Sodium atoms have been cooled in two and three dimensions with stimulated Raman transitions.Atoms in 2D have been cooled to v,m, =1. 2hk/M, corresponding to an effective temperature of T,tt= 1.7 pK while atoms in 3D have been cooled to v, , =2. 3hk/M, or T,tv=4 3p.K. PACS numbers: 32.80.Pj Methods for laser cooling of atoms continue to improve rapidly. Atoms have been laser cooled by polarization gradient molasses in three dimensions to temperatures as low as -20T, «, where T«, =(hk) /2Mktt is defined as the photon recoil temperature [1]. There have been several proposals [21 and two experiments [3,4] to cool atoms along one dimension to effective temperatures below the photon recoil temperature. We report here the first results of the extension of our Raman cooling method [4] to two and three dimensions. We have cooled sodium atoms to an effective temperature [5] of 1.7 p K, or -1.5T",in two dimensions and to 4.3 p K, or -3. 5T", in three dimensions. The cooling represents a velocity phase space compression of -18 and -15 times over polarization gradient cooling for two and three dimensions, respectively.The basic idea of cooling with stimulated Raman transitions has been previously described in our demonstration of ID cooling [4]. Consider an atom with two ground states~1) and~2) separated by a hyperfine splitting htoHFs and an excited state~3). If the atom initially in state~l) is irradiated with pulses of light from two counterpropagating laser beams at frequencies mi and m2 (and wave numbers k = [kl~= )k2~), where to~-to2 -toHFs, the two-photon Raman transition from~1& 2) has twice the Doppler sensitivity of a single-photon transition. If the Raman frequency difference is tuned to the red of the two-photon resonance, an atom moving with velocity +v (towards the tot beam) will Doppler shift the transition into resonance. During the transitioñ I&~2&, the atom receives a momentum kick 2hk towards v=0. By varying the difference frequency, atoms with any positive velocity can be pushed towards v =0. If the directions of the two Raman beams are reversed, an atom moving with velocityl. can be made to receive a momentum kick towards v =0.An optical pumping pulse tuned to the~2&~3& transition is used to return the atoms back to state~1& after each Raman pulse. During the optical pumping process, the spontaneous emission back into the~1) state has a chance of leaving the atom near the v =0 state. The stimulated Raman excitation/optical pumping cycle is repeated, each time pushing more atoms towards the i =0 state.If the process is to be eAective, atoms must be loaded into the trapped velocity state more eSciently than they are ejected from it. In practice this means that atoms near i =0 must be able to survive the application of many pulses before being excited out of the velocity trapped state. Thus, both the line shape and linewidth of the Raman transitions are tailored to minimize un~anted excitations. We use Blackman pulses [41 to reduce the offresonant excitation due to the frequency sidelobes of the Raman pul...
