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Physical Review A

Quantum statistics of the decay of a Raman soliton

R. C. Swanson, David C. MacPherson, Philip R. Battle, John L. Carlsten

Published Jan 1, 1992• 3 citations
Publisher

Abstract

Recent studies of soliton formation in a Raman amplifier by a \ensuremath{\pi} phase shift have shown that the soliton will decay if the input Stokes beam is off resonance. Initial experiments indicated that this soliton decay is related to frequency shifts of the input Stokes beam that result from quantum fluctuations. In this paper we use the quantum statistics of the Raman spectral fluctuations to compare the predicted decay statistics of the soliton decay with the experimentally measured distribution. We find that, as conjectured, the soliton decay is directly related to the statistics of the initiating quantum fluctuations.

DOI
10.1103/physreva.45.450

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Recent studies of soliton formation in a Raman amplifier by a \ensuremath{\pi} phase shift have shown that the soliton will decay if the input Stokes beam is off resonance. Initial experiments indicated that this soliton decay is related to frequency shifts of the input Stokes beam that result from quantum fluctuations. In this paper we use the quantum statistics of the Raman spectral fluctuations to compare the predicted decay statistics of the soliton decay with the experimentally measured distribution. We find that, as conjectured, the soliton decay is directly related to the statistics of the initiating quantum fluctuations.
Although \ensuremath{\pi} phase shifts in an input Stokes beam are known to initiate soliton formation in a Raman amplifier, the observed shot-to-shot amplitude fluctuations have gone unexplained. It has been suggested that recently observed frequency shifts caused by quantum fluctuations may be related to the observed soliton decay. We show that frqequency shifts of the magnitude observed from these quantum fluctuations lead to soliton decay, and thus, are indeed the probable cause of observed soliton decay.
When vacuum fluctuations at the Stokes frequency are amplified through the interaction of a coherent pump with a Raman medium, large phase shifts in the Stokes field may survive well into its macroscopic regime. Because the response time of the medium’s polarizability is finite, the relative phase of the polarizability and the Stokes field exhibits a peak, called a phase wave. Correspondingly, the pump reacts to a sufficiently large phase shift by briefly repleting before continuing its depletion, thus forming a solitary wave or soliton. It is possible to use the statistical properties of phase waves to predict such observables as the frequency of soliton production, the distribution of soliton amplitudes, and the soliton delay-time statistics.
Measurements on soliton decay in stimulated Raman scattering have led to the study of frequency fluctuations in the single shot Stokes linewidth. These spectral measurements show that the spectrum of a single shot can be considerably narrower than the gain narrowed profile predicted by quantum mechanics for the ensemble average. However when spectra of many shots are averaged together the predicted result is recovered. The fluctuations seen are thought to be related to the quantum fluctuations associated with the initiating spontaneous emission. Theoretical results based on coherent mode theory are shown to be in agreement with the data.
Theoretical and experimental details of initiating and amplifying a Stokes pulse using stimulated Raman scattering in H2 are presented.Statistics associated with the spectral fluctuations of a Stokes seed pulse have been measured and theoretically calculated.The spectral fluctuations are shown to result from quantum noise associated with spontaneous initiation.These spectral fluctuations are an example of an easily measurable macroscopic fluctuation of quantum origin.The effects of frequency fluctuations on the generation of solitons in the nonlinear regime of stimulated Raman scattering are calculated and measured.A detailed derivation of the fully quantum mechanical stimulated Raman scattering equations is given along with their solution for various approximations.The driven Maxwell's equation for the Raman system is derived from the system Hamiltonian.For treating the quantum initiation of stimulated Raman scattering, the radiation field is expanded in localized coherent modes.The details of calculating and using these modes to generate an ensemble of Stokes pulses are presented along with specific examples and ensemble average statistics.The use of localized modes for treating the pulsed cavityless Raman laser gives insight into the spontaneous initiation of Stokes pulses.iv ACKNOWLEDGMENTS I feel very fortunate to have had Dr. John Carlsten for my thesis adviser.I would like to thank John for making graduate school an enjoyable part of life and for the many hours o f stimulating discussions on fundamental physics.I am also greatly indebted to my wife, Susie, for filling my big lunch bag every morning and for her many hours spent typing this thesis
The formalism of Englund and Bowden [Phys. Rev. A 42, 2870 (1990)] is used to conduct a detailed investigation into the statistics of spontaneously generated Raman solitons and their origin in phase waves. Two approaches are adopted. In one, a Monte Carlo simulation of the stochastic differential equations describing stimulated Raman scattering is carried out, with quantum noise entering through the Stokes vacuum. The other involves determining analytically the field statistics in the quantum-initiation regime, finding the corresponding phase-wave statistics, and determining numerically the class of phase waves that appear in the nonlinear regime as solitons. Computations involving quasi-Gaussian and rectangular pump-pulse profiles consistently indicate soliton yields of roughly 10% and 4%, respectively; differences in the distributions of soliton delay times and peak intensities are also indicated. The Monte Carlo method is adapted to the experimental parameter values of MacPherson et al. [Phys. Rev. A 40, 6745 (1989)], and gives yields and distribution in good accord with the experiment.