Israel Journal of Chemistry Vol. 47 2007 pp. 67–73 *Author to whom correspondence should be addressed. E-mail: jg.muga@ehu.es Quantum Motion Effects in Atom Interferometry DIrk SEIDEl AnD J. GonzAlo MuGA* Departamento de Química-Física, universidad del País Vasco, Apartado Postal 644, 48080 Bilbao, Spain (Received 29 September 2006) Abstract. We study the ramsey interference pattern of ultracold atoms crossing two electromagnetic felds, taking into account quantum motion effects. It is shown that quantum refection and transmission at the felds lead to a modifcation of the standard fringes. The implications on present frequency standards are discussed. For weak coupling, the difference between the exact quantum result and the semiclas- sical result is small but results in a central peak shift that may become important for future accuracies of atomic clocks. In the strong coupling regime, a resonance structure with respect to the detuning is observed and the ramsey setup acts as a matter–wave Fabry–Perot device. Our results question the advantage of using increasingly lower velocities in frequency standards because the peak shift and the resonance positions depend sensitively on very minor variations of the atomic veloc- ity and are diffcult to control. IntroductIon Matter–wave interferometry with separated oscilla- tory felds, as proposed by Ramsey, 1 has contributed to enormous progress in high-precision metrology and frequency standards. After the frst experimental dem- onstration by Essen and Parry, 2 intense research in na- tional laboratories led to a new defnition of the unit of time in terms of the hyperfne frequency of Cs in 1967 3 and to modern atomic clocks with fractional uncertain- ties of the order of 10 –16 . 4 Also, development in industry resulted in many advanced applications, such as time- keeping, digital communication, positioning, geodesy, and navigation systems (GPS, Glonass, Loran C, or Galileo). reviews on the numerous present implemen- tations of ramsey interferometry, such as cesium beam standards, atomic fountains, optical clocks, etc., can be found in refs 5 and 6. A basic feature of the observed interference fringes in a standard Ramsey experiment is that their width is determined by the inverse of the time taken by the atoms to cross the intermediate drift region. For precision mea- surement purposes, as in atomic clocks, this motivates the use of very slow (ultracold) atoms and therefore the development of laser cooling techniques has changed the entire prospect of frequency standards. 7 Experimen- tally, atomic velocities of the order of 1 cm/s can be achieved, and space-based clocks are in development to eliminate gravitational effects in the motion of such slow particles. 8 However, if the kinetic energy becomes comparable with the atom–feld interaction energy, one has to take into account the quantized center-of-mass motion of the atom and the well-known semiclassical