Two-Photon Absorption and Field Correlation Functions

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 $w_{2}^{}{}_{}{}^{(\mathrm{ch})}$ for chaotic or Gaussian light to the rate $w_{2}^{}{}_{}{}^{(l)}$ 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 $b$ of the field, we obtain the previously derived result $\frac{w_{2}^{}{}_{}{}^{(\mathrm{ch})}}{w_{2}^{}{}_{}{}^{(l)}}=2$. 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.