OPTICAL PUMPING AND STATE SELECTION

During the loading of the trap and launching by molasses, two laser beams are present. The main beam is tuned slightly below the F=4 $\rightarrow$ F'=5 cycling transition (figure 2) and provides the cooling and trapping forces. Off-resonnant excitation of the F=4 $\rightarrow$ F'=4 transition causes some of the atoms to leak into the lower hyperfine level (F=3), where they are lost. Therefore, a second laser beam is necessary, tuned to the F=3 $\rightarrow$ F'=3 or F'=4 transitions, to repump those atoms.

Figure 2: Energy level scheme $D_{2}$ line in cæsium. The transitions used are: (a) repumper, (b) trapping and cooling, (c) pumping.

Cæsium atomic clocks are based on the magnetic dipole transition $\left\vert 3,0 \right>$ to $\left\vert 4,0 \right>$ between the ground state hyperfine levels since neither of these states has any first order Zeeman shift [7]. Thus to observe the clock transition there must be a state selection process to create a population imbalance between these two states. The current working primary time standards use magnetic state selection but optical pumping is the the natural choice for laser cooled atoms since no additional lasers are required. The advantages of optical pumping have long been recognized and there are a considerable number of published papers in which various techniques have been analyzed theoritically and experimentally [8] [online] . Optical pumping methods for clocks can be divided into two categories, namely one-laser and two-laser schemes; we have used both types.

In a simple one-laser scheme all the atoms are transfered into one of the hyperfine levels. This hyperfine-pumping was carried out in our initial experiments (and those of Clairon et al.) by using a laser resonant with the F=4 $\rightarrow$ F'=4 transition which emptied the upper level into F=3 with each atom scattering an average of 2.4 photons. We have achieved effective pumping by this method by simply cutting the repumping beam after the cooling period in molasses (when the main laser is detuned 65 MHz below F=4 $\rightarrow$ F'=5) and deliberately allowing the atoms to leak out of the cooling cycle. Experimentally we have found that this alternative method does not always give complete pumping and the slower rate of pumping will lead to a spread in the vertical velocity distribution (this is possibly an advantage since it reduces the atomic density without atoms being lost by transverse spreading). However this simplified method can be used as part of a two-laser scheme.

Two-laser schemes exploit the fact that the electric dipole matrix element between two $M_{F}$ = 0 states of the same total angular momentum is zero e.g. $\left< F = 3, M_{F} =0 \mid \mathbf{ d \cdot e }\mid F' = 3, M_{F} =0 \right> = 0$ for the scheme which we consider here. Thus the combisation of one laser effecting hyperfine-pumping out of the F=4 level and a second laser resonant with the $F=3 \rightarrow F'=3$ transition (linearly polarized along the B-field) wich excites $\pi$-transitions, the atoms cycle many times until they fall into the only state not being excited, $\left\vert F = 3, M_{F} =0 \right>$. Although a high degree of pumping has been achieved in thermal beams [8] [online] it involves the scattering of many photons, and would cause considerable heating. However a compromise can be achieved by only allowing a few optical pumping cycles since a worthwile number of atoms are transfered into $M_{F}=0$ after scattering up to two photons and those already in this state are not heated at all. Other possible schemes are discussed in [8] [online] , in particular some which use $\pi$-pumping on the F=4 $\rightarrow$ F'=4 transition. The increase in the signal for a given atomic number density will be particularly important if collisional shifts are significant.