Doppler-Free Two-Photon Absorption

We have already discussed the two-photon absorption process [9.187] (Sect. 9.1.3c). Normally, the signals are Doppler broadened, and high resolution is not obtained even if narrow-band lasers are used. However, a very important observation was made as early as 1970 by Chebotayev and co-workers [9.188]. The Doppler broadening can be eliminated if the two photons are extracted in such a way that one is supplied from one of two counter-propagating laser beams and one from the other beam. For a certain atom with a velocity component v along one direction of propagation, the energy in- 

We will also discuss another series of investigations on hydrogen performed by Hmsch and co-workers, which is of fundamental importance 

Future possibilities for accurate H spectroscopy have been discussed in [9.208,209]. The optical analogy to the Ramsey-fringe technique (Sect. 7.1.2) has been demonstrated for the case of two-photon absorption. In Fig.9.51 the inevitable Fourier broadening of a short pulse is illustrated. 

We will also discuss another series of investigations on hydrogen initiated by Hdnsch and co-workers, which is of fundamental importance [9.388-9.391, 9.396]. The experiment deals with the determination of the Lamb shift in the ground state (n = 1) (Fig. 9.63). In contrast to the situation 

Ah 1/10 Hz = 100 MHz). The measurement yields a Lamb shift of the Is state of about 8170MHz (best value is 8172.876(29) MHz [9.396]), which is in close agreement with the theoretical predictions. Since the natural life-time of the 2s state is about 10 s, extremely narrow lines should, in principle, be attainable. Narrow-band 243 mn radiation has been genera- 

An example of high-resolution spectroscopy for hydrogen and deuterium is given in Fig. 9.64. Many groups have been very active in the field of precision hydrogen spectroscopy [9.397-9.399]. Frequently, combinations of atomic states and utilization of simple relationsliips between transition frequencies as given by the Balmer-Rydberg formula have been utihzed [9.351]. 

To relate optical frequencies to the cesium time standard remains a very important issue in precision metrology. In this context the development of the opticai-frequency-comb technique using mode-locked lasers has been very important [9.400]. 

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Figure 1. Linewidlhs of different rotational transitions in the 14q1q vibronic band of benzene measured with Doppler-free two-photon absorption. The observed strong dependence on the quantum number J of the rotational angular momentum is evidence for a rotationally dependent intramolecular coupling process. (Taken from Ref. 3.)...

Doppler-free two-photon absorption was observed in a study of the V2 °P(5,3) transition by laser Stark spectroscopy using the 10 P(18) CO2 laser line. It is caused by accidental overlapping of the °P(5,3) line in the V2 band with the °P(4,3) line in the hot band 2V2-V2 [14, 16]. 

Figure 2.32 shows a possible experimental arrangement for the observation of Doppler-free two-photon absorption. The two oppositely traveling waves are formed by reflection of the output beam from a single-mode tunable dye laser. The Faraday rotator prevents feedback into the laser. The two-photon absorption is monitored by the fluorescence emitted from the final state Ef into other states Em - From (2.66) it follows that the probability of two-photon absorption is proportional to the square of the laser intensity. Therefore, the two beams are focused into the sample cell by the lens L and the spherical mirror M. 

The isotope shift between different stable lead isotopes shown in Fig. 2.36 has been determined by Doppler-free two-photon absorption of a cw dye laser beam at X = 450.4 nm on the transition 6p Po lp Po [250] using the experimental arrangement of Fig. 2.32. 

In Sect. 2.4 we saw that the first-order Doppler effect can be exactly canceled for a two-photon transition if the two photons hcoi = fuo2 have opposite wave vectors, i.e., k = —k2. A combination of Doppler-free two-photon absorption and the Ramsey method therefore avoids the phase dependence (p Vx) on the transverse velocity component. In the first interaction zone the molecular dipoles are excited with the transition amplitude a and precess with their eigenfrequency (jl> 2 = ( 2 — E )/h. If the two photons come from oppositely traveling waves with frequency u), the detuning... 

R. Guccione-Gush, H.P. Gush, R. Schieder, K. Yamada, C. Winnewisser, Doppler-free two-photon absorption of NH3 using a CO2 and a diode laser. Phys. Rev. A 23,2740 (1981)... 

FIGURE 35 Example of high-resolution spectrum in sodium vapor obtained with two-photon Doppler-free spectroscopy. [Reproduced from Bloembergen, N., and Levenson, M. D. (1976). Doppler-free two-photon absorption spectroscopy. In High Resolution Laser Spectroscopy (K. Shimoda, ed.), p. 355, Springer, New York.l... 

Assumed. Absorption spectroscopy. Doppler-free two-photon absorption. g=f assumed in conversion of units. g=f assumed in conversion of units. Authors calculation. ... 

B.P. Stoicheff, E. Winebergen Doppler-free two-photon absorption spectrum of rubidium. Can. J. Phys. 57, 2143 (1979)... 

F1q.l0.49. Experimental arrangement for the observation of Doppler-free two-photon absorption... 

The first experiments on Doppler-free two-photon absorption have been performed on the 3S 5S and 3S 4D transitions in sodium atoms [10.74-76a]. The energy defect to the intermediate 3P level is small and... 

The range of nuclei of interest in the types of studies mentioned above is extensive. Correspondingly, the range of spectroscopy is also rather broad. One has at the long wavelength end to deal with fine structure and hyperfine structure in, e.g., positronium and muonium. Also optical spectroscopy is possible for positronium, especially the recently demonstrated Doppler-free two photon absorption Is -> 2s [32], These spectral regions have been already mentioned above along with their problems in scale normalization. 

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