Atomic fountains

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. 

The reservoir for the cold atom can be either a magneto-optical trap or a BEC. A short laser pulse with a wavelength tuned to the atomic absorption line travelling into the +z-direction pushes the atoms out of the trap. The recoil momenrnm hvic gives the atoms the initial velocity vo = h- vl mc). 

Example 9.16 The mean velocity of sodium atoms with m =23 AMU at a temperature of T = 10 mK is obtained from mv ll = /2kT as wo = kT= 1.9 m/s — h= 0.18 m. The rise time until the turning point is th = vo/g 0.2 s. The time between the two crossings is then At 0.4 s. The minimum spectral width of the central Ramsey fringe is Av = 1 /At = 2.5 Hz. Since there are other limiting factors for the spectral width one reaches in real experiments about Av = 10 Hz. The initial velocity caused 

If such an atomic fountain is used as atomic clock [1271, 1272] one can obtain a relative frequency stability of Av/v = 5 x 10  

---

Figure 1. Principle of the atom-fountain-based gravimeter achieved in S. Chu group at Stanford. The right figure shows a two days recording of the variation of gravity. The accuracy enables to resolve ocean loading effects.

We wish to point out, that by use of a suitable fiber which further broadens the spectrum, this fs laser frequency measurement technique has now been simplified to a setup with a single laser, as described elsewhere in this volume [6]. With the technique of Fig. 6, the 15 — 25 transition frequency was measured twice, first with a GPS referenced commercial Cs clock [29], and second with a transportable Cs atomic fountain clock constructed by A. Clairon and coworkers in Paris [30]. A total of 614 spectral lines was recorded in the latter measurement during ten days, and fitted with the described line shape model [13]. After adding a correction of 310 712 233(13) Hz to account for the hyperfine splitting of the 15 and 25 levels, we obtain for the hyperfine centroid [28] ... 

Despite all of the above-mentioned limitations in accuracy of optical interferometry, it is still widely used in the determination of the wave-numbers of atomic transitions, since optical frequency metrology (synthesis chains, optical frequency combs, etc, 4) does not yet have the wide spectral coverage provided by the broad-band interferometers. As an example, a recent absolute wave-number determination of the Cs D2 resonance line at 852 nm is with a Fabry-Perot interferometer, saturated absorption and a grating-eavity semiconductor laser [76]. These results are of interest to various Cs atomic fountain measurements and lead to better determinations of fundamental constants, such as h/mp and a, [77] as well as of the acceleration due to gravity, g [78,79]. 

Both microwave and optical frequency standards have benefited greatly from the development of the laser and the methods of laser spectroscopy in atomic physics. In particular, the ability to determine both the internal and external (that is, motion) atomic states with laser light - by laser cooling for example - has opened up the prospect of frequency standards with relative uncertainties below lO, for example, the Cs atomic fountain clock. The best atomic theories in some cases at starting to match in accuracy that of measurement, providing thereby refined values of the fundamental, so-called atomic constants. Even quite practical measurements (such as used in GPS navigation and primary standards of length) have advanced in recent years. 

Different atom species, for example, ytterbium and barium, were considered. Mercury offered the best capability, such that RF Unear traps with mercury ions are the only competitors of cesium atomic fountains. A project to place an ensemble of atomic clocks in space, including atomic fountains and clocks involving trapped ions, is being undertaken currently. 

Up to now the hyperfine transition in the ground state of the Cs-atom at 9.192 GHz represents the accepted frequency standard. An alternative to the cesium atomic fountain is the dark resonance of Cs atoms in a cell when a coherent dark state of the hyperfine levels is realized where the optical transition is excited by a frequency modulated laser with a modulation frequency which matches the hyperfine splitting in the Cs ground state. This modulation frequency can be used for the stabilization of the microwave which modulates the laser output. Since the dark resonance is very narrow, the uncertainty of the stable frequency is small. 

In this section we discuss the new technique of optical cooling, which decreases the velocity of atoms to a small interval around v = 0. Optical cooling down to temperatures of a few micro Kelvin has been achieved by combining optical and evaporative cooling even the nanoKelvin range was reached. This brought the discovery of quite new phenomena, such as Bose-Einstein condensation or atom-lasers, and atomic fountains [1109-1 111]. 

A very interesting application of cold trapped atoms is their use for an optical frequency standard [1210]. They offer two major advantages reduction of the Doppler effect and prolonged interaction times on the order of 1 s or more. Optical frequency standards may be realized either by atoms in optical traps or by atomic fountains [1211]. 

For the realization of an atomic fountain, cold atoms are released in the vertical direction out of an atomic trap. They are decelerated by the gravitational field and return back after having passed the culmination point with = 0. 

Fig. 9.71 (a) Paths of the atom in a Mach-Zehnder-type atomic interferometer (b) momentum transfer by stimulated Raman transitions applied to rubidium atoms in an atomic fountain where the atoms move parallel to the laser beams [1291] (c) level scheme for Raman transitions... 

One example of an application is the measurement of the gravitational acceleration g on earth with an accuracy of 3 x 10 g with a light-pulse atomic interferometer [1291]. Laser-cooled wave packets of sodium atoms in an atomic fountain (Sect. 9.1.9) are irradiated by a sequence of three light pulses with properly chosen intensities. The first pulse is chosen as 7r/2-pulse, which creates a superposition of two atomic states 1) and 2) and results in a splitting of the atomic fountain beam at position 1 in Fig. 9.71 into two beams because of photon recoil. The second pulse is a tt-pulse, which deflects the two partial beams into opposite directions the third pulse finally is again a tt/2-pulse, which recombines the two partial beams and causes the wave packets to interfere. This interference can, for example, be detected by the fluorescence of atoms in the upper state 2). 

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]...

J.L. Hall, M. Zhu, P. Buch, Prospects for using laser prepared atomic fountains for optical frequency standards applications. J. Opt. Soc. Am. B 6, 2194 (1989)... 

M.A. Kasevich, Atomic Interferometry in an Atomic Fountain (Stanford Dep. of Appl. Phys., Stanford, 1992)... 

Laser cooled and confined atoms open the possibility for a variety of novel experiments. Atoms cooled and confined in a mostly uniform magnetic field [27], or in free fall as in an atomic fountain [28], will have the long coherence times needed for precision spectroscopy. In addition to improv frequency standards, small frequency shifts due to feeble physics effects can be explored. For example, an electron dipole moment d, will induce a linear Stark shift in a nondegenerate state of an atom. The present limit of s 2 x cm [29] corresponds... 

Once the kinetic energy has been reduced to a few raK, the earth s gravitational field could be used to further slow the atoms in an atomic "fountain," so that the projectiles can be observed for extended periods in free fall near the turning point of their parabolic trajectories. Optical two-photon Ramsey spectroscopy of such freely falling atoms is possible with a single standing wave laser field which the atoms traverse on their way up and again on their way down (Fig. 9). >25 as in ordinary Ramsey... 

Fig. 9. Scheme for optical Ramsey spectroscopy of an atomic fountain.24,25... 

Marion, H. et al.. Search for variations of fundamental constants using atomic fountain clocks, Phys. Rev. Lett., 90,150801, 2003. 

---