MTS Laser Locking Theory

Laser Locking

The MOT requires laser beams with two different frequencies at cooling and repumping transitions in Fig. 3. Each beam must be at a frequency locked to a Rubidium transition. To lock the beam frequencies, we used Modulation Transfer Spectroscopy (MTS). MTS is a powerful locking technique that is suitable for our purpose of locking to the 85Rb F = 3 → F′ = 4 transition. It can achieve sub-Doppler resolution on a transition while producing a dispersive signal (better for locking). Moreover, it is robust to fluctuations in temperature, polarization, and magnetic field [5].

Figure 3: 85Rb Hyperfine splitting energy levels adapted from [4](not to scale). (a) and (b) show the transitions of the closed optical path, driven by cooling light. (c) and (d) display for- bidden transitions. (e) shows the spontaneous emission tran- sition which puts the atoms in a ”dark” state, unreachable by the red-detuned photons. Repumping light is used to induce (f) and bring these atoms back into the closed loop cycle. Thus, to continue the cooling cycle, repump light is needed. The repump light has a higher frequency than the cooling light by 3.03 GHz.

Figure 4: Output signals (in volts) generated from Modulation Transfer Spectroscopy (MTS) and Doppler Free Spectroscopy (DFS). The horizontal axis is frequency in MHz, with 0 corresponding to the 85Rb F = 3 → F′ = 4 transition. The red x corresponds to the transition frequency needed for the MOT. The two groups of absorption curves are from 85Rb (right) and 87Rb (left). This is a simplified figure based off experimental data from McCarron et al [5].

Modulation Transfer Spectroscopy Overview

The output of MTS is shown in Fig. 4. It is compared to a signal generated by Doppler Free Spectroscopy (DFS). We need to lock to the spot marked with a red x. The signal from DFS is more difficult to use in a feedback loop since it is difficult to lock to an extrema. The signal from MTS is easier to lock to since the locking point is a zero-crossing and has a non-zero slope. Moreover, MTS signals are generated mainly at frequencies forming closed optical paths. The red x in Fig. 4 is the 85Rb F = 3 → F′ = 4 closed optical path transition frequency, which is 6 MHz from the frequency needed for the MOT. This 6 MHz offset will be accounted for in the PID reference voltage.

MTS Optical Setup

The optical setup for MTS is shown in Fig. 5. The single-frequency laser (around 780 nm) entering the MTS setup is split into two beams (of about equal power), a pump beam and a probe beam. The pump beam goes from left to right in the Rb cell. The probe beam is passed through an Electro-Optic Modulator (EOM). This EOM uses a 5 to 20 MHz sinusoidal voltage from a function generator. After passing through the EOM, the probe beam has a center frequency of the laser diode, plus two sidebands at +10 MHz and -10 MHz from the center frequency (assuming the EOM is operating at 10 MHz). The probe beam goes into the Rb cell from right to left. Thus, the pump and the probe beam are counter propagating. The probe beam then goes to the photodiode. The signal from the photodiode is mixed with the signal from function generator. The resulting signal is then low-pass filtered to get the final output voltage.

FIG. 5. Experimental setup. Abbreviations: PBS (Polarizing Beam Splitter), EOM (Electro-Optic Modulator), VCO (Voltage- Controlled Oscillator), MTS (Modulation Transfer Spectroscopy), PID (Proportional-Integral-Derivative), MOT (Magneto- Optical Trap), PD (Photodiode), OSC (Oscillator, or Function Generator), MIX (Mixer), LP (Low-Pass Filter). Simplified experimental setup as used in McCarron et al [5].

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