Two-photon absorption without Doppler broadening

J. P. Woerdman

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.

N. Bloembergen, M. D. Levenson

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.

Vladilen S Letokhov, Veniamin P. Chebotayev

Kening Jia, Liu Zhong-Bo, Liang Ying +2 more

Using the numerical result, the influence of the Doppler broadening on the two-photon absorption related to vacuum induced coherence is discussed. In the absence of Doppler broadening, when VIC is absent, the absorption curve has a double-peak structure and the electromagnetically induced transparency phenomenon can occur; when VIC is present, the absorption curve has a single-peak structure and EIT phenomenon does not appear. In the presence of Doppler broadening, regardless of VIC being present or not, EIT phenomenon always can occur; when VIC is absent, no matter whether the propagation directions of the probe and driving fields are the same or opposite, with the Doppler broadening width (D) increasing, the absorption first increases and then decreases and the absorption curve changes gradually from a double-peak structure to a single-peak structure; when VIC is present, if propagation directions of the probe and driving fields are the same, with the value of D increasing, the absorption first increases and then decreases and the absorption curve changes gradually from a single-peak structure to a double-peak structure; if propagation directions of the probe and driving fields are opposite, with the value of D increasing, the absorption decreases monotonieally and the absorption curve remains a single-peak structure.