Classical Model of the Hanle Effect

A typical experimental arrangement for level-crossing spectroscopy is depicted in Fig. 12. Atoms or molecules in a homogeneous magnetic field B = 0,0, B are excited by the polarized optical wave E = Ey cos(cot — kx) and tuned to the transi- 

In a classical, vivid description, the excited atom is represented by a damped oscillator that oscillates in the y-direction with a spatial emission characteristics 7( 7) a sin depending on the angle between observation direction and dipole axis (Fig. 7.3a). If the atom with an excited-state lifetime t2 = 1//2 is excited at t = toby 2L 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 IjL = gjfjio (gj Lande factor /xq- Bohr s magneton) will process for B 0 around the z-axis with the precession frequency 

Together with the dipole axis the direction of maximum emission, which is perpendicular to the dipole axis, also processes with 2p around the z-axis while the amplitude of the dipole oscillation decreases as exp[—(y /2)t] (Fig. 7.3b). If the fluorescence is observed in the y-direction (Fig. 7.2a) behind a polarizer with the transmission axis tilted by the angle a against the v-axis, the measured intensity /fi(0 becomes 

This intensity can either be monitored in a time-resolved fashion after pulsed excitation in the constant magnetic field B quantum beats, Sect. 7.2), or the time-integrated fluorescence intensity is measured as a function of B (level crossing), where the excitation may be pulsed or cw. 

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