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Quantum Electronics and Laser Science Conference

Quantum noise and thermal noise in optical soliton propagation

Robert M. Shelby, E. H. Whittaker, P. D. Drummond, S. J. Carter, M. Rosenbluh

Published May 10, 1992• 0 citations
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Abstract

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.

Related papers

Squeezed solitons: quantum and thermal noise effects

Robert M. Shelby, M. Rosenbluh, P. D. Drummond +1 more

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.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

Squeezing of optical solitons

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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 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

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P. D. Drummond, S. J. Carter

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.

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Summary form only given. Optical solitons in fibres are attractive macroscopical quantum objects, which are particle-like pulses propagating over large distances without distortion due to the balance between Kerr nonlinearity and group velocity dispersion effects. However, in the frame of the quantum theory, they exhibit a complicated internal quantum structure with nontrivial nonlinear dynamics. In the process of the propagation along a fiber, the nonlinear dynamics of secant hyperbolical shaped optical pulses lead to the formation of classically stable soliton pulses with a rich variety of nonclassical properties, such as quantum noise reduction, spectral quantum noise correlations, and quantum non-demolition interactions. We discuss the experimental characterisation of these quantum properties of femtosecond optical solitons at the telecommunication wavelength of 1.5 /spl mu/m experiencing nonlinear-interactions in silica fibres.

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Quantum diffusion in soliton position measurements

P. D. Drummond, Y. Yamamoto

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.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations
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.
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
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.
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.
Summary form only given. Optical solitons in fibres are attractive macroscopical quantum objects, which are particle-like pulses propagating over large distances without distortion due to the balance between Kerr nonlinearity and group velocity dispersion effects. However, in the frame of the quantum theory, they exhibit a complicated internal quantum structure with nontrivial nonlinear dynamics. In the process of the propagation along a fiber, the nonlinear dynamics of secant hyperbolical shaped optical pulses lead to the formation of classically stable soliton pulses with a rich variety of nonclassical properties, such as quantum noise reduction, spectral quantum noise correlations, and quantum non-demolition interactions. We discuss the experimental characterisation of these quantum properties of femtosecond optical solitons at the telecommunication wavelength of 1.5 /spl mu/m experiencing nonlinear-interactions in silica fibres.
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.