Ramsey interference fringes

In Equation 15.23, we found an expression for the lineshape using two short tt/2-pulses separated by a time T. In order to pick out the Ramsey interference, we suggested introducing a phase shift ([) between the first and second pulse and taking the difference between ( ) = n and ([) = 0. This is expected to give fringes of the... 

M.M. Salour, C. Cohen-Tannoudji Observation of Ramsey s interference fringes in the profile of Doppler-free two-photon resonances. Phys. Rev. Lett. 38, 757 (1977)... 

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]. 

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... 

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. ... 

However, by applying a further pulse at a delay T, a sharp interference pattern in the two-photon signal can be obtained. It is important that the signal is Doppler-free so that the phase memory from the first pulse is not lost through the velocity spread. Ordinary signals and Ramsey fringes for the two-photon transitions 3s 4d 3/2,5/2 Na are shown in... 

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