Broadening and saturation in n-photon absorption

Stephen V. Kershaw

A. S. Marathay, Barbara A. Capron, M. Sargent

Reference 1 derives the two-photon probe-absorption coefficient for a homogeneously broadened medium subjected to an arbitrarily intense saturator wave. We have generalized this theory to allow for Doppler broadening with a counterrunning probe and saturator waves. We have carried out integrals over a Lorentzian Doppler distribution analytically and have specialized to a number of limits, such as extreme Doppler broadening. In this limit, we find the simple probe absorption coefficient α 1 ≃ 2 α 0 ( γ D 1 I 2 − i ω s T 1 ) , where α0 is the unsaturated two-photon absorption coefficient, I2 is the saturator intensity, γ is the two-photon coherence decay rate constant, ω s is the Stark shift parameter, T1 is the population difference decay time, and D 1 = 1 / [ γ+ i ( ω+ω s I 2 − ν 2 − ν 1 ) ] . For vanishing Stark shifts (ω s = 0), this is the standard two-photon probe absorption coefficient, but for large ω s , the complex Lorentzian D 1 becomes detuned. In the homogeneously broadened limit, the absorption spectrum resembles the one-photon case. In this paper we show the transition between these two limits.

Hendrik F. Hameka

Barbara A. Capron, A. S. Marathay, M. Sargent

We generalize the two-photon probe-absorption coefficient to include any amount of Doppler broadening and an arbitrarily intense saturator wave. By analytically performing integrals over a Lorentzian velocity distribution we are able to examine the transition from homogeneous broadening to extreme Doppler broadening for both zero and nonzero Stark shifts. For Doppler widths much larger than the saturator Rabi flopping frequency, the probe-absorption spectrum approaches a Doppler-free Lorentzian with width equal to the homogeneous linewidth and center displaced by the dynamic Stark shift.

Suhui Yang, Dong Wang, Xu-Zhen Guo +2 more

Ming Chiang Li

Separated-beam experiments for both the Doppler-free two-photon and saturated absorptions are under consideration. In the Doppler-free two-photon absorption, the experimental arrangement is important. Such important has not been recognized before. Three different arrangements are discussed here. In the first one, the separated-beam experiment is not coherent and the Ramsey fringe variation cannot be observed. In the second, the transit-time broadening is present and the Ramsey fringe variation depends on the atom's time of flight as well as the transit time. Finally, in the third arrangement, the transit-time broadening is eliminated and the Ramsey fringe variation depends on the atom's time of flight alone. These examples have shown that in the Doppler-free two-photon absorption, the elimination of the transit-time broadening is through a mechanism other than the beam separation. In the saturated absorption the situation is quite different. Even in the presence of transit-time broadening, the Ramsey fringe spacing depends only on the atom's time of flight.