Spectroscopy level crossing

Level-crossing spectroscopy is based on the measured change in the spatial intensity distribution or the polarization characteristics of fluorescence that is emitted from coherently excited levels when these levels cross under the influence of external magnetic or electric fields. Examples are fine or hyperfine levels with different Zeeman shifts, which may cross at a certain value Be of the magnetic field B (Fig. 12.1). A special case of level crossing is the 

Level-crossing spectroscopy is based on the measured change in the spatial intensity distribution or the polarization characteristics of fluorescence that is emitted from 

A typical experimental arrangement for level-crossing spectroscopy is depicted in Fig. 12.2. Atoms or molecules in a homogeneous magnetic field B = 0,0,Bj are excited by the polarized optical wave E = EyCos(wt-kx) and tuned to the transition l) — 2). The fluorescence Ipi(B) emitted from the excited level 2) into the y direction is observed behind a polarizer as a function of the magnetic field B. 

In a classical, vivid description the excited atom is represented by a damped oscillator, that oscillates in the y direction with a spatial emission charactistics I(t ) a sin t depending on the angle against the dipole axis. (Fig.l2.3a). If the atom with an excited-state lifetime = I/72 is excited at t = to by a short laser pulse, the amplitude of the emitted radiation is for B = 0  

With the angular momentum J in level 2) the atomic dipole with the magnetic dipole moment = gjHo (Sj- Lande factor /uq Bohr s magneton) will process for B 0 around the z-axis with the precession frequency 

Together with the dipole axis also the direction of maximum emission, which is perpendicular to the dipole axis, process with tip around the z-axis while the amplitude of the dipole oscillation decreases as exp[-(7/2)t] (Fig.l2,3b). If the fluorescence is observed behind a polarizer with the transmission axis tilted by the angle a against the x-axis, the measured intensity Ipj(t) becomes 

Let us consider two magnetic sublevels belonging to an excited state of lifetime r. Li a particular field Bq the two levels cross. We also consider two sublevels belonging to the ground state. In Fig. 7.13 we assume that the magnetic quantum nmnbers M are 1 and 3 in the excited state and 2 and 3 in the ground state. 

The complete theory of resonance scattering is given by Breit [7.33] and Pranken [7.34]. The Breit formula from 1933 gives the mtensity S of emitted photons with polarization vector eg obtained after absorption of photons 

If the excited state has magnetic sublevels with indices M and M and the ground state has sublevels with indices ijl, and fj/, the Breit formula can be written 

Since tlie order of summation is immaterial we can write 

Because of the selection rule AM = 0, 1 we find that only for 

The atoms are irradiated with light that is polarized at right angles to the external magnetic field. Such light will induce and a transitions 

Because of the selection rule AM = 0, 1 we find that Kj 0 only for M-M = 0, 1 or 2. For M-M = 0 a level crossing cannot occur because of the non-crossing rule. Instead a related phenomenon, anti-crossing can be observed under certain circumstances [7.29]. For the arrangement shown in Fig.7.13 it can be shown that Kj = 0 for M-M = 1. If we now consider the special case where the sublevels of the excited state are linear Zeeman levels we have Ij m m I = 2/iggB/h for M-M = 2 yielding 

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Polik W F, Guyer D R and Moore C B 1990 Stark level-crossing spectroscopy of Sq formaldehyde eigenstates at the dissociation threshold J. Chem. Phys. 92 3453-70... 

Level crossing spectroscopy has been used by Fredriksson and Svanberg44 to measure the fine structure intervals of several alkali atoms. Level crossing spectroscopy, the Hanle effect, and quantum beat spectroscopy are intimately related. In the above description of quantum beat spectroscopy we implicitly assumed the beat frequency to be high compared to the radiative decay rate T. We show schematically in Fig. 16.11(a) the fluorescent beat signals obtained by... 

Dohnt, G., Hese, A., Renn, A. and Schweda, H.S. (1979). Molecular electric field level crossing spectroscopy The dipole moment in the A1E+ state of BaO, Chem. Phys., 42, 183-190. 

Moruzzi, G. and Strumia F. (1991). Hanle Effect and Level-Crossing Spectroscopy (Plenum Press, New York, London). 

Zare, R.N. (1966). Molecular level-crossing spectroscopy, J. Chem. 

Fig. 7.2 Level-crossing spectroscopy (a) experimental arrangement (b) level scheme and (c) Hanle signal...

The quantum-mechanical treatment of level-crossing spectroscopy [834,837] starts with the Breit formula... 

In Fig. 7.6 the level scheme of the hyperfine levels in the 5P3/2 level of the Rubidium atom is shown with level crossings at B = 0 and B 0. Therefore level crossing spectroscopy of the Rb-atom will give several signals at different magnetic fields B. 

Level-crossing spectroscopy was used in atomic physics even before the invention of lasers [831, 842-844]. These investigations were, however, restricted to atomic resonance transitions that could be excited with intense hollow-cathode or microwave atomic-resonance lamps. Only a very few molecules have been studied, where accidental coincidences between atomic resonance lines and molecular transitions were utilized [836]. 

Optical pumping with tunable lasers or even with one of the various lines of fixed-frequency lasers has largely increased the application possibilities of level-crossing spectroscopy to the investigation of molecules and complex atoms. Because of the... 

Level-crossing spectroscopy with lasers has some definite experimental advantages. Compared with other Doppler-free techniques it demands a relatively simple experimental arrangement. Neither single-mode lasers and frequency-stabilization techniques nor collimated molecular beams are required. The experiments can be performed in simple vapor cells, and the experimental expenditure is modest. In many cases no monochromator is needed since sufficient selectivity in the excitation process can be achieved to avoid simultaneous excitation of different molecular levels with a resulting overlap of several level-crossing signals. 

There are, of course, also some disadvantages. One major problem is the change of the absorption profile with the magnetic field. The laser bandwidth must be sufficiently large in order to assure that all Zeeman components can absorb the radiation independent of the field strength B. On the other hand, the laser bandwidth should not be too large, to avoid simultaneous excitation of different, closely-spaced transitions. This problem arises particularly in molecular level-crossing spectroscopy, where several molecular lines often overlap within their Doppler widths. In such... 

A large number of atoms and molecules have been investigated by level-crossing spectroscopy using laser excitation. A compilation of the measurements up to 1975 can be found in the review of Walther [846], up to 1990 in [847], and up to 1997 in [848]. 

The iodine molecule has been very thoroughly studied with electric and magnetic level-crossing spectroscopy. The hyperfine structure of the rotational levels affects the profile of the level-crossing curves [849]. A computer fit to the non-Lorentzian superposition of all Hanle curves from the different hfs levels allows simultaneous determination of the Landd factor g and the lifetime t [850]. Because of different predissociation rates the effective lifetimes of different hfs levels differ considerably. 

So far we have considered level crossing monitored through spontaneous emission. A level-crossing resonance can also manifest itself as a change in absorption of an intense monochromatic wave tuned to the molecular transition when the absorbing levels cross under the influence of external fields. The physical origin of this stimulated level-crossing spectroscopy is based on saturation effects and may be illustrated by a simple example [845]. 

Fig. 7.7 Stimulated level-crossing spectroscopy with a common lower level (a) level scheme and (b) saturation holes in the Doppler-broadened population distribution with and without magnetic field...

J. Alnis et al.. The Hanle effect and level crossing spectroscopy in Rb-vapour under strong laser excitation. J. Phys. B, At. Mol. Opt. Phys. 36, 1161 (2003)... 

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