Multi-Wavelength with Simultaneous Phase and Amplitude Control

trol

The approaches of the multi-wavelength technique from Section 2.4 and the simultaneous phase and amplitude control from Section 2.5 can easily be combined for further flexibil- ity of atomic trapping with an SLM. In order to showcase the compatibility of the two methods, we created a ring and barrier pattern similar to that of Figure 2.20(b), but with a phase winding for the ring. The pattern was calculated for the far-field with an FFT propagator, where the results are shown in Figure 2.33.

The 1/e2 half-width of the incident beam σ for the calculation was 1.5mm, whilst the guess phase curvatureR was 4.5mrad px−2. The phase was left unconstrained for the barrier and therefore the fidelity was only taken for the ring which had an ROI diameter of 65px. The fidelity gives a result of 1−F = 3.8×10−6. The light efficiencyη of the pattern was 24.6%, whilst Φ was 0.0002 and the non-uniformity nu was 0.001. These errors are comparable to that of Table 2.2 and exemplify the ease with which a multi-wavelength pattern with a constrained output phase can be created.

The techniques outlined in the previous sections therefore present exciting develop- ments for flexible atom trapping with a single SLM which can be combined where desired. The full realisation of such methods however, requires an experimental setup for ultracold atoms where the SLM traps can be utilised. The next chapter will therefore outline the systems we have built for such a task.

(a)

(b)

(c)

Figure 2.33: Multi-wavelength ring and barrier pattern for 1064 nm and 670 nm light, similar to that of Figure 2.20 b), except there is a phase winding from 0 to 2π now on the ring. The colours denote the same values as in Figure 2.25. (a) Target intensity (colour) and phase (gray), where the phase constraint is only applied to the ring. (b) Resulting intensity (colour) and phase (gray) from the calculation. (c) Simulated intensity if 1064 nm light (colour) and 670 nm light (white) were applied to the SLM. The image was created by resizing the pattern by the ratio 670/1064 and overlaying it on top of the original pattern.

Chapter 3

Cold Atoms Setup

3.1

Overview

In this chapter I will detail the apparatus that we have constructed in order to realise the first BECs in St Andrews. The process of producing an atomic BEC is well-covered in the literature (reviews can be found in [134, 24, 10]). Briefly, atoms are introduced to an Ultra High Vacuum (UHV) chamber, and subjected to initial laser cooling in a magneto- optical trap (MOT). These pre-cooled atoms are neither sufficiently cold nor dense enough to undergo Bose-Einstein condensation. Thus a second phase of evaporative cooling in a conservative trap must be used. The atomic species of interest in our experiment is87Rb. Regardless of what trap is employed, background pressure will negatively effect the trapping lifetime of the atoms as collisions with hot background atoms will cause losses. Ultimately, if the pressure is too high we can not condense the atoms as they will leave the trap too quickly for our cooling process. A pressure of the order of 10−11 mbar is needed to have a sufficiently long lifetime (∼100s) for typical BEC experiments [135].

There are essentially two main vacuum chamber designs for cold atomic experiments: the single chamber setup and the double chamber setup. The single chamber setup has both the BEC experiment and the atomic species loading done in the same environment, giving a compact and simple design. However, the atom loading process contributes consid- erably to the background pressure, resulting in worse lifetimes. Alternatively the double chamber setup has a first, high pressure “loading chamber” from which the atoms are transferred to a second, lower pressure “science” chamber for the BEC experiment.

The main goal of our experiment is the flexible trapping of BECs using holographic patterns. In a previous incarnation of our experiment we had a single chamber design, which only achieved moderate lifetimes and atom numbers during the MOT stage (6 s and 1×108 respectively). We therefore opted for a double chamber design for our new experiment.

Loading atoms into the science chamber is the initial step of the experimental sequence. We accomplish this by using a 2D magneto-optical trap (MOT) [136, 137, 138]. The op- erating principles of the MOT are comprehensively explained in [24, 139]. In brief, laser beams which are slightly detuned below atomic resonance are shone from multiple direc- tions. Photons which are moving counter to the atomic motion (Doppler shifted higher in frequency) become more favourably absorbed, whilst the spontaneously re-emitted pho- tons are isotropically directed, resulting in a damping force which opposes the atomic motion. A position-dependent force can be added by using a linear magnetic field gradi- ent and circularly polarised beams: the combination of the Zeeman effect and selection rules ensure that atoms are pushed towards a zero-point of the magnetic field.

If pairs of counter-propagating beams are used along three orthogonal directions with a single pair of coils in anti-Helmholtz configuration, the atoms will be cooled and trapped at a point: this configuration is the standard three-dimensional (3D) MOT. However, using counter-propagating beams in only two directions and a spatially varying magnetic field with a zero-field line orthogonal to the beams realises a two-dimensional MOT (2D MOT). This results in an atomic beam where the atoms are free to propagate along the zero-field line, but are confined and cooled in the transverse axes. Such an atomic beam is ideal for transferring a high flux of atoms from the “loading” chamber in to the low-pressure “science chamber”, where we then trap and cool them in a fully confining 3D MOT.

After laser cooling in the 3D MOT, the magnetic field gradient can be increased and the laser beams turned off such that the atoms are kept in a purely magnetic trap. At this point the atoms are evaporatively cooled. This process selects the higher energy atoms in the trap and removes them, the same principle as blowing on the steam from a coffee cup, such that the remaining atoms then thermalise to a colder temperature. We remove the hottest atoms with a sweeping RF knife, which transfers the trapped atoms to an anti-trap state, expelling them out of the ensemble. This cooling technique is naturally a lossy process (and it is necessary to trap as many atoms as possible prior to this stage), but further losses are also taken in our quadrupole configuration magnetic trap due to Majorana spin flips. The coldest atoms near the center of the magnetic trap experience such small magnetic fields that the Zeeman sub levels are near-degenerate, leading to atoms spin-flipping in to an anti-trap state and leaving the system. To minimise such losses we transfer the atoms to a hybrid trap where the final evaporation is performed, following a similar approach outlined in [140].

The hybrid trap consists of a gravity-compensating magnetic trap and single focused- beam optical dipole trap (ODT). The ODT light is sufficiently far red-detuned that photon scattering is negligible, but powerful enough that the AC Stark effect is prominent. A shift in the energy levels of the atoms will then occur, such that the ground state energy lowers in the presence of the light, creating a trapping profile in the shape of the beam. The gravity-compensating magnetic field is created by the same quadrupole field as the magnetic trap (with reduced magnitude), and provides levitation as well as confinement along the ODT axis. Further evaporative cooling can be done during this stage by simply lowering the laser intensity to reduce the trap depth and expel the hottest atoms. With enough cooling, the BEC in our experiment is created. Furthermore, at this stage where the atoms have been cooled sufficiently, a separate, holographic ODT is employed in a crossed configuration with the first ODT to create arbitrary trapping configurations for the atoms.

For diagnostics of the atoms we use absorption imaging, where a pulsed resonant laser beam (“probe beam”) illuminates the cloud and is imaged on to a camera. The atoms absorb the light and re-emit the photons isotropically, resulting in a shadow being cast on the camera. The depth of the shadow corresponds to the density of the atoms.

In the rest of this chapter, the details and implementation of the above experimental scheme are covered.