Hanle effects

Magnetics depolarization of resonance radiation - the Hanle effect 

Historical introduction. In one of the earliest investigations of resonance fluorescence. Lord Rayleigh (1922) showed that the radiation scattered from mercury vapour was polarized when the atoms were excited by polarized light. 

Soon afterwards Wood and Ellet (1924) showed that the polarization of the fluorescent light was destroyed by applying small magnetic fields to the resonance cell. Further experimental studies of this effect were made by Hanle (1924), who also worked out a classical theory describing the influence of the magnetic field on the polarization of the 

The fluorescent light emitted in a direction at right-angles to the direction of the incident radiation is collected 

The excitation process is treated by assuming that the electron in one of the atoms receives an impulse at the moment of excitation, t, which starts it oscillating in a direction specified by the polarization vector of the incident radiation. This simple representation of the excitation process is valid provided that the width of the resonance line emitted by the lamp is very broad in comparison with both the natural linewidth and the Zeeman splitting of the atoms in the resonance cell. The excited electron, oscillating at the angular frequency, ioq, now radiates in the usual dipole distribution pattern producing an electric field at a point on the axis of observation given by 

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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... 

Let us now turn to molecules. In 1966 Zare [399] was the first to treat in detail the problem of applying magnetic level crossing to molecular objects. He used both the classical and quantum mechanical approachs. Three years later he and his collaborators obtained the first experimental results on the Hanle effect with Na2(H1nu) [290], OH(A2 +) [165]. Among the works performed through 1969-1970 one may mention the... 

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... 

Note that the superpositional Hanle signal, reflecting overlapping of effects from both levels, coupled with optical excitation, is sensitive to the signs of the Lande factors gj> and gj even with Lorentzian geometry, where

linear Hanle effect. This is easily understood, since there is a large difference between the cases... 

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 ... 

The first term in curly brackets does not depend on t and represents the usual Hanle effect. The second term oscillates at modulation frequency fii, with the modulation amplitude growing in resonance fashion if Qojj> = fii holds (see Fig. 4.22). For u>j> T, when degeneracy is completely removed, we may write in the vicinity of resonance for Q > 0 ... 

Let us assume the geometry of excitation and observation (see Fig. 5.1) as being similar to that used in the registration of traditional Hanle effect signals (Chapter 4). Substituting into Eq. (5.10) the cyclic components Eq for the E-vector of the exciting light (see (A.4)) we obtain expressions for the non-zero elements /mm of the density matrix of the excited state J ... 

Fig. 5.1. Hanle effect analogue in the case of the quadratic Stark effect.

This peculiarity in the behavior of polarization of radiation under the electric field effect ought to be easily understood from an analysis of Eq. (5.14). As can be seen, the intensities of the two fluorescence components differ in the sign of the second term, which is proportional to (T2 + w+i)-1- the case of the Hanle effect at increase in magnetic field strength all increase, and the second term becomes... 

Linear approximation excited state Hanle effect... 

The result obtained reflects linear approximation, i.e. manifestation of the usual linear (observable signal is proportional to Tp) Hanle effect (Section 4.2). This contention becomes obvious if we substitute the polarization moments obtained into the expression for fluorescence intensity (5.34) and find the form of the degree of polarization V = (Iy — Ix)/(Iy + Ix) (Fig. 5.8). For instance, for a radiative transition (J = 1) -> (J" = 1), and using Table C.3 for numerical values of 6j-symbols and for values of from Table 2.1, we obtain... 

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

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