Experiments to Control Atom Number and Phase-Space Density in ...

Single-mode operation of all lasers can thus easily be verified.
The beat frequency of the lasers determines the required bandwidth of the pho-
todiodes. For detecting the beat of the spectroscopy and the master laser a Thorlabs
photodiode (PDA10A) is used. The bandwidth of this photodiode is 150 MHz. How-
ever, for the beat of the spectroscopy and the imaging laser much larger beat frequencies
have to be detected. A faster photodiode (Hamamatsu, G4176-03) with a bandwidth of
10 GHz is therefore used.
The beat frequency f1 of the lasers is mixed with the frequency f2 supplied by a
voltage controlled oscillator (VCO) [107]. The mixed signal is then low-pass filtered. The
remaining frequency component after this filter is f1 − f2. This signal is subsequently
split into two, and recombined at a phase detector. One of the signals passes through a
delay line, so that the signals arrive with a different phase at the phase detector. This
phase is given by φ = 2π(f1 −f2)τ, where τ is the time delay between the signals. The
phase signal is sent to the PID regulator used to lock the laser frequency.
The beat frequency can be directly measured using a frequency counter. There-
fore a coupler is added to the electronics to divert a small amount of signal to frequency
counters.
A schematic of the electronics used to create the frequency-offset lock signals are
shown in figures 7.31 and 7.32. All components are manufactured by minicircuits.
The value of φ can be changed by manipulating either f1 or f2. f1 can be
modulated by changing the current in the laser diode and/or changing the grating angle
in the laser cavity using the piezo actuator. With a constant f2 this method is used to
generate the error signals shown in figure 7.33. During the experimental sequence the
frequency f1 is fixed and f2 is changed. The VCO frequency f2 is controlled by an analog
out of the experiment control electronics. Because the phase φ is fixed as the lock point,
the PID will feedback onto the piezo actuator to keep f1 − f2 constant, changing the
laser frequency f1 in the process. Using this method the frequency of the master laser
can be changed by 50 MHz in a few ms without unlocking.
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