Laser-frequency stabilization using a lock-in amplifier

We describe how a lock-in amplifier can be used in a feedback loop to lock the frequency of a laser to an atomic transition in Rb-85. A simple physical explanation is presented to describe the shape of the feedback signal generated by the "lock in" and the dependence of this signal on the phase of the reference signal. We also present a mathematical model of the feedback signal. Using the output of the lock in as feedback, we show that the laser frequency can be stabilized to a few MHz. The experiment is relatively simple to set up and could easily be adapted as an undergraduate laboratory experiment.