Preparation sequences

I describe here the typical atom preparation sequences used in both experiments, at LKB and ANU.

LKB experiment

The atomic transitions involved in the elongated MOT for caesium-133 atoms at LKB are shown in figure 2.3. The preparation features dynamic compression, a polarisation- gradient-cooling phase and depumping to the lower ground state F = 3, as shown in the preparation sequence presented in figure 2.4.

trapping

repump depump

Figure 2.3: The atomic level scheme for the MOT preparation at LKB. During loading, the three retro-reflected 50-mm-diameter cooling beams have a total power around 300 mW and the repump beams have 10 mW. At the end of the preparation sequence, the atoms are “depumped” to the lower ground state, in|gi=

6S1/2, F = 3 E

, in a superposition of all the Zeeman sub-levels. This is performed by a depump beam resonant with the |si →

6P3/2, F 0_{= 4}E transition, accompanied by a the trapping beams relatively close to resonance and the repump off. The repetition rate of the complete sequence is 16 Hz. The two-dimensional magneto-optical trapping consists of a set of rectangular coils for radial confinement, completed by a pair of cap coils to generate a shallow gradient along the optical axis. Three retro-reflected 50-mm-diameter cooling beams have a total power around 300 mW, corresponding to a density of 17 mW cm−2, and the repump

beams 10 mW, which corresponds to 0.5 mW cm−2. At the end of the preparation sequence, the atoms are “depumped” to the lower ground state, in |gi=

6S1/2, F = 3 E

, in a superposition of all the Zeeman sub-levels. This is performed by a depump

2.3 Large cold atomic ensembles 49 26 G/cm 6.5 G/cm -17 MHz 0.5 mW/cm² 17 mW/cm² Transverse magnetic field Repump Experiment (2 ms) Preparation (2 ms) Compression (8 ms) Loading (37.5 ms) Cooling beams time -107 MHz Depump 0 mW/cm² 0 mW/cm² 0.1 mW/cm²

Figure 2.4: The typical atomic ensemble preparation sequence at LKB. An elongated en- semble of caesium atoms is prepared by loading a two-dimensional magneto- optical trap with a magnetic gradient of 6.5 G cm−1.

beam resonant with the |si →

6P3/2, F

0= 4E transition, with an intensity around 0.1 mW cm−2, accompanied by the trapping beams relatively close to resonance and the repump off.

The ambient magnetic field is compensated by a set of three orthogonal coils and measured by the Raman spectroscopy technique presented in section 2.3.5. The com- pensation is performed down to 20 mG, corresponding to an inhomogeneous broadening because of the equally-populated Zeeman sub-levels around 50 kHz. It is equivalent to a 8 mG cm−1 gradient over the 2_.5-cm length of the atomic cloud.

ANU experiment

The atomic transitions involved in the elongated MOT for rubidium-87 atoms at ANU are shown in figure 2.5. The preparation features dynamic compression, a cooling phase and optical pumping to the edge Zeeman sub-level, as shown in the preparation sequence presented in figure 2.6.

The two-dimensional magneto-optical trapping consists of a set of rectangular coils for radial confinement, completed by a pair of coils for longitudinal capping, and three retro- reflected 50-mm-diameter cooling beams that intersect at the zero-magnetic-field location. The cooling beams have a total power around 400 mW, which corresponds to a intensity

∼20 mW cm−2. During loading, repump has a total power of and 40 mW, which provide

50-mm-diameter beams of intensity 2 mW cm−2on the

5S1/2, F = 1 E

→

5P3/2, F 0= 2E transition combined with the cooling beams. Follows a 20-ms sequence where the atomic ensemble is radially compressed and further cooled down by a “temporal” dark spontaneous-force optical trapping technique. Last, a uniform bias magnetic field of 0.5 G is applied along the optical axis direction to lift the degeneracy between the Zeeman sub-levels and the atoms are transferred to the |gi =

5S1/2, F = 2, mF = +2

E

state by employing a ∼0.7 mW cm−2 σ+-polarised optical pumping beam resonant with the

trapping

repump optical_pumping

Figure 2.5: The atomic level scheme for the MOT preparation at ANU. During loading, the three retro-reflected 50-mm-diameter cooling beams have a total power around 400 mW and 40 mW for repump light. At the end of the preparation sequence, the atoms are optically-pumped to the edge Zeeman state by a σ+-polarised beam, at the same frequency as the cooling beams. The

optical pumping is accompanied by a resonant repump to leave the atoms in the ground state |gi=

5S1/2, F = 2, mF = +2 E . 28 G/cm 6 G/cm -24 MHz 2 mW/cm² 20 mW/cm² Optical pumping 0.1 mW/cm² -68 MHz Transverse magnetic field Repump

Available for experiments (2 ms) Preparation (1 ms) Compression (20 ms) Loading (400 ms) Cooling beams 0 MHz -9 MHz -32 MHz time

Figure 2.6: The typical atomic ensemble preparation sequence at ANU. The sequence is divided in a MOT loading phase, a compression and a final preparation phase. The magnetic gradient, intensity and detuning profile is as represented here. The repetition rate is around 2 Hz The atoms are optically-pumped to the edge Zeeman state by a σ+-polarised beam, sent along a resonant repump

to leave the atoms in the ground state |gi=

5S1/2, F = 2, mF = +2

E

2.3 Large cold atomic ensembles 51

|gi →

5P3/2, F

0 = 2Etransition. The Earth magnetic field is cancelled by a set of three orthogonal 1-meter-diameter coils.