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Physical Review Letters

Two-Photon Absorption from a Phase-Diffusing Laser Field

Daniel S. Elliott, M. W. Hamilton, K. Arnett, Stephen J. Smith

Published Jul 30, 1984• 59 citations
Publisher

Abstract

We report the first quantitative measurements of the effect of a phase-diffusing laser field on a nonlinear optical interaction. Using a nearly Lorentzian laser power spectrum, we have measured the spectral linewidth of an unsaturated two-photon absorption process. We find that the measured width scales as four times the laser width, in agreement with the theoretical predictions of Mollow.

DOI
10.1103/physrevlett.53.439

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Physical Review A•Jul 1, 1989•18 citations
We report the first quantitative measurements of the effect of a phase-diffusing laser field on a nonlinear optical interaction. Using a nearly Lorentzian laser power spectrum, we have measured the spectral linewidth of an unsaturated two-photon absorption process. We find that the measured width scales as four times the laser width, in agreement with the theoretical predictions of Mollow.
Experimental evidence of field-correlation effects on weak-field two-photon absorption in atomic sodium is presented. In the case of a nearly Lorentzian laser power spectrum the absorption profile has four times the spectral width of the exciting field, in agreement with predictions by Mollow. The measurement is carried out with counterpropagating laser beams to cancel Doppler broadening. The width of the two-photon absorption spectrum is decreased by partially decorrelating the counterpropagating laser beams. Increasing the correlation time of the frequency fluctuations, resulting in a nearly Gaussian laser power spectrum, has also been observed to decrease the width of the absorption spectrum. An extension of the time-dependent second-order perturbation theory to these additional cases yields good agreement.
Measurements of two-photon absorption spectra have been made for the case where the exciting laser has a random-telegraph phase. The resulting spectral shapes are compared to theoretical predictions and to previous data taken with a phase-diffusing laser field [Elliott et al., Phys. Rev. A 32, 887 (1985)]. A striking dependence of the absorption spectrum on the second-order coherence of the field was observed. Using the theory for the propagation of second-order spatial coherence, we draw an analogy between diffraction and two-photon absorption which we use to interpret the two-photon absorption spectra.
We have measured the variance in fluorescence intensity and the spectrum of those fluctuations for two-level atoms in a phase-diffusing laser field. We compare our results with recent theoretical predictions that have been extended to include the effects of Doppler broadening and spatial variation of the laser intensity. Our study includes the effects of laser power, bandwidth, and shape (Lorentzian and non-Lorentzian) of the laser spectrum. At lower laser intensities, our measured variances versus detuning are in quantitative agreement with the theoretical predictions. At intensities above saturation, the variance is sensitive to inhomogeneities in the distribution of laser intensity in the interaction region, and only qualitative agreement is achieved. Asymmetries in the variance versus detuning resulting from correlated amplitude and phase noise have been observed. Spectra of the phase-noise-induced fluorescence-intensity fluctuations are shown to contain contributions from transients excited by the phase noise and are more sensitive to artifacts in the noise modulation process than the intensity spectrum of the laser field itself.
The dependence of the optical Autler-Townes effect on laser field phase fluctuations describable by a two-dimensional Markovian process (phase-diffusion model with a non-Lorentzian line shape) is investigated experimentally in atomic sodium. An intense cw laser tuned to near resonance with the 3S1/2{3\mathrm{S}}_{1/2}3S1/2​(F=2,MF{\mathrm{M}}_{\mathrm{F}}MF​=2)\ensuremath{\rightarrow}3P3/2{3\mathrm{P}}_{3/2}3P3/2​(F=3,MF{\mathrm{M}}_{\mathrm{F}}MF​=3) transition was frequency modulated to generate phase fluctuations with the desired characteristics. A weak probe laser coupling to the 4D5/2{D}_{5/2}D5/2​(F=4, MF{M}_{F}MF​=4) state was used to obtain the double-peaked optical Autler-Townes absorption profiles in order to investigate their dependencies on band shape, bandwidth, intensity, and detuning of the intense fluctuating laser field. Reversals of the peak-height asymmetry and reversion to normal asymmetry with increased detuning were observed and measured. Quantitative studies of the spectral widths and splittings of the peaks are also reported. Measured absorption profiles are in excellent agreement with calculations based on previous theoretical work.
The time dependence of the two-photon absorption process is experimentally investigated in the low intensity regime as a function of laser linewidth, Doppler width, polarisation and delay between pulses, using 5 ns pulses at two different frequencies. Excellent agreement is found between experiment and the theoretical predictions of Allen and Stroud. The experiment arguments and expands earlier work on the dependence of linewidth in the two-photon process. The lineshape of the Hansch-type laser producing the pulses is shown to be best described by a Gaussian rather than a Lorentzian or as the result of an Ornstein-Uhlenbeck process.
A phase-diffusion stochastic field with frequency fluctuations obeying Gaussian Markovian statistics is produced at microwave frequency and used to drive a two-level spin system. The system is tuned to the two-photon (TP) resonance and its TP-induced second-order response is measured as a function of the characteristic parameters of the frequency noise. It is found that, when the statistics of the driving field are varied from the fast- to the slow-modulation limit, the power spectrum of the nonlinear response of the system varies in a continuous way from a Lorentzian form toward a Gaussian one, and its relative width (normalized to the input spectral width) varies from 4.0\ifmmode\pm\else\textpm\fi{}0.4 to 2.0\ifmmode\pm\else\textpm\fi{}0.2. The experimental results are interpreted on the basis of a semiclassical calculation which takes into account the stochastic nature of the field. The effect of the filter action of the cavity modes is discussed. The relationship with previous experiments and theoretical calculations of TP absorption is also examined.