Loading Chamber

Our loading chamber houses four dispensers that release rubidium into the 2D MOT where they are cooled into an atomic beam. The atomic beam is then used for loading the 3D MOT in the science chamber. In order to ensure that the pressure of the science chamber is unaffected as the rubidium is dispensed, we use the low-conductance tube to separate the two chambers.

Glass Cell Low conductance Tube To Octagon 2D MOT Beams 2D+ _{MOT Beams} Push Beam

Figure 3.3: A diagram of the glass cell and low conductance tube along with the 2D MOT beams. Six 2D MOT beams are retro-reflected back in to the cell. A longitudinal cooling beam (2D+ beam) reflects off of the 45 degree polished surface of the conductance tube, and is paired with another counter-propagating cooling beam and a push beam which pass through a viewport at the end of the chamber.

Gas flowing through a pipe can produce a pressure differential at the ends of the piping [141]. If we assume the pressure difference between the two chambers is large, the pressure ratio achieved between the ends of the piping can be approximated as

pscience ploading

= C

S, (3.1)

wherepscience is the pressure in the science chamber,ploading is the pressure in the loading chamber,Cis the conductance andSis the science chamber pumping speed. For molecular flow conditions, the conductance of air at 20◦C in a pipe is given by C= 12.1d3/l, where dis the diameter of the pipe in cm,lis the length of the pipe in cm andCis given in units of Ls−1_{. To minimise the conductance and therefore maximise the pressure ratio between} the two chambers, a small diameter tube with a large length is required. However, there is a limit to the size requirements of the tube set by the atomic beam. Typical atomic beams emerging from a 2D MOT have divergence angles ranging from 10 - 45 mrad [136, 137, 138]. We therefore chose our low conductance tube to have a diameter of 1.2 mm and a length of 12.7 mm, which should allow for an atomic beam with a divergence angle of 47 mrad to pass through. If we take the pumping speed of the science chamber to be the 55 Ls−1 _of our ion pump, then we get a pressure ratio ofpscience ∼10−4ploading. This lets us reach up to∼10−6 mbar with the rubidium dispensers in the loading chamber and still maintain good UHV conditions in the science chamber. The flux of 2D MOT atomic beams tends towards a maximum at rubidium vapour pressures of 1×10−6 mbar [136, 137], thus our vacuum setup should allow for an optimal atomic beam in this regard. The 3D MOT in our setup benefits from this as a high atomic flux leads to larger and faster MOT loading. Since a larger cooling volume leads to a stronger atomic beam [137], we chose a cylin- drical glass cell for large optical access for our 2D MOT. The glass segment is 152 mm long, although the region of ideal optical access is ∼ 110 mm due to distortions of the glass at the ends of the cylinder and the KovarR _{sleeves. The inner diameter of the glass} cell is 33 mm. Large rectangular optics and mirrors could be used to capitalise on this optical access as much as possible, however, such large optics are often expensive and can be quite impractical. We therefore used standard 25.4 mm diameter optics, but arranged them with minimal separation so as to fill the glass cell with three cooling regions ap-

proximately 4 mm apart, giving us an effective cooling volume of ∼ 75×25×25 mm.

The three cooling beams are retro-reflected after passing through the cell (see Figure 3.3). Without anti-reflection coating on the glass cell, the power of the retro-reflected beams is 17% lower at the position of the atoms. The cylindrical glass cell also acts as a cylindrical

lens with focal length −350 mm. We counteract these two effects with an f = 300 mm

cylindrical lens placed behind the glass cell to collimate and increase the peak intensity of the retro-reflected beams.

To incorporate longitudinal cooling (the 2D+ MOT configuration [136]) and aid our

atomic beam further, we have our low conductance tube also act as a mirror. The tube is made from stainless steel and has a 25.4mm outer diameter (and a small 1.2mm inner diameter). The end has a 45 degree polished cut, allowing a beam from above the chamber to be reflected with 60% efficiency along the atomic beam axis (although with a small hole in the centre). A viewport at the end of the loading chamber allows a counter-propagating beam to pass through, forming the cooling pair.

Since the atomic beam has no preferred direction in which to propagate, a “push” beam is used to introduce a radiation pressure imbalance in the 2D MOT which aids the atomic beam propagation through the low conductance tube and in to the science chamber. A diagram of the scheme is shown in Figure 3.3.

Short flexible Bellow Glass Cell Spherical Octagon (Science Chamber) Low Conductance Tube Atomic Beam

Figure 3.4: A cut through of the glass cell, low conductance tube, bellow and octagon. The atomic beam emerges from the low conductance tube and enters the science chamber.

The linear magnetic field gradients and zero-field line required for the 2D MOT are created by two pairs of rectangular coils in anti-Helmholtz configuration. The coils are approximately 196 mm long and 50 mm wide, where the coil separation is 82 mm. A single coil has 96 turns of 1 mm diameter copper wire, hand-wound around nylon formers (to avoid circulating currents). This geometry gives a field gradient of 6 Gcm−1A−1 along the two transverse axes of the atomic beam. The operating current used for the coils during the experiment was 2.5 A. As the coils were only used at low currents they did not require water cooling. Background magnetic fields were compensated for by two pairs of shim coils in Helmholtz configuration which were wrapped around the 2D MOT coils. Each shim coil has 20 turns with 0.8 mm diameter wire, creating a field of 2.5 GA−1.

In order to ensure that we could optimally align the atomic beam onto the 3D MOT, we designed the entire 2D MOT and loading chamber to be position-adjustable. The coils and vacuum chamber were mounted on the optics breadboards. The entire assembly was then attached via height-adjustable posts to two “skis”, one for the ion pump, the other for the rest of the chamber. The skis are aluminium plates with a large footprint, allowing them to be slid across the table. The short flexible bellow between the octagon and low conductance tube meant that the assembly could be moved in the two transverse axes of the atomic beam propagation, allowing us to align the atomic beam to the 3D MOT. The maximum distance (short bellow uncompressed) between the 3D MOT and the opening of the low conductance tube on the loading chamber side is 280 mm. Over this distance, an atomic beam with a divergence angle of 47 mrad will spread out to approximately 26 mm. Our 3D MOT beams are 20 mm in diameter, leading to reasonably good overlap. Figure 3.4 shows a diagram of the atomic beam entering the science chamber, whilst the general apparatus of the adjustable loading chamber is shown in Figure 3.5.

Chamber mount Height adjustable post Mounting ‘Ski’

Figure 3.5: The vacuum chamber with the 2D MOT optics in place. The lower mounts for the optics board are height adjustable. The entire optics configuration and loading chamber can be moved as one piece.