Ramsey fringes

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

Figure 22. Ramsey fringes showing dephasing for two densities (a) 7.6 and (b) 1.9 x 109 cm-3.

One of the most important yet simple ideas that ignited excitement about fem-tochemistry is wavepacket interferometry (Salour and Cohen-Tannoudji, 1977 Scherer, et al., 1990, 1991, 1992 Jonas and Fleming, 1995 Weinacht, et al., 1999), an optical form of Ramsey-fringe spectroscopy (Ramsey, 1990). A molecular system is subjected to two identical optical pulses created by splitting one pulse at a beam splitter. The two pulses are called the pump and the probe . The time delay between pump and probe pulses is scanned systematically using an optical delay line. The optical arrangement is very similar to that of a Fourier Transform Spectrometer (Heller, 1990). The difference in the paths traveled by the pump and probe pulses, Ad, before the two pulses are recombined at a second beam splitter corresponds to a time delay, At = Ad/c, where c is the speed of light. 

Figure 6.10 shows the time-of-flight resonance spectrum with the typical Ramsey fringe pattern fitted with the Kretzschmar algorithm for a three-pulse excitation. 

Some techniques of laser spectroscopy, such as the method of separated fields optical Ramsey fringes. Sect. 9.4), coherent transient spectroscopy (Sect. 7.6), or polarization spectroscopy (Sect. 2.4) allow one to distinguish between phasechanging, velocity-changing, or orientation-changing collisions. 

Fig. 9.54 Signal power absorbed by the molecules in the second field as a function of detuning Q =(o — coq (Ramsey fringes) for a narrow velocity distribution N(v)...

Measured as a function of the field frequency co, this signal exhibits an oscillatory pattern called Ramsey fringes (Fig. 9.54). The full halfwidth of the central fringe, which is 8oo = 7r(n/L), decreases with increasing separation L between the fields. 

A similar situation is observed for the Ramsey fringes. Since the velocities of the molecules in the molecular beam are not equal but follow a Maxwellian distribution, the phase differences (coq — co)Llv show a corresponding distribution. The interference pattern is obtained by integrating the contributions to the signal from all molecules N(v) with the velocity v... 

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. 

Fig. 9.57 Experimental arrangement for the observation of two-photon Ramsey fringes [1261]...

Nonlinear Ramsey Fringes Using Three Separated Fields... 

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 capability of this combination of saturation spectroscopy with optical Ramsey fringes has been demonstrated by Bergquist et al. [1265] for the example of the neon transition Iss 2p2 atk = 588.2 nm (Fig. 9.61). A linewidth of 4.3 MHz for... 

Fig. 9.65 Optical two-photon Ramsey fringes with multiple light pulses (pulse repetition rate 50 kHz) [1270]...

Because of the small velocity the time difference Ar = 2vo/g is very long. According to Eq. (9.57) the spectral width An of the central Ramsey fringe is accordingly small. 

C. J. Borde, Density matrix equations and diagrams for high resolution nonlinear laser spectroscopy application to Ramsey fringes in the optical domain, in Advances in Laser Spectroscopy, ed. by F.T. Atrecchi, F. Strumia, H. Walther (Plenum, New York, 1983), p. 1... 

J. Helmcke, D. ZevgoUs, B.U. Yen, Observation of high contrast ultra narrow optictil Ramsey fringes in saturated absorption utilizing four interaction zones of travelling waves. Appl. Phys. B 28, 83 (1982)... 

C.J. Borde, C. Salomon, S.A. AvriUier, A. Van Lerbeighe, C. Breant, D. Bassi, G. Scoles, Optical Ramsey fringes with travelling waves. Phys. Rev. A 30,1836 (1984)... 

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