Nutation and free induction decay

Other coherent interactions include optical nutation and free induction decay, in which the population oscillates be-... 

The difference between optical nutation and free induction decay should be clear. While the optical nutation occurs at the Rabi frequency which depends on the product of laser field intensity and transition moment, the free induction decay is monitored as a heterodyne signal at the beat frequency 0) 2 which depends on the Stark shift. The importance of these coherent transient phenomena for time-resolved sub-Doppler spectroscopy is discussed in the next section. Its application to the study of collision processes is treated in Chap.12. For more detailed information the excellent reviews of BREWER [11.43,48] are recommended. 

E. Optical Free Induction Decay and Optical Nutation in a Multilevel System.. 481... 

Selective excitation was accomplished by using a delays alternating with nutations for tailored excitation (DANTE) sequence of 20 short rf pulses of x =0.6 is duration [4]. The pulse separation used was 20 ps resulting in the total duration of the DANTE sequence of x,=400 [iS and the corresponding spectral excitation width A of the center band of 2.5 kHz. The excitation sidebands were separated from the centerband by (Xp) = 50 kHz and did not affect the NMR spectrum. After a recovery period,x of at least 35 ps a final 90° pulse was applied followed by the detection of the free induction decay. 

Fig. 7.24 (a) Optical nutation in CH3p observed with CO2 laser excitation at A = 9.7 pm. The Rabi oscillations appear because the Stark pulse lower trace) is longer than in Fig. 7.23. (b) Optical free-induction decay in I2 vapor following resonant excitation with a cw dye laser at = 589.6 nm. At the time = 0 the laser is frequency-shifted with the arrangement depicted in Fig. 7.22 by Au = 54 MHz out of resonance with the I2 transition. The slowly varying envelope is caused by a superposition with the optical nutation of molecules in the velocity group Vz = o) — (oo)/k, which are now in resonance with the laser frequency oj. Note the difference in time scales of (a) and (b) [705]... 

In the case of coherent laser light, the pulses are characterized by well-defined phase relationships and slowly varying amplitudes (Haken, 1970). Such quasi-classical light pulses have spectral and temporal distributions that are also strictly related by a Fourier transformation, and are hence usually refered to as Fourier-transform-limited. They are required in the typical experiments of coherent optical spectroscopy, such as optical nutation, free induction decay, or photon echoes (Brewer, 1977). Here, the theoretical treatments generally adopt a semiclassical procedure, using a density matrix or Bloch formalism to describe the molecular system subject to a pulsed or continuous classical optical field, which generates a macroscopic sample polarization. In principle, a fully quantal description is possible if one represents the state of the field by the coherent or quasi-classical state vectors (Glauber, 1965 Freed and Villaeys, 1978). For our purpose, however. 

This optical induction free decay can be measured with a beat technique at time r = 0 the frequency cu of a cw laser is switched from co = con to aJ o) 2 out of resonance with the molecules. The superposition of the damped wave at o) 2 emitted by the coherently prepared molecules with the wave at co gives a beat signal at the difference frequency Aco = co 2— o), which is detected [12.70]. If Aco is smaller than the Doppler width, the laser at cu interacts with another velocity subgroup of molecules and produces optical nutation, which superimposes the free-induction decay and which is responsible for the slowly varying envelope in Fig. 12.21b. 

In case the effective laser linewidth is less than the hyperfine splitting(s) excitation will prepare a two-level system. The effect of spin-flips on the coherence in this system will then manifest itself as a 7 ,-type process. No beats are expected in the decay of the optical free induction. With broadband excitation that spans some of the hyperfine splittings spin-flips will be monitored as 7 2-type processes and quantum beats are expected in the photon-echo intensity vs probe delay. Burland et al. also demonstrated the feasibility of optical nutation in this system from which in principle, as from the OFID, the transition dipole could be calculated. 

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