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Physical Review A

Quantum statistics of the gain-narrowed Raman linewidth in H2

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

Published Dec 1, 1990• 13 citations
Publisher

Abstract

Recent studies have shown that single-shot spectra in stimulated Raman scattering can be much narrower than the quantum-mechanical gain-narrowed linewidth. However, shot-to-shot fluctuations in the single-shot spectra are such that the ensemble average gives the gain-narrowed linewidth. This happens because the mean frequencies of the single-shot spectra fluctuate from shot to shot under the gain-narrowed linewidth, and because some ``noisy'' shots are broadened or display multipeaked spectra. The nature of these quantum-noise-initiated fluctuations will be discussed in this paper, with both numerical and experimental results presented. Noisy, multipeaked, single-shot spectra will be shown to have a broader distribution of mean frequencies than the distribution of near-Fourier-transform-limited spectra.

DOI
10.1103/physreva.42.6774

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Recent studies have shown that single-shot spectra in stimulated Raman scattering can be much narrower than the quantum-mechanical gain-narrowed linewidth. However, shot-to-shot fluctuations in the single-shot spectra are such that the ensemble average gives the gain-narrowed linewidth. This happens because the mean frequencies of the single-shot spectra fluctuate from shot to shot under the gain-narrowed linewidth, and because some ``noisy'' shots are broadened or display multipeaked spectra. The nature of these quantum-noise-initiated fluctuations will be discussed in this paper, with both numerical and experimental results presented. Noisy, multipeaked, single-shot spectra will be shown to have a broader distribution of mean frequencies than the distribution of near-Fourier-transform-limited spectra.
Studies of quantum noise initiated stimulated Raman scattering in H2 show that single shot Stokes spectra can be narrower than the quantum mechanical gain narrowed linewidth. The ensemble average of these single shot spectra, however, agrees quite well with the quantum mechanical prediction.1 Additionally, the mean frequencies of near Fourier transform-limited shots have a narrower distribution than the distribution of means of the entire ensemble. We present evidence in support of these statements as well as presenting arguments that yield a qualitative understanding of these results.
Measurements of the single-shot power spectrum of stimulated Raman scattering from an H2{\mathrm{H}}_{2}H2​ Raman generator at 10 and 32 atm using a Fabry-Perot interferometer are presented. The results show that the single-shot linewidth can be much narrower than the ensemble average predicted by quantum mechanics. However, when the spectra of numerous shots are averaged together the resulting linewidth is in close agreement with the predicted result. In addition, the power spectrum exhibits large shot-to-shot fluctuations within the gain-narrowed profile which may be related to observed soliton decay in stimulated Raman scattering.
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.
Results from a study of quantum noise and its macroscopic manifestations in stimulated Raman scattering are presented.Shot to shot fluctuations in quantum noise initiated Stokes spectra are considered.The Stokes spectra were recorded experimentally using a Fabry-Perot interferometer.For comparison, numerically generated Stokes spectra were produced using the semi-classical model of stimulated Raman scattering with a numerically generated "vacuum" input field.The amount of structure on each spectrum was quantified by calculating the spectrum's standard deviation from its mean frequency.It was found that ensembles with the noisy spectra removed had narrower distributions of mean frequencies than ensembles that included noisy spectra.
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
Manifestations of quantum fluctuations in stimulated Raman scattering ( SRS ) have been intensively studied lately1. Quantum noise present in spontaneous scattering stimulates fluctuations both in phase and in amplitude characteristics of output Stokes emission. At present statistical properties of amplitude fluctuations are studied in detail and it is shown that in linear transient regime of SRS without pump depletion statistical scatter of Stokes energy Es has negative exponential distribution2. In saturation regime of SRS the amplitude fluctuations are almost suppressed simultaneously with pump depletion. The phase fluctuations manifest both in linear and in nonlinear SRS and produce beam pointing fluctuations3, a change in Stokes emission spectra from pulse to pulse4 and cause soliton appearance in Rayleigh component of SRS5. Phase noise is observed in saturation regime due to relation between phases of Stokes and phonon waves which is preserved in processes of stationary and quasistationary SRS amplification. Spectrum phase fluctuations manifest as fine structure of SRS spectrum4, fluctuations of average Stokes frequency and Stokes linewidth fluctuations. The evolution of phase fluctuations in time is determined by the nature of spontaneous scattering and polarization of Raman media and is of great interest as one can follow its development from vacuum modes level to saturation regime. However up to now this problem has not been studied yet.