Once a stable BEC source has been created, steps are taken to transfer the atoms into an optical waveguide where they will propagate and coherently split. The waveguide is derived from the same laser used to generate the dipole beams and is tightly focused at its waist. It holds the atomic sample in an optical potential with no reliance on magnetic fields. Two identical overlapping waveguides creates a periodic potential, the amplitude of which is dependent on the relative polarisation between the waveguides. The resulting band structure explained in Chapter 4.6 creates regions of high reflectance and atoms are deflected into the second waveguide depending on their initial velocity.
4.1 Generation of Optical Waveguides
To form a trapping potential, the wavelength of light for the waveguides must be red detuned relative to the atoms and be tightly focused. In this sense they are similar to the dipole beams used to form the dipole trap, but with significantly lower intensities. Because of this, the dipole and waveguide beams are derived from the same laser. Using the same laser mitigates interference arising from frequency fluctuations, helping to reduce excitations.
The laser used to form the waveguides is fibre coupled, and therefore emits a good approxima-tion of a Gaussian beam, minimising the need for shaping optics. A schematic of the optical layout is shown in Figure 4.1. Two waveguides, referred to as WG1 and WG2, are generated
62 Waveguides and Beamsplitter Implementation
WG2 WG1
DT
Cuvette Beam dump
AOM
Laser
λ/2 waveplate beam expander
Fig. 4.1 Paths of the dipole trapping beam and the two waveguides. A single dipole beam is recirculated and crosses inside the science chamber. WG1 and WG2 intersect close to the dipole trap intersection. The photodiodes are used for independent power stabilisation.
using a fraction of light from the dipole beam before it passes through an AOM. The two waveguide beams then pass through two separate AOMs to allow independent control of their power. This has an additional advantage of shifting the frequency of the waveguides to the dipole beam by an additional 80 MHz, avoiding any cross interference. After the AOM, a small fraction of light is removed and sent to a photodiode for use in stabilising the intensity as described in Chapter 3.10. A λ /2 waveplate is used to create linearly polarised light before passing through a beam expander, increasing the diameter by a factor of 3, to 12 mm. A larger waist results in a smaller minimum beam waist when focused using the relation
2w0= 4λ π
f D
, (4.1)
and is valid for f ≫ zR, where zR is the Rayleigh length. w0is the minimum beam waist, f is the focal length of the lens and D is the diameter of the collimated beam.
The waveguide potential is affected by the minimum beam waist, intersection angle and intensity of the waveguides. Figure 4.2 shows the potential depth for a waveguide with a 23 µm waist and 15 mW of power intersecting a second identical waveguide with an angle
4.2 Improved BEC Loading using Waveguides 63
Fig. 4.2 Potential depth of the waveguides along two axis for a 15 mW horizontal beam with a 23 µm waist. Figure 4.2a represents the potential along the direction of the waveguide.
Figure 4.2b is the potential along the axis of gravity.
θ = 90°. The trap depth is 5 µK along the axial direction of the waveguide. Due to the low power of the waveguides atoms are only weakly held against gravity with a trap depth of 2 µK.
Fluctuations in intensity can be large enough to push atoms out without additional power stabilisation. Additionally, the waveguides must be horizontal to minimise the component of gravity. This is especially important once the BEC is released and permitted to travel along the length of the waveguide. If the waveguide is angled away from the horizontal gravity will impart an additional force on the atoms, causing them to be accelerated out of the waveguide.
As it is difficult to guarantee the horizontality of the optical bench to the level of precision required, a kinematic mount provides additional alignment in the vertical axis. The best method of aligning the waveguide to be horizontal is to allow a BEC to propagate in the waveguide. It will naturally oscillate around the focus of the waveguide for a horizontal beam.
Any vertical offset will cause the BEC to oscillate off centre. By adjusting the kinematic mount and monitoring the BEC oscillation a good approximation of a horizontal beam can be made.
4.2 Improved BEC Loading using Waveguides
WG1 will overlap with the crossed dipole trap, enabling the waveguide to serve a dual-purpose and help to load more atoms at a faster rate into a BEC state. A common technique used to
64 Waveguides and Beamsplitter Implementation
load more atoms into a BEC from a dipole trap is with the use of a dimple beam [120, 121].
This is an additional beam usually derived from the same laser to prevent excitations which also intersects at the dipole beam focus. Due to the low power in the dimple, its additional trapping potential is negligible when the dipole trap is formed. As the power is slowly lowered for evaporative cooling, the trapping potential from the waveguide becomes significant. The smaller beam waist of the dimple helps to spatially confine atoms as they undergo evaporative cooling, keeping density high. In this experiment, WG1 intersects the dipole beam 500 µm to 800 µm from the focus of WG1. The distance between the intersection and the focus of WG1 is typically less than one Rayleigh length. Increasing the distance beyond this point reduces the trapping potential felt by the atoms, to the point where they will fall out of the trap due to gravity. The Rayleigh length is calculated as
ZR=π ω02
λ , (4.2)
giving an effective maximum separation between the dipole beams and the focus of WG1 of 1.5 mm.
4.3 Transfer from the BEC
Once a BEC is formed in the dimple assisted trap, the dipole trap beams are abruptly switched off using the AOM shown in Figure 4.1. A diagram describing the relative positions of the dipole and waveguide beams is shown in Figure 4.3. The orientation is simplified to increase clarity. With the dipole beam off, WG1 becomes the sole trapping potential. Once released, the atoms can no longer be described as a BEC, but are instead an ultra-cold atomic wave packet, and are highly coherent. An adiabatic transfer to the waveguides will cause multiple transverse modes of the waveguide to be occupied. As the atoms are no longer in the centre of a potential, they will begin to accelerate towards the focus of WG1, a region of lower potential. After passing the minimum beam waist the atoms begin to climb the potential and start to oscillate. The oscillation is measured and used to calculate the axial frequency of the trap.
Measurements are taken of the BEC position as a function of time as it oscillates in WG1 and are shown in Figure 4.4. As absorption imaging is destructive a new BEC is required for each data point, necessitating a need to minimise the length of a full experiment cycle. Otherwise
4.3 Transfer from the BEC 65