Doppler-free multiphoton spectroscopy

In the methods discussed in Sects. 7.3 and 7.4, the Doppler width had been reduced or even completely eliminated by proper selection of a velocity subgroup of molecules with the velocity components Vy=0 Av, due to selective saturation. The technique of Doppler-free multiphoton spectroscopy does not need such a velocity selection because all molecules in the absorbing state, regardless of their velocities, can contribute to the Doppler-free transition. 

While the general concepts and the transition probability of multiphoton transitions are discussed in Sect. 7.5.1, we concentrate in this subsection on Doppler-free multiphoton spectroscopy [7.43-7.47]. 

Assume a molecule moves with a velocity v in the laboratory frame. In the reference frame of the moving molecule the frequency co of an EM wave with 

If the two photons are absorbed out of two light waves with equal frequencies (o =(02 CO, which travel in opposite directions, we obtain k = k2 and (2.62) shows that the Doppler shift of the two-photon transition becomes zero. This means that all molecules, independent of their velocities, absorb at the same sum frequency (o - -(02 = 2co. 

The considerations above can be generalized to many photons. When the moving molecule is simultaneously interacting with several plane waves with wave vectors ki and one photon is absorbed from each wave, the total Doppler shift V ki becomes zero for ki = 0. 

For illustration the examples in Fig. 7.29 show the Doppler-free two-photon spectra of the 3S 5S transition in the Na atom with resolved hyp-erfine structure [7.38]. 

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G. Grynbeig, B. Cagnac, Doppler-free multiphoton spectroscopy. Rep. Prog. Rhys. 40,791... 

G. Grynberg, B. Cagnac Doppler-free multiphoton spectroscopy. Rpt. Progr. Phys. 40, 791-841 (1977)... 

G. Grynberg, B. Cagnac, Doppler-free multiphoton spectroscopy. 

Multiphoton resonant processes with simplest fundamental quantum systems exposed to sufficiently strong laser fields attracted conspicuous attention over last years. Currently, this interest is being especially strongly stimulated by dramatic improvements in the precision of measurements presently attainable in spectroscopic experimental studies of hydrogenic and few-particle atoms. Using methods of ultra high precision Doppler-free spectroscopy, particularly impressive results have been recently obtained in studies of fundamental bounded systems such as hydrogen (H) and its natural isotopes deuterium (D) and tritium (T) [1,2,3,4,5,6,7], positronium [8,9], denoted Ps = (e+ — e ), muonium [10,11,9,12,13,14,15], denoted (M = — e ), and the helium atom (He) [16[... 

The few examples shown above illustrate that nonlinear spectroscopy represents an important branch of laser spectroscopy of atoms and molecules. Its advantages are the Doppler-free spectral resolution if narrow-band lasers are used and the possibilities to reach high-lying states by multiphoton absorption with pulsed or cw lasers. Because of its relevance for molecular physics, numerous books and reviews cover this field. The references [203, 205, 281-289] represent only a small selection. 

Really impressive progress toward higher spectral resolution has been achieved by the development of various Doppler-free techniques. They rely mainly on nonlinear spectroscopy, which is extensively discussed in Chap. 7. Besides the fundamentals of nonlinear absorption, the techniques of saturation spectroscopy, polarization spectroscopy, and multiphoton absorption are presented, together with various combinations of these methods. 

The goal of this book is to present in a coherent way the problems of the laser control of matter at the atomic-molecular level, namely, control of the velocity distribution of atoms and molecules (saturation Doppler-free spectroscopy) control of the absolute velocity of atoms (laser cooling) control of the orientation, position, and direction of motion of atoms (laser trapping of atoms, and atom optics) control of the coherent behavior of ultracold (quantum) gases laser-induced photoassociation of cold atoms, photoselective ionization of atoms photoselective multiphoton dissociation of simple and polyatomic molecules (vibrationally or electronically excited) multiphoton photoionization and mass spectrometry of molecules and femtosecond coherent control of the photoionization of atoms and photodissociation of molecules. 

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