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

3.5. THE OPTICAL DIPOLE TRAP
The heating rate τ in this equation relates to the noise of the laser as
1
τ = π2 ν 2 S(2ν) (3.2)
where ν is the trap frequency and S(ν) is the power spectral density.
Equation (3.2) shows that the most disturbing noise is around twice the
trapping frequency, which we expect since parametric heating is the
dominating process.
The laser was shipped back for repair. A feedback loop was installed
in the factory, but this and various changes in the laser geometry had
only minor effect, the peak noise did not drop below -100 dB/Hz. The
good news was that the noise peak had moved to higher frequencies:
the main peak was now at 32 kHz, see figure 3.10. The heating times
calculated for the laser are shown in figure 3.11. Since we work at lower
frequencies, the atoms see less of the noise. The noise is very different
for single mode or multi-mode operation. The noise peak at 32 kHz is
narrower, but the noise at low frequencies increases tremendously for
multi-mode operation. This makes single mode the favorable way of
operating.
The only way to use this laser was to install a feedback loop. A
photodiode, installed after the trap, detects the intensity of the laser. We
designed a PI controller, which feeds back onto the AOM installed after
the laser. The electronic circuit is shown in figure 3.12. The photodiode’s
signal enters on the left. It get summed with the reference voltage using
an operational amplifier. As the photodiode’s signal is negative, and the
reference positive, the sum of the two give directly the error signal. A
potentiometer, wired as a voltage divider, determines the overall gain of
the feedback loop. The core part of the controller is the integrator in
its center. The gain G of the shown circuit is proportional to
G ∝ RGRτ
R0
� �
1
1 +
iωRτC
(3.3)
where RG is the setting of the overall gain potentiometer and C is the
value of the capacitor in the integrator. Rτ is the setting of the variable
resistor named time constant in the figure, and looking at the equation
we note that it can be indeed used to set the time constant τ = RτC of
the system.
The output from this controller is connected to voltage controlled
attenuators (PAS-3 from Minicircuits) which attenuate the radio frequency
power sent to the AOM. As their working point is normally not around
57