Experimental methods
2.1.3 Optical system
Here I summarise the optical setup for cooling, pumping and imaging the atoms. The optical setup for the fibre cavities is described later in the dedicated section.
2.1.3.1 Geometry of fields
Let me start with an overview of the geometry of all relevant optical and magnetic fields, shown in Fig. 2.5, to facilitate the perception of the experimental details. The reference frame is consistent with that shown in Fig.2.1, which we will use throughout the thesis.
The current sources used in TACC-1 are all unipolar, rendering the directions of fields and polarisations of laser beams almost uniquely determined. In TACC-2, the transport of atoms, achieved by a rotation of the magnetic trap (see Sec.2.2.2), requires at least one bias B-field to change sign. In fact, later we found it necessary to switch the directions of multiple fields, and we do have some freedom in choosing the field configuration in the end.
To illustrate the determination of field directions, I give one example of the optical pumping. To prepare a pure state in one of our clock states |1, −1i and |2, 1i (we will note the ground state manifold as |F, mFi), only the former is directly accessible through optical pumping. Therefore the pumping beam is fixed to σ−polarisation and can only be delivered through the detection beam path along ~x, due to limited optical access along ~y. The layout of the optics (Fig. 2.8) determines that the MOT cooling beams along ~x can only have the orthogonal polarisation. Therefore the MOT B-fields are also determined, et cetera.
Fiber cavity (LF)
← input
CCD (Andor)
CMOS (Ueye) x
y z
σ+
σ-Stripline σ+
Macro-U Bx
σ-σ+
By
Op�cal pumping
& Detec�on X
Detec�on Y
By Dimple
MOT & cooling beams
gravity
Figure 2.5 Geometry of fields. On the left, the stripline, dimple wire, and the fibre cavity is sketched in our reference frame. Dimple current is inverted for the traps either on the MOT site or on the cavity site. The reason is explained in Sec. 2.2.6.3. On the right, cooling beams and B-fields for the MOT are depicted. For clarity, Macro-I is not depicted, but its current is locally the same as the Macro-U at the MOT site. Note that the polarisations are defined with respect to the coordinates, except that for the 45° beams, the polarisation is defined with respect to the propagation direction. LF: low finesse or the science cavity, detailed in Sec.2.3.1. Andor and Ueye are two cameras.
2.1.3.2 Lasers
The optical table and the associated electronics are barely modified from the previous setup [107]. Two SYRTE-made extended-cavity diode lasers (ECDLs) and a slave diode provide the four frequencies and all six laser beams needed (as depicted in Fig. 2.5).
Frequency generation The frequency diagram of the lasers and their generations are sketched in Fig.2.6. All frequencies are referenced through the repumper laser to a standard saturated absorption spectroscopy (SAS). The repumper is locked in between |F = 1i →
|F0 = 1i(1-1) and 1-2 transitions to easily access either transition for pumping and repump-ing, respectively. The master laser (master in the sense for the slave diode) is locked to the repumper by beat-note, hence more widely tunable, to generate either the cooling beams near 2-3 transition, or the pumping beam at 2-2 transition. The layout of the optical table is shown in Fig. 2.7(a).
Optical power The four cooling beams are powered by the slave diode and can deliver
∼10 mW power each. But as an ECDL has only 30 mW output power, for optical pumping and detection, power is not ample. It is worth noting that the two optical pumping beams are combined with the detection beams with polarising beam splitters (PBSs) before coupling into the detection fibres (Fig.2.7(a)). Therefore the powers of optical pumping and detection are mutually exclusive in each direction: if all the detection power goes to ~x, then all the pumping power will be in ~y. It may lead to power shortage in certain imaging configurations.
267 MHz
Figure 2.6 Diagram of laser frequency generation, including that of the 2D-MOT. AOM:
acousto-optic modulator
Repumper for detection The repumper is previously only present in the 45° beams, so that it does not enter the camera if used during the imaging. Otherwise it would compromise the atom number estimation. In the new setup, imaging the atoms inside the cavity with this repumper wouldn’t work since the 45° beams don’t enter the cavity. We have to send repumper colinear with detection beam in ~y. To couple some repumper into the detection fibres without losing too much power, it is first combined with the master pump beam line with orthogonal polarisation (Fig.2.7(a)), therefore mutually exclusive in their powers. This temporary solution might also limit the available power in certain cases.
2D-MOT The existing laser bench has neither extra space nor power to feed the additional cooling and repumper beams for the 2D-MOT. A small breadboard is set to have a minimalist but stand-alone module to power the 2D-MOT. The layout is shown in Fig. 2.7(b).
Due to the relaxed requirement on the frequency or amplitude noise for the 2D-MOT lasers, we implemented a simpler SAS to lock the repumper ECDL, by directly modulating the diode current at 70 kHz. The cooling laser is a self-seeded tapered amplifier (TA) laser (TAL-780-1000)[111], frequency locked by beating with the repumper. The small extended cavity at the back side of the TA chip is of a cat-eye design. The spectral linewidth and the output mode are worse than a standard ECDL, while sufficient for our 2D-MOT.
For simplicity, the push beam is split from the cooling beam, incapable of independent frequency tuning. While a detuning might be optimal (see for example [112]), it works well for us in this simple configuration. It turned out to be important though to focus the push beam onto the 2D-MOT, which increases the flux reaching the 3D-MOT by a factor of 10 compared to a collimated push beam. Due to the long distance (∼ 0.7 m) between the 2D-MOT and the atom chip, the MOT loading is very sensitive to the push beam power,
ECDL
Figure 2.7 Layout of the optical table. (a) the main bench for cooling, pumping and detection. (b) the 2D-MOT module. Laser beams are coloured by functionalities: green:
SAS; orange: offset lock; yellow: repumping; blue: optical pumping; purple: imaging; grey:
monitoring; red: cooling and others. ISO: optical isolator; HWP: half waveplate; QWP:
quarter waveplate; (N)PBS: (non-)polarising beam splitter; PD: photodiode.
exhibiting a clear optimum.
The characteristics of the atomic beam out of the 2D-MOT have not been rigorously examined. But loading the mirror-MOT works reasonably well so that 107 atoms can bee loaded in the MOT within 0.5 s, sufficient for our experiments.
2.1.3.3 “Optical hat”
The optical components around the vacuum cell and inside the µ-metal shield are home-made to meet the spatial constraints and non-magnetic requirement, mostly inherited from the previous setup. In the elegant design of our predecessors, components were pre-aligned on an aluminium plate to be put around the vacuum cell as a hat. In our new situation with the fragile fibres in place, the “hat” can only be assembled around the cell with great caution.
CCD (Andor)
CMOS (Ueye)
Polariser aperture cavi�es
Horizontal MOT beam
Horizontal MOT beam Detec�on X
& op�cal pumping Detec�on Y
PD CCD (figer camera)
f = 40
f = 100
QWP (unless specified) PBS
Achromat spherical lens
sampler f = 25
f = 30
f = 50
f = 60
Dielectric mirror MOT fluorescence
Imaging beam shaping
y
x
Figure 2.8 Schematics of the optics on the optical hat. The magnification in either direction can be easily modified by changing the last lens (therefore not specified).
Imaging through cavity The layout of the optics has been adapted to the presence of the cavity. The imaging beam along ~y axis, i.e. through the cavity, needs to be shaped to avoid scattering on the fibres or the bridge. Beam shaping is done by imaging an aperture (which properly cuts a collimated beam) to the atoms’ plane in the cavity. This plane is again imaged to the CCD camera, completing the absorption imaging. At the same time, however, atoms at the MOT site cannot be properly imaged with this camera. The imaging scheme and other optics on the optical hat are sketched in Fig.2.8.
MOT fluorescence Having a real-time monitor of the MOT7 has been an omnipresent and indispensable tool in many cold-atom labs. We managed to fit on the optical hat a
“finger” camera and a photodiode, to obtain a MOT image together with a fluorescence signal on the photodiode during the MOT phase. This signal allows us to perform feedback control of the MOT loading time, obtaining a more stable atom number in the molasses phase.