Doppler-free saturation spectroscopy

In the following I want to attempt a sort of unification of different sources of optical rotation and dichroism and show that far from being a narrow specialist s area of laser spectroscopy it is an enormously rich and varied field of study. I will therefore take as my starting point the famous and well-known dispersion relations and develop from these the form of the Faraday, Stark and PNC optical rotation. I shall also consider very briefly the extension of these ideas to the case of Doppler-free polarimetry and later I shall discuss how the use of lasers themselves brings in a variety of problems, in particular that of saturation. Finally, I will say something about the form of the weak interaction in so far as it enters the atomic Hamiltonian as a weak (no pun really intended ) perturbation. 

This very sensitive Doppler-free spectroscopic technique has many advantages over conventional saturation spectroscopy and will certainly gain increasing attention [225, 226]. We therefore discuss the basic principle and some of its experimental modifications in more detail. 

In the methods discussed in Sects. 2.3 and 2.4, the Doppler width had been reduced or even completely eliminated by proper selection of a velocity subgroup of molecules with the velocity components = 0 zb Ai , 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. Therefore the sensitivity of Doppler-free multiphoton spectroscopy is comparable to that of saturation spectroscopy in spite of the smaller transition probabilities. 

Fig. 2.48 Early experimental setup for measurements of the Lamb shift in the 1S state and of the fine structure in the Pi/2 state of the H atom by combination of Doppler-free two-photon and saturation spectroscopy [261]...

The experimental arrangement is shown in Fig. 2.48. The output of a tunable dye laser at X = 486 nm is frequency-doubled in a nonlinear crystal. While the fundamental wave at 486 nm is used for Doppler-free saturation spectroscopy [261] or polarization spectroscopy [278] of the Balmer transition 2Si/2- P /2 the second harmonics of the laser at X = 243 nm induce the Doppler-free two-photon transition 15 i/2 25 i/2. In the simple Bohr model [279], both transitions should be induced at the same frequency since in this model v(lS-2S) = 4v(2S-4P). The measured frequency difference Av = v(lS-2S) — 4v(2S-4P) yields the Lamb shift vlCI ) = Av — 8v] 2S) — Avfs(45 i/2 4Pi/2) <5vl(45 ). The Lamb shift (5vl(2/S) is known and Avfs(45i/2-4Pi/2) can be calculated within the Dirac theory. The frequency markers of the FPI allow the accurate determination of the hfs splitting of the 15 state and the isotope shift Avis( H- H) between the 1S-2S transitions of hydrogen and deuterium (Fig. 2.38). 

The low translational temperature achieved in supersonic beams allows the generation and observation of loosely bound van der Waals complexes and clusters (Sect. 4.3). The collision-free conditions in molecular beams after their expansion into a vacuum chamber facilitates saturation of absorbing levels, since no collisions refill a level depleted by optical pumping. This makes Doppler-free saturation spectroscopy feasible even at low cw laser intensities (Sect. 4.4). 

Additionally, several experiments on saturation spectroscopy of molecules and radicals in molecular beams have been reported [454, 455] where finer details of congested moleeular speetra, sueh as hyperfine structure or A-doubling can be resolved. Another alternative is Doppler-free two-photon spectroscopy in molecular beams, where high-lying molecular levels with the same parity as the absorbing ground state levels are aeeessible [456]. 

Fortunately, several methods have been developed that overcome these difficulties and that allow ultranarrow Ramsey resonances to be obtained. One of these methods is based on Doppler-free two-photon spectroscopy, while another technique uses saturation spectroscopy but introduces a third interaction zone at the distance z = 2L downstream from the first zone to recover the Ramsey fringes [1257-1259]. We briefly discuss both methods. 

Figure 3 Spectral separation of two Doppler-broadened profiles by saturation spectroscopy (A) profiles of Doppler-broadened absorption lines with Lamb dips (B) observed Doppler-free profiles (cross-over signals omitted).

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. 

If the discharge cell has windows of optical quality, it can be placed inside the laser resonator to take advantage of the -fold laser intensity (Sect. 6.2.2). With such an intracavity arrangement. Doppler-free saturation spectroscopy can also be performed with the optogalvanic technique (Sect. 7.2 and [6.101]). An increased sensitivity can be achieved by optogalvanic spectroscopy in thermionic diodes under space-charge-limited conditions (Sect. 6.4.5). Here... 

A further method of monitoring Doppler-free signals using transmitted beams is also possible. In this technique (saturated interference spectroscopy) [9.175,176], the change in refractive index for the atoms at the "hole" position is used to influence the light interference condition in a two-beam interferometer. If the set-up is initially adjusted for destructive interference an increase in light intensity will be observed at the line centre. 

Returning to the field of saturation spectroscopy we note, that it is also possible to observe Doppler-free saturation signals in cell experiments without detecting the intensities of the transmitted beams. Fluorescence, opto-galvanic and opto-acoustic detection can all be used. However, since the... 

The laser control of the velocity distribution of atoms or molecules at particular quantum levels that emerged in the course of development of saturation spectroscopy free of Doppler broadening (Lamb 1964) is fairly close to the ideas considered in this book. I myself started to work on the problem of laser elimination of Doppler broadening as far back as 1965 and gradually progressed to ideas of laser confinement of atomic motion within a volume of about A . Therefore, I have decided to include a brief description of the ideas of laser velocity-selective control of atoms and molecules. 

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. 

In the same period, it was understood that the trapping of atoms by laser light might give birth to what is now called particle-trapping spectroscopy (Letokhov 19756). This would be an important supplement to the Doppler-free laser spectroscopy techniques developed earlier, namely standing-wave absorption saturation spectroscopy... 

Fig. 5.3 Three methods of Doppler-free optical spectroscopy, which differ in the contribution of the transit-time broadening Autr- (a) saturation spectroscopy in a standing wave (b) two-photon spectroscopy in a standing wave (c) particle trapping in a 3D standing wave. (Prom Letokhov 19756.)...

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