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Physical Review Letters

Two-photon absorption from the real Gaussian field

Ce Chen, Daniel S. Elliott, M. W. Hamilton

Published Jun 15, 1992• 35 citations
Publisher

Abstract

We have measured the absorption line shape for two-photon absorption from a broadband field known as the real Gaussian field. We observe that, in the case of large optical bandwidth, the width of the absorption spectrum is narrower than that of the optical field. Agreement with calculated line shapes and widths is excellent.
DOI
10.1103/physrevlett.68.3531

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We have measured absorption spectra for Doppler-free two-photon absorption from a laser field characterized by strong amplitude fluctuations. This field, known as the real Gaussian field, is generated by randomly modulating the amplitude of the output of a cw stabilized dye laser. The absorption rate from this field is enhanced over that from a field whose intensity is nonvarying and of the same average value. When the laser bandwidth is very large, the absorption spectrum is limited, not by the laser width, but by the width of the atomic resonance. Our measurements are in excellent agreement with calculated spectra.
The probability of an atom undergoing a transition to a given final state by means of two-photon absorption is expressed for arbitrary field states in terms of the second-order normally-ordered field correlation function, evaluated at the position of the atom. In the case of stationary fields, an expression for the absorption rate is found which reduces to a particularly simple form for narrow-bandwidth fields near resonance. The effect of field statistics is illustrated by comparing the absorption rate w2(ch)w_{2}^{}{}_{}{}^{(\mathrm{ch})}w2​​(ch) for chaotic or Gaussian light to the rate w2(l)w_{2}^{}{}_{}{}^{(l)}w2​​(l) for laser light. The rate for laser light is calculated within the context of a particular model based on the assumption of fixed field amplitude and random frequency modulation, and the chaotic light to which it is compared is assumed to have the same (Lorentzian) power spectrum. When the width ${\ensuremath{\kappa}}_{f}$ of the final atomic level is much greater than the bandwidth bbb of the field, we obtain the previously derived result w2(ch)w2(l)=2\frac{w_{2}^{}{}_{}{}^{(\mathrm{ch})}}{w_{2}^{}{}_{}{}^{(l)}}=2w2​​(l)w2​​(ch)​=2. When ${\ensuremath{\kappa}}_{f}\ensuremath{\ll}b$, on the other hand, the ratio between the two rates depends on the (mean) frequency of the field, and assumes the (maximum) value 4 when the field is exactly on resonance.
We have developed a method of generating a field whose amplitude is a randomly fluctuating variable, known as a real Gaussian field, as a means of testing the effect of laser bandwidth on nonlinear optical interactions. The frequency of this field is constant, and its amplitude, restricted to real values, varies about a mean value of zero. We have measured the intensity autocorrelation function of the light, and it shows good agreement with expected results. We are now measuring the effect of this field on nonlinear systems. The first is the 3S-5S two-photon resonance in atomic sodium. Enhancement of the two- photon absorption rate by a factor of three over the absorption rate from a monochromatic field of the same average intensity is expected. The real Gaussian field is also being applied to studies of transmission through a Fabry-Perot interferometer. The intensity spectrum is expected to consist of peaks centered at zero frequency and at the difference between the laser frequency and that of the peak of the interferometer transmission.
We report measurements of the absorption spectrum for two-photon absorption from a variety of randomly amplitude-modulated laser fields. The fields are generated by modulating the output of a stabilized tunable ring dye laser external to the laser cavity. As such, the field statistical properties are controllable and well characterized. The fields which we have used in this investigation include the real Gaussian field, the complex Gaussian field, and the real Gaussian field with a coherent component. For the last field, an interesting correlation effect is seen when the coherent component is in phase or 90\ifmmode^\circ\else\textdegree\fi{} out of phase with the stochastic component. We have also investigated the effect of partial correlation of the two counterpropagating fields used in the measurements. In all cases we find excellent agreement between the measured absorption spectra and those calculated from the known fourth-order field-correlation functions.
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.