Beat signal of two lasers

The detuning of the collimator laser should be in the order of -110 to -120 MHz. If we applie the magnetic field of about 80 Gauss over the vapor cell, the Lamb dip can not be seen well enough to stabilize the laser with this method. The reason that with higher detunings the detection of the Lamb dip gets more difficult, is that the magnetic field generated by the coil is not completely homogeneous, since the cylinder does not have an infinite length. The magnetic field is weaker at the ends of the vapor cell, and the energy difference between the two states is not the same everywhere in the vapor cell. This broadens the Lamb dip, and the detection of the Lamb dip gets more difficult. So for the collimator laser another way of stabilizing the laser is needed. The method we use to stabilize the collimator laser is by making use of the beat signal of the collimator laser and the MOC laser.

To stabilize the collimator laser, we split off a small laser beam with a glass plate, and lead it with some mirrors through a beam splitter (see fig. 2.10). Another beam, coming from the MOC laser, is led through the same beam splitter, after which the two beams overlap completely, and are focussed on a fast photo diode with a lens. The two laser beams have an intensity of the same order of magnitude. The two overlapping laser beams give rise to a frequency $\omega_{MOC}-\omega_{coll}$ and a frequency $\omega_{MOC}+\omega_{coll}$, the frequency difference between the MOC laser and the collimator laser, and the sum of the two frequencies. The photo diode can detect frequencies up to 1 GHz. So the sum of the frequencies is too high to be detected, and the frequency difference $\omega_{MOC}-\omega_{coll}$ can only be seen if the two frequencies are very close to each other.

Figure 2.10: Setup of the laser stabilization of the Collimator laser.

The frequency of the MOC laser is stabilized using the saturation spectroscopy, so by observing the photo diode signal, the fluctuations of the frequency of the collimator laser can be detected. A home-built electronical device divides the frequency of the signal of the photo diode by 2048, and compares this value with a reference signal which is provided by the sync output of a function generator.

If the frequency difference $\omega_{MOC}-\omega_{coll}$ becomes larger, the collimator is drifting away from resonance to the red, and a small correcting current is sent to the fast entrance of the power supply of the laser to correct for this drifting. This correction signal is sent once every second, and keeps the collimator locked with an accuracy of a few MHz. Unlike the laser stabilizing method making use of saturation spectroscopy, this method of stabilizing the laser will find the correct frequency again even if the laser has drifted away up to a 100 MHz. This can be simply seen by the fact that the increase or decrease of the beat signal implies a decrease or increase respectively of the frequency of the collimator laser. Only when the beat signal gets higher than 1 GHz, or when the collimator laser is detuned to the blue instead of the red, the correct frequency can not be found. A disadvantage of this method of stabilizing is that the frequency is determined less accurate, but for the collimator laser a spread of a few MHz is accurate enough.