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Physical Review A

Field-correlation effects in two-photon absorption from randomly amplitude-modulated laser fields

Ce Chen, M. Rifani, Jongwhan Cha, Yi-Yian Yin, Daniel S. Elliott

Published Jan 1, 1994• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.49.461

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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.
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.
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.
The generation of a broadband laser field with well-defined and controllable statistical properties, known as the real Gaussian laser field, has been achieved through the random modulation of the amplitude of a stabilized laser beam. The verification of the field-generation technique is provided by measurements of the laser power spectrum (Lorentzian) and by measurements of the intensity autocorrelation function. The latter is shown to decrease exponentially from an initial value of nearly 3 to a final value of 1 with a decay time related to the inverse bandwidth of the field. The techniques for generating this field and for its characterization are discussed in this paper.
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.
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.
A model of two photon absorption in a cavity with an external driving field is presented. Phase and amplitude fluctuations in the driving field are taken into account to model a partially coherent multimode source. The photon statistics of the light in the cavity are investigated through a calculation of the second-order correlation function of the light field in the steady state. For a coherent driving field the field inside the cavity will exhibit photon antibunching for low intensities. As the fluctuations in the driving field are increased the photon antibunching is lost. For a particular coherent field, g (2) (0) is reduced with increasing laser intensity. This reduction with laser intensity is slower with increasing laser amplitude fluctuations. This could provide a possible explanation for the recent experimental observations of Kransinski and Dinev (1976).