Hanle effect excited state

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... 

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 ... 

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 ... 

Linear approximation excited state Hanle effect... 

Auzinsh, M.P., Tamanis, M.Ya. and Ferber, R.S. (1987). Determination of the sign of the Lande factor of diatomic molecules in the ground and excited states by the Hanle effect, Opt. Spectrosc. (USSR), 63, 582-588. 

From the measured halfwidth AB /2 the product gjTeff of Lande factor g/ of the excited level 2) times its effective lifetime teff can be derived. For atomic states the Lande factor gj is generally known, and the measured value of A i/2 determines the lifetime teff. Measurements of teff (p) as a function of pressure in the sample cell then yield by extrapolation p 0 the radiative lifetime (Sect. 6.3). The Hanle effect therefore offers, like other Doppler-free techniques, an alternative method for the measurement of atomic lifetimes from the width AB /2 of the signal [832]. 

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 excited-state density matrix. We now apply the general formalism developed in the previous paragraphs to the particular case of the Hanle effect. In these experiments the excited atoms are subjected to a static external magnetic field B whose direction is chosen as the axis of quantization. In the absence of hyperfine structure the time-independent Hamiltonian for the system becomes... 

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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