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Physical Review Letters

Macroscopic Manifestation of Quantum Fluctuations in Transient Stimulated Raman Scattering

N. Fabricius, Kurt Nattermann, Dietrich von der Linde

Published Jan 9, 1984• 57 citations
Publisher

Abstract

The statistical distribution of the Stokes pulse energy is measured for transient stimulated Raman scattering in pressurized hydrogen gas. Large fluctuations of the Stokes energy obeying an exponential distribution law are observed. These macroscopic energy fluctuations are caused by quantum noise in the initial state of the system.
DOI
10.1103/physrevlett.52.113

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We calculate the probability distribution P(W) for the energy W of pulses generated by transient stimulated Raman scattering and find that 100% macroscopic fluctuations are predicted. In the limit of large numbers of Stokes photons we find that P(W) is essentially exponential, implying that the most probable value for Stokes pulse energy is near zero. The macroscopic energy fluctuations, whose origin is quantum mechanical, may impose a fundamental limitation on the stability of the Raman generation process.
It is shown that transient anti-Stokes stimulated Raman scattering (SRS) acts as a vacuum field fluctuations amplifier at Stokes frequency, the fluctuations being amplified up to macroscopic values. This makes their investigation possible by studying macroscopic energy fluctuations of transient SRS anti-Stokes pulses. The proposed theory also gives a quantitative description of angular distribution of self-generated anti-Stokes emission around the exact phase-matching angle recently observed by Duncan et al. ( Opt. Lett. , 11 (1986) 803) in the transient regime.
From a classical point of view the generation of Stokes light by stimulated Raman scattering (SRS) is not possible unless a Stokes input signal is supplied. On the other hand, the gain in SRS can be so large that without input the spontaneous build-up of strong Stokes waves can be observed. A proper quantum theoretical description1 shows that this spontaneous initiation of Stokes generation is due to microscopic random fluctuations originating from quantum noise associated with the dynamical variable Q(t) which is active in the Raman process, e.g., a molecular normal mode coordinate. In highly transient SRS -when the duration of the excitation pulse is shorter than the dephasing time- the Stokes field is proportional to the initial Heisenberg operator Q(0) describing the state of the system just before the excitation pulse is turned on (t=0). In this case the statistics of the final Stokes pulse energy is determined by quantum mechanical uncertainties associated with the random Raman polarization of the initial state2. On the other hand, in a steady state situation the Stokes pulse fluctuations are substantially reduced and the Stokes pulse energy is stabilized as a result of damping processes.
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.
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.