Ramsey fringe method

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]. 

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. 

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. 

Silverans et studied interference effects between ground (or metastable) and excited states in a setup that is analogous to Ramsey s separated microwave field method. In comparison with other optical experiments, the interference conditions are easy to establish with fast ion beams, and the observed fringes are consistent with a Fourier analysis of the evolution in time of the laser frequency probed by the ions. ... 

---