Martin Teichmann Atomes de lithium-6 ultra froids dans la ... - TEL

3.7 MOT imaging
3.7. MOT IMAGING
When optimizing the MOT, it is of crucial importance to know the
number and temperature of the trapped atoms. The old MOT imaging
system had long stopped working, mostly due to the fact that the
frame grabber card to read the camera did not fit into new computers.
Therefore we decided to install a completely new system.
As for the camera, we decided to buy a cheap and especially small
camera, as we do not need precision measurements for the characterization
of the MOT. We chose the uEye UI-1410-M from IDS, an eight
bit CMOS camera, which is triggerable via a TTL signal and can be
connected to a computer using the USB port, which at the same time
is its power supply, limiting the number of cables on the experimental
table. There was a problem with that camera. A glass slide, meant to
protect the camera, created strong fringes on the camera, such that the
images were destroyed by the interference fringes. Unfortunately, while
breaking this glass slide we destroyed some pixels on the camera, but
there were enough left over to work with the camera.
As with the main imaging system, we use absorption imaging, since
this gives an absolute number of atoms. Assuming we correctly installed
the imaging lenses, each pixel of the camera will “see” a column of
the imaged cloud. If the cross section of this column is A, and the
scattering cross section of a photon with an atom is σ, a photon traveling
along this column has a probability of σ/A to scatter with an atom.
Considering many photons, there will be 1 − σ/A of the incident light
intensity transmitted. For N atoms Iout/Iin = (1−σ/A) N will be left, calling
Iin and Iout the incident and transmitted light intensities, respectively. In
order to know the number of atoms, we take the logarithm, leaving
us with N = ln(Iout/Iin)/ ln(1 − σ/A) ≈ − ln(Iout/Iin)A/σ. Note that σ/A
is normally sufficiently small that the last approximation is very good.
The term − ln(Iout/Iin) is called the optical density. The advantage of
absorption imaging is clearly visible: the calculated number of atoms
only depend on the ratio between two intensities, which can be easily
determined by taking two images, one with, one without the atoms to be
imaged, and we take the ratio of the two. Therefore there is no need to
calibrate the calculated number of atoms. The formula for the scattering
cross section is
σ = 3c2λ2 2π (1 + 4(∆/Γ)2 ) −1
(3.4)
with λ = 671 nm the wavelength of the transition, Γ = 5,9 MHz its
line width, c the corresponding Clebsch-Gordon coefficient, and ∆ the
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