Ramsey resonances

Fortunately, several methods have been developed that overcome these difficulties and that allow ultranarrow Ramsey resonances to be obtained. One of these methods is based on Doppler-free two-photon spectroscopy, while another technique uses saturation spectroscopy but introduces a third interaction zone at the distance z = 2L downstream from the first zone to recover the Ramsey fringes [1257-1259]. We briefly discuss both methods. 

The first two terms describe the conventional two-photon transitions in the first and second zones, while the third term represents the interference leading to the Ramsey resonance. Due to the longitudinal thermal velocity distribution /(u ), only the central maximum of the Ramsey resonance is observed with a theoretical halfwidth (for negligible natural width) of... 

The achievable spectral resolution is demonstrated by Fig. 9.58, which shows a two-photon Ramsey resonance for a hyperfine component of the two-photon Ryd-... 

The quantitative description of the two-photon Ramsey resonance [1262] starts from the transition amplitude per second... 

Fig. 9.61 Lamb dip of nonlinear Ramsey resonance for the neon transition Iss 2p2 at X = 588.2 nm, measured in a fast beam of metastable neon atoms (a) reduced Doppler profile in the collimated beam with the Lamb dip obtained with three laser beams (b)-(d) expanded section of the Lamb dip for three different beam geometries the atom interacts only with two standing waves (b), three equally spaced interaction zones (c), and four zones (d) [1265]...

Adjusting the phases (pn 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 [1264]. 

With four interaction zones the contrast of the Ramsey resonances can still be increased [1266]. This was also demonstrated by Borde and coworkers [1267], who used four traveling waves instead of three standing waves, which crossed a supersonic molecular beam of SFe perpendicularly. The Ramsey signal for vibration-rotation transitions in SFg around k = 10 pm was monitored with improved contrast by an optothermal detector (Sect. 1.3.3). 

For transitions with small natural linewidths the Ramsey resonances can be extremely narrow. For instance, the nonlinear Ramsey technique applied to the resolution of rotational-vibrational transitions in CH4 in a methane cell at 2 mbar pressure yielded a resonance width of 35 kHz for the separation L = 7 mm of the laser beams. With the distance L = 3.5 cm the resonance width decreased to 2.5 kHz, and the Ramsey resonances of the well-resolved hyperflne components of the CH4 transition at k = 3.39 pm could be measured [1263]. 

It is also possible to observe the Ramsey resonances at z = 2L without the third laser beam. If two standing waves at z = 0 and z = L resonantly interact with the molecules, we have a situation similar to that for photon echoes. The molecules that are coherently excited during the transit time t through the first field suffer a phase jump at r = T in the second zone, because of their nonlinear interaction with the second laser beam, which reverses the time development of the phases of the oscillating dipoles. At r = 2T the dipoles are again in phase and emit coherent radiation with increased intensity for co = a>ik (photon echo) [1258,1263]. 

Fig. 9.62 Ramsey resonances of the calcium intercombination line at X = 657 nm, measured in a collimated Ca atomic beam ...

Optical Ramsey Resonances Obtained Through an Equidistant Train of Laser Pulses... 

Fig. 9.70 Optical Ramsey scheme of an atomic beam passing through four traveling laser fields, interpreted as matter-wave interferometer. Solid lines represent the high-frequency recoil components, dotted lines the low-frequency components (only those traces leading to Ramsey resonances in the fourth zone are drawn) [1290]...

Ramsey s method for the observation of narrow radiofre-guency (rf) resonances is well known from atomic and molecular beam experiments . In this contribution, we demonstrate the occurence of similar Ramsey resonances in an atomic vapor due to collisional velocity diffusion of sublevel coherence within an optical Doppler distribution. This new phenomenon is observed using coherent resonance Raman processes to optically induce and detect Zeeman coherence in the Sm A=570.7 nm J=1-J =0 transition. 

Fig. 14.43a,b. Ramsey resonances of the calcium intercombination line at A. = 657 nm, measured in a collimated Ca atomic beam (a) Doppler profile with a reduced Doppler width and a central Lamb dip, if only one interaction zone is used (b) expanded section of the Lamb dip with the two recoil components observed with three interaction zones with separations L = 3.5 cm and L = 1.7 cm. The dashed curves show results with partial suppression of one recoil component [14.114]... 

Fig. 14.44a-c. Suppression of one recoil component by optical pumping with a second laser (a) experimental setup (b) level scheme and (c) Ramsey resonance of the remaining recoil component [14.115]... 

Y.V. Baklanov, B.Y. Dubetsky, V.R. Chebotayev Nonlinear Ramsey resonance in the optical region. Appl. Rhys. 9, 171 (1976)... 

Clairon A, Salomon C, GueUati S, PhilUpe WD. (1991) Ramsey resonance in a Zacharias formtain. Europhys. Lett. 16 165-170. 

Baklanov, E. V., Dubetsky, B. Ya., and Chebotayev, V. P. (1976a). Nonlinear Ramsey resonance in the optical range. Applied Physics, 9, 171-173. 

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