Nonlinear Ramsey Fringes Using Three Separated Fields

3 Nonlinear Ramsey Fringes Using Three Separated Fields 

The macroscopic polarization at (L,X2), which equals the vector sum of all induced atomic dipoles, averages to zero because molecules with different ve- 

The detailed calculation, using third-order perturbation theory [14.103,14.109], demonstrates that the power absorbed in the third field zone leads to the signal 

Adjusting the phases cpn properly, such that 2cp2 = (pi +(P3, allows optimization of the signal in the third zone. A detailed calculation of nonlinear Ramsey resonances, based on the density matrix formalism, has been performed by Borde [14.110]. 

The capability of this combination of saturation spectroscopy with optical Ramsey fringes has been demonstrated by Bergquist et al. [14.111] for the example of the neon transition Iss - 2p2 at = 588.2 nm (Fig. 14.42). A linewidth of 4.3 MHz for the Lamb dip has been achieved with the distance L = 0.5 cm between the interaction zones. This corresponds to the natural linewidth of the neon transition. 

Another solution to restore the Ramsey fringes, which are generally washed out in the second field, is based on the introduction of a third field at the distance 2L downstream from the first field. The idea of this arrangement was first pointed out by Chebotayev and coworkers [1257]. The basic idea may be understood as follows In Sect. 2.2 it was discussed in detail that the nonlinear absorption of a molecule in 

The macroscopic polarization at (L, 2), which equals the vector sum of all induced atomic dipoles, averages to zero because molecules with different velocity components Vx arrive at X2 from different points (0, x ). Note, however, that the population depletion AA a in the second field depends on the relative phase A p and therefore on Vx. If the phases p(xi) and (p(x2) of the two fields are made equal for x = X2, the phase difference (p(x ) — (p(x2) = (p(x — X2) = (p(Vx T) between the two fields at the intersection points depends only on Vx and not on xi. After the nonlinear interaction with the second field the number n(Vx) of molecular dipoles shows a characteristic modulation (Fig. 9.60b). This modulation cannot be detected in the second field because it appears in Vx but not in x. For the interaction of all molecules with the 

With 4 interaction zones the contrast of the Ramsey resonances can still be increased [14.91]. This was also demonstrated by Borde and coworkers [14.92] who used 4 travelling waves instead of 3 standing waves which crossed a supersonic molecular beam of SFg perpendicularly. The Ramsey signal for vibration-rotation transitions in SFg around A = 10 pm was monitored with improved constrast by an optothermal detector (Sect.6.3.3). 

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