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Laser Spectroscopy

Squeezing of Quantum Solitons in Optical Fibers in the Presence of Thermal Phase Noise

Robert M. Shelby, M. D. Levenson, Stephen H. Perlmutter, P. D. Drummond, S. J. Carter

Published Jan 1, 1989• 0 citations
Publisher
DOI
10.1016/b978-0-12-251930-7.50055-8

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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.

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Squeezing of quantum solitons (A)

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We treat the scaling of thermal phase-noise effects and quantum fluctuations for solitons in optical fibers. The central result is that the size of the thermal noise relative to quantum noise is reduced in proportion to the soliton duration for solitons whose duration is less than the thermal correlation times, suggesting that squeezed quantum solitons should be realizable in optical fibers. The physical basis for this effect is largely the fact that squeezing, which is nonlinear, occurs more rapidly for shorter pulses.
We develop a quantum theory of propagation in dispersive nonlinear media via a quantized field theory and a coherent state expansion. The resulting stochastic nonlinear Schrodinger equation includes both quantum fluctuations and thermal noise due to refractive-index fluctuations in the medium. The theory can describe either cw propagation with dispersion or soliton propagation. In the cw case, enhanced squeezing occurs with anomalous dispersion. This is reduced by thermal noise, just as it is in the normal dispersion case. The noise-induced reduction in squeezing is more severe with normal dispersion owing to the intrinsic lack of phase matching in the normal dispersion regime. With anomalous dispersion, the cancellation of nonlinear by linear dispersion allows squeezing to occur over a wide bandwidth even in the presence of thermal fluctuations. Our theory is also able to treat soliton propagation in the anomalous dispersion case. A substantial degree of pulsed squeezing is obtained, and we point out that an optimal detection scheme requires a pulsed local oscillator. Results for the effects of thermal noise on soliton propagation are presented, in which case improvement is obtained by reducing the soliton time duration.
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.