Atom interferometry

The Talbot effect plays an important role in atomic interferometry (see Section 7.5). Also, this effect provides an excellent example of near-field atom optics because selfimaging of the grating take place in the near field, where the curvature of the atom wave fronts must be considered (Fresnel diffraction of atomic waves). 

We know of many types of optical interferometer (the simple double-slit Young interferometer, the Mach-Zehnder interferometer, the Fabry-Perot interferometer, the Talbot interferometer, etc.). A similar situation occurs in atom interferometry. Artificial laboratory devices exploit various types of structure for atom interferometry both material bodies (slits and gratings) and nonmaterial light structures. All these atom interferometers will be considered very briefly we refer readers for details to the book by Berman (1997) and reviews by Baudon et al. (1999), Kasevich (2002), and Chu (2002). 

1 Matter-wave interferometry with material structures 

A simple Young s double-slit atom interferometer was demonstrated by Carnal and Mlynek (1991). This experiment is schematically illustrated in Fig. 7.11. It used a 

The matter-wave interferometry of large molecules is another a very interesting line of research, allowing one to investigate the wave properties of massive particles 

Atomic particles moving with the momentum p can be characterized by their de Broglie wavelength A, = h/p. If beams of such particles can be split into coherent partial beams, which are recombined after traveling different path lengths, matter-wave interferometry becomes possible. This has been demonstrated extensively for electrons and neutrons, and recently also for neutral atoms [1278, 1279]. 

The matter-wave interferometry has already found wide applications for testing basic laws of physics. One advantage of interferometry with massive particles, for instance, is the possibility of studying gravitational effects. Compared to the neutron interferometer the atomic interferometry can provide atomic fluxes which are many orders of magnitude higher than thermalized neutron fluxes from reactors. The sensitivity is therefore higher and the costs are much lower. 

One example for the application is the measurement of the gravitational acceleration g on earth with an accuracy of 3 10 g with a light-pulse atomic interferometer [14.101]. Laser-cooled wave packets of sodium atoms in an atomic fountain (Sect. 14.1.8) are irradiated by a sequence of 3 light pulses with properly chosen intensities. The first pulse is chosen as 7r/2-pulse which creates a superposition of two atomic levels a) and b) and results in a splitting of the atomic fountain beam into two beams due to 

For momentum transfer stimulated Raman transitions between the two hyperfine levels a) and b) of the Na(32Si/2) state are used, which are induced by two laser pulses with light frequencies and 0 2 = hfs) 

Although transit-time broadening is greatly reduced by the Ramsey technique, the quadratic Doppler effect is still present and may prevent the complete resolution of the recoil components. This may cause asymmetric line profiles where the central frequency cannot be determined with the desired accuracy. As was shown by Helmcke et al. [14.115,14.116], one of the recoil components can be eliminated if the upper level Pi of the Ca transition is depopulated by optical pumping with a second laser. In Fig. 14.44 the relevant level scheme, the experimental setup, and the measured central Ramsey maximum of the remaining recoil component is shown. 

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Abstract The techniques of atom cooling combined with the atom interferometry make possible the realization of very sensitive and accurate inertial sensors like gyroscopes or accelerometers. Below earth-base developments, the use of these techniques in space, as proposed in the HYPER project (ass.stud), should provide extremely-high sensitivity for research in fundamental physics. 

Keywords atom interferometry, laser cooling, Raman transition... 

Laser cooling can efficiently reduce the velocity of the atoms but cannot circumvent the acceleration due to gravity. On the ground the 1-g gravity level sets clear limitations to the ultimate sensitivities. The HYPER project (Hyper precision cold atom interferometry in space) will follow precisely this line and will benefit from the space environment, which enables very long interaction time (few seconds) and low spurious vibrational level. The sensitivity of the atomic interferometer can achieve few 10 rad.s. Hz to rotation and to acceleration. This very sensitive and accurate apparatus... 

Atom Interferometry, ed. Paul R. Berman (Aeademic Press, 1997). 

A preliminary result from measurements based on the atom beam interferometry of the Cesium atom has also been reported [37]. The He atom fine structure will become another source of high precision a when the current theoretical work is completed [38,39,40,41,42]. fo js fortunate that so many independent ways are available for obtaining high precision a. Precision of some measurements may exceed 1 in 108 in the near future. Even higher precision might be achieved by techniques based on the atom interferometry [43] and the single electron tunneling [44]. 

In this paper, we propose an experiment to test neutrality of isolated lithium atoms. Atom interferometry has been shown to be the ideal technique to measure weak interactions of an atom with its environment [1,2]. In particular, in 1991, Kasevich and Chu have mentionned the test of neutrality of atoms as a possible utilisation of their atomic interferometer [2], As far as we know, no further details have been published. The experimental set-up we propose is based on a Mach-Zehnder atom interferometer like the ones developped by the research groups of D. Pritchard [3], Siu Au Lee [4], A. Zeilinger [5] and the one under construction in our group [6]. If the same uniform electric field E is applied on both arms of the interferometer, a phase shift of the interferometric signal will appear. This phase shift will be proportional to the residual charge of lithium atom and to the electric field E. 

B. Young, M. Kasevich and S. Chu Precision atom interferometry with light pulses , in Atom Interferometry, edited by P. Berman (Academic Press, 1997), pp. 363-406... 

The phenomenon of atomic state interference has been investigated. The frequency of the (2sjy2 F=0) - (2p F=l) transition in the hydrogen atom has been measured using atomic interferometry. The Lamb shift was found to be 5 = 1057. 8514 ... 

Berman P. R., editor, Atom Interferometry, (Academic Press, New York, 1997). 

Currently, a major theme in atomic, molecular, and optical physics is coherent control of quantum states. This theme is manifested in a number of topics such as atom interferometry, Bose-Einstein condensation and the atom laser, cavity QED, quantum confutation, quantum-state engineering, wavepacket dynamics, and coherent control of chemical reactions. 

The gravitational constant G is from all physical constants the one with the largest experimental uncertainty. Therefore new measuring techniques have been invented to reach a higher accuracy. One of these techniques is based on atom interferometry. Its basic principle can be understood as follows The acceleration of atoms in two clouds in an atomic fountain is measured with stimulated Raman transitions (Fig. 9.71). Two heavy masses at two different positions are added (Fig. 9.72). In the first position one mass was located above the upper atom cloud and the other below the lower cloud. Then the masses were shifted into a position where one mass was below the upper cloud and the other above the lower cloud. The change of the atom acceleration for the two positions were determined [1276]. 

Fig. 10.27 Quantum gravity gradient gravitometer based on atomic interferometry in an atomic fountain [1487]...

Quantum gravity gradiometers based on atomic interferometry provide high sensitivity for the high resolution mapping of mass distribution above and below the surface of the earth (see Sect. 9.1.7). They can be used in the lab as ground-based version or in a satellite as space-born system. They measure differential acceleration with high precision. Their basic principle is shown in Fig. 10.27 [1487]. 

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