Ground state Hanle effect

Due to the fact that the effect of a magnetic field on the ground state angular momenta distribution pa(0, ip) causes changes in the excited state distribution pb(9,(p) (see Figs. 4.9 and 4.10), one may expect to observe the ground state Hanle effect in fluorescence intensity difference I — I or in the degree of polarization V B). Indeed, since we have gj"/yK 2>... 

Fig. 4.11. Hanle effect on the degree of linear polarization V = (/y — Iff/(I + Iff) at (P, f )-excitation 1 - superpositional signal calculated at the same conditions as Fig. 4.10, dots refer to the positions a, b, c, d as in Fig. 4.10 2 - pure excited state signal at x = 0 3 - pure ground state signal at gj> = 0 4 - experimentally measured dependence for Te2 under conditions as given in Fig. 4.6, curve 1, but in the region of weaker magnetic field and at strong pumping (x 3).

Fig. 4.11 reflects a superpositional Hanle effect from both the ground (initial) and excited states. To demonstrate this in Fig. 4.11 we depict the pure ground state effect (supposing gj> = 0) (see curve 3), as well as the pure excited state effect (supposing = 0) (see curve 2). In this favorable situation both effects are well distinguished in the observable superpositional signal. 

The superpositional Hanle effect may lead to some, at first glance, unexpected peculiarities. Firstly we wish to draw attention to one interesting fact [17] under conditions where the effect has already developed from the ground state (ujj"/jk S> 1), but that from the excited state... 

Fig. 4.12. Experimental signal (dots) showing additional structure of the nonlinear ground state Hanle effect for K2. The solid line is the result of approximation at 7 = 0.35 106 s-1, rp = 2.4 106 s 1, the other data are taken from Tables 3.7 and 4.2. The broken line is calculated for the same parameters, but with gjn and gj> of equal sign.

Curves 2 (Ei E) and 5 (Ei L E) in Fig. 4.15 refer to the uoj Jj/T 1 scale, in which the excited state Hanle effect manifests itself (the ground state Hanle effect is already fully developed and does not manifest itself in this scale). The signal is of Lorentz shape ... 

Examples of handling the equations of motion 2 Ground state Hanle effect... 

This leads to the manifestation of the non-linear Hanle effect in the ground state (the observed signal is proportional to T2). The non-linearity of the effect is not obvious in this case and consists of the following fact. Despite the fact that the approximation (5.63), (5.64), (5.65) and (5.66) is linear with respect to the light field (proportional to Tp), it is necessary for observation of the Hanle signal (5.61) to calculate the second (2) (i)... 

As can be seen, the signal (5.61) also reflects the ground state Hanle effect signal which is proportional to T2 as it must be in the second-order approximation. It may be of interest that we do not find any terms containing in f 2. This peculiarity is due to the zero value of the... 

Fig. 5.9. Ground state Hanle effect in molecules for the transition (J" — 1)...

Auzinsh, M.P. and Ferber, R.S. (1983). Manifestation of the sixth-order polarization moment in the Hanle-effect signal of the electronic ground state of dimers, Opt. Spectrosc. (USSR), 55, 674-675. 

Ferber, R.S., Shmit, O.A. and Tamanis, M.Ya. (1978). Ground state Hanle effect in optically aligned diatomic molecules, Abstr. VI Intern. Conf. Atomic Physics, Zinatne, Plenum Press, Riga, New York,... 

Next we proceed to develop the theory o resonance fluorescence experiments using the ensemble density matrix to describe the system of atoms. The important concepts of optical and radio-frequency coherence and of the interference of atomic states are discussed in detail. As an illustration of this theory general expressions describing the Hanle effect experiments are obtained. These are evaluated in detail for the frequently employed example of atoms whose angular momentum quantum numbers in the ground and excited levels are J =0 and Jg=l respectively. Finally resonance fluorescence experiments using pulsed or modulated excitation are described. 

It is difficult to apply the Hanle effect to levels above the resonance level using optical excitation from the ground state because of the low oscillator strength and short wavelength of many of the absorption lines. Thus in an effort to extend the number of accessible levels several investigators have used electron impact excitation. 

The polarization of the fluorescent light. The Hanle effect signal is usually obtained by measuring the intensity of the fluorescent light with polarization vector d emitted in some well-defined direction r. From equations (2.70) and (5.8) it can be shown (Problem 15.4) that the intensity of light with this polarization emitted when an excited atom in the sub-state m> decays to the ground-state sub-level y > is... 

We see that field-dependent terms appear in the denominator of equation (15.27) when m m, i.e. the Hanle effect signal is a direct result of the Hertzian coherence created in the excited state by excitation with coherently polarized light. We can describe the phenomenon as the result of a quantum-mechanical interference between the scattering amplitudes for the two possible routes from the initial ground level sub-state y > to the final sub-state... 

These experiments are in fact entirely analagous to the Hanle effect or zero-field level-crossing experiments involving excited atoms discussed in Chapter 15. The coherent polarization of the pumping light referred to the quantization axis Oz in Fig.17.12 prepares the atoms in a coherent superposition of ground-state Zeeman sub-levels. The ensemble density matrix now has finite off-diagonal elements... 

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