C’était une de ces machines d’express, à deux essieux couplés, d’une élégance fine et géante, avec ses grandes roues légères réunies par des bras d’acier, son poitrail large, ses reins allongés et puissants, toute cette logique et toute cette certitude qui font la beauté souveraine des êtres de métal, la précision dans la force.
La Bête Humaine – Émile Zola
This chapter describes the apparatus built during my PhD to cool atoms to degeneracy, and motivates the technical decisions made.
We built the apparatus, from the ground up, in an empty lab, and moved it from Orsay to Palaiseau half way through the construction. Technical choices on the experiment have been guided by the scientific goal of the project: pave the road to long-interrogation-time atom interferometry with degenerate atomic sources. Our first step was to develop scalable and robust laser sources suitable for laser cooling both species, a fully-semiconductor room-temperature laser system described in the previous chapter. In the atom-optics apparatus, care has been taken in the design and the construction to choose robust and compact solutions to make it possible to adapt the apparatus to an experiment in the Zero-G Airbus. We use a 2D-MOT as an atomic source and a fiber laser for the optical dipole trap. The large science chamber, very homogeneous magnetic field, wide field of view imaging have been designed with large expanding clouds in mind.
In this chapter, I go into the technical details of the design choices and the per- formance of the implementation. First, I discuss the design and performance of our laser-cooling stages: a 2D-MOT loading a 3D-MOT. Then I describe the compressible optical-dipole trap, and the coils used for Feshbach resonances. Finally I present how these components are assembled in a compact atom-optic apparatus, while leaving as much flexibility as possible.
Although the experiment has been designed to cool to quantum degeneracy a mixture of bosonic 87Rb and fermionic 40K, no work has been started on 40K, and,
at the time of the writing of this manuscript, Bose-Einstein condensation of 87Rb has
Chap V - Building a transportable boson-fermion coherent source
1
2
3
4
5
Figure V.1 – Cooling to quantum degeneracy: the different steps
1 A dilute atomic vapor is created in the collection chamber using alkali-metal dispensers. 2 A 2D-MOT transversally cools atoms to send a slow and collimated atomic jet in the
science chamber.
3 A 3D-MOT captures the atoms in the jet and further cools them to 50 µK.
4 The atoms are transferred to a conservative optical-dipole trap.
5 Evaporative cooling is performed in the optical-dipole trap by lowering the depth of the trap to remove the most energetic atoms and waiting for rethermalisation.
Steps 1, 2 and 3 are described in §V.1, step 4 is described in §VI.1, and step 5 has not yet been experimentally achieved.
1
A 2D-MOT loading a 3D-MOT
We use the near-resonance semiconductor laser sources to laser cool the atoms and, from a dilute high-temperature vapor, prepare a dense and cold atomic cloud in a Magneto-Optical Trap (MOT). After this laser-cooling stage, the atoms are evapo- ratively cooled to degeneracy. Evaporative cooling is an atom-consuming process; it requires a high initial number of atoms to be efficient. This is more easily achieved when loading the MOT from a relatively high-pressure background atomic vapor. Evaporation is also a time-consuming process; evaporation time is limited by the re- thermalization of the trapped cloud. However lifetime of the cloud in the trap is limited by collisions with the background vapor. These opposite constraints have lead to two-chamber designs in which a first, low-vacuum, chamber serves as a source of slow atoms to load a MOT in a second, high-vacuum, chamber.
In our apparatus, atoms are collected from dilute vapor and pre-cooled in a first low-vacuum chamber, then sent in a slow beam to a second ultra-high vacuum chamber (the science chamber) where they are captured by a MOT and will be evaporatively cooling to degeneracy (see Figure V.1).
To load our MOT in the science chamber, we need a high-flux collimated beam of atoms below the capture velocity of the MOT. A Zeeman slower (Metcalf and van der Straten [60]) is a proven solution that has been successfully used at the Institut d’Optique for many years on previous experiments. However, it is a bulky solution, as a tube long enough for the atoms to be slowed down from hypersonic velocities to MOT-capture velocities is needed. It is not suited for our compact design. Moreover, we plan to use an isotopically-enriched source of fermionic potassium. Such material
1 A 2D-MOT loading a 3D-MOT is very expensive1. An oven-based setup, such as a Zeeman slower, consumes a lot of material, and would be too costly to run.
Double-MOT systems are also widely used. In these apparatuses a high-background- pressure collection MOT allows fast accumulation of a high number of atoms, which are then transferred to the high-vacuum MOT in the science chamber. As the trans- fer process should not perturb too strongly the operation of the collection MOT, the achievable flux is limited. We chose to use a third solution: a 2D-MOT set-up to collect atoms from a background vapor and load the science chamber MOT. Unlike 3D-MOTs, 2D-MOTs are purposely unbalanced and do not aim to trap atoms, but simply to collimate an atomic jet. They have been demonstrated for87Rb to produce a flux of 9 · 109atoms· s−1 with low velocities (Dieckmann et al. [144]).
In this section I develop simple models for the capture process of an atom in a 3D-MOT and the collimation in the 2D-MOT to estimate the capture velocity of the 3D-MOT and the velocity distribution of the atomic jet loading it. Then I discuss the dependence of the number of atoms captured in the 3D-MOT on the experimental parameters. I will mainly base my discussion of the laser-cooling stages of the apparatus on Doppler cooling and trapping of the rubidium atom, as we have not yet worked with potassium on the experiment. The physical processes involved are similar, although a few constants like the mass of the atom change.
1.1
Estimation of the capture velocity of a MOT
In a MOT, atoms are trapped using the radiation pressure of near-resonance lasers. Briefly2, the lasers communicate momentum to the atoms via photon scattering. As
the scattering cross-section depends strongly on frequency near an atomic resonance, this radiation pressure force is rendered velocity-dependent through the Doppler effect, and position-dependent by the Zeeman shift created by a magnetic gradient. In a 3D-MOT, the total force resulting from six laser beams coming from all principal directions damps and traps the atom.
Several different experimental parameters come into play when designing a MOT with the goal to capture as many atoms as possible from an atomic beam:
rc the radius of the laser beams. It defines the size of the region in which the atoms
are subject to the MOT force, we use 1.25 cm.
I the laser intensity. The relevant dimensionless parameter for the atoms is the
saturation parameter: s0 = I/Isat where Isat is the atomic transition saturation
1Roughly $3000 per 100 mg, available from Trace Sciences
2Laser cooling and trapping of atoms has been reviewed in many theses. I will not discuss the
physics and processes involved. The reader is invited to refer to Metcalf and van der Straten [60] or Dalibard [145] for a lecture on the subject.
Chap V - Building a transportable boson-fermion coherent source intensity, Isat = 1.6 mW · cm−2 for the rubidium laser cooling transition. We
have a 25 mW of laser light per beam3, and s 0 ∼ 3.