science Conference

Quantum Noise Limits On Spatial Soliton Propagation

Elna M. Nagasako, Robert W. Boyd, G. S. Agarwal

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

It is well known that through amplification, quantum noise can grow to affect the propagation characteristics of temporal solitons.1 We discuss an analogous effect in spatial soliton propagation, where vacuum fluctuations are amplified by four-wave mixing and can grow to change the propagation characteristics of spatial solitons.

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Classical optical solitons propagate in optical fibers without temporal or spectral distortion as a result of a balance between phase shifts due to group velocity dispersion and those due to nonlinear self-phase modulation. This balance is achieved by the proper choice of pulse shape and duration for a given pulse energy. The quantum fluctuations associated with a coherent soliton do not undergo stationary propagation, however, and a number of effects are predicted, including the evolution of vacuum noise associated with the input coherent pulse into squeezed fluctuations and the temporal spreading of the soliton pulse because of dispersion acting on quantum fluctuations of the pulse frequency.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary distortion-free propagation only requires the proper choice of pulse width and shape for a given pulse energy. However, quantum fluctuations do not undergo stationary propagation but rather evolve due to dispersion and self-phase modulation. As a soliton pulse propagates, zero-point or vacuum noise associated with the pulse evolves into squeezed noise. Vacuum fluctuations are responsible for the fundamental detector noise floor known as the shot noise limit. Reduction of the noise in the detection of squeezed soliton pulses has achieved a noise level 34% below this limit. In optical fibers, thermal fluctuation of the refractive index limit the noise reduction that can be achieved by adding phase fluctuations in excess of the vacuum noise. At low frequencies thermal noise originates from local structural dynamics of fused silica which produces a 1/f power spectrum and from guided acoustic wage Brillouin scattering which modulates the refractive index at frequencies characteristic of the fiber structure. The bandwidth of these fluctuations is ~2 GHz; and for soliton pulses with spectral bandwidth much >2 GHz, we have shown that this noise can be made insignificant. For very short pulses, however, noise from Raman scattering must be considered. Recent calculations incorporating this noise mechanism are compared with experiment.
We study the possibility of employing phase-sensitive parametric amplifiers to compensate for losses incurred by solitons propagating in optical fibers. As phase-sensitive amplification is free from the excess spontaneous noise associated with laser amplifiers, the only quantum noise source in such a system arises from the fiber losses. In addition, under phase-sensitive amplification, fluctuations in the soliton frequency are squeezed to one half of the vacuum level, thus producing a negligible contribution to the fluctuations in the soliton arrival time. This greatly reduces the Gordon–Haus jitter of the solitons. The performance of the phase-sensitive amplifier is compared with that of alternative noise-reduction schemes employing phase-insensitive amplifiers and spectral filters as well as with the limits on long-distance data transmission imposed by quantum mechanics.
The usual view of a soliton in an optical fiber is that it obeys the classical Maxwell equations, and propagates unchanged down a lossless fiber. Of course, it is well known that an optical amplifier introduces noise in position. It is less well known that even a perfectly lossless fiber, without an amplifier, is unable to support the classical invariant solution. Instead, all solitons experience quantum noise in position and phase, and this noise increases with propagation distance. Experimenters at IBM laboratories have recently observed the first quantum effects in solitons. These experiments focussed on quadrature squeezing, and were able to detect the large increase in phase-quadrature noise that is predicted quantum-mechanically. In this paper we treat the effects of pulse-position noise, and indicate how this noise source can limit information transmission using solitons. While these effects are small in currently proposed communication systems, they place a fundamental limit on future enhancements of soliton communications using pulse-position modulation. Of most scientific interest is the macroscopic nature of the quantum fluctuations, which can alter the location of a huge number of cooperatively positioned photons, and possible implications for QND momentum measurements.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary, distortion-free propagation requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2
Summary form only given. The quantum properties of the interaction between an electromagnetic field and a nonlinear media have been widely studied, theoretically and experimentally, but so far these studies concerned mainly measurements performed on the total intensity of light beams, integrated over all the transverse plane. However, the details of the noise distribution inside the transverse plane, as well as the spatial quantum correlation between two different points, can be also very instructive, on a fundamental side in order to understand the propagation of the quantum noise, but also on a practical side to generate special configurations of the field which allow us to increase the spatial resolution of measurements in the transverse plane. We study here the spatial properties of the quantum fluctuations for a field freely propagating in a thick nonlinear medium, and in a case where the interaction distance is not limited by the diffraction : the spatial soliton regime, where diffraction effects are counterbalanced by nonlinearity and which exists in /spl chi//sup (2)/ and /spl chi//sup (3)/ media.