Optical Phase Lock Loops
The renowned physicist Paul Dirac wrote in his famous book, The principles of Quantum Mechanics, that "A photon interferes only with itself. Interference between two different photons never occurs." A common (and wrong) interpretation of this statement is that one can never observe interference from two different laser sources. In fact, such an interference was demonstrated experimentally over and over again.
Conducting this experiment is not an easy task. The main challenge is simply that two different lasers are hardly ever at the exact same frequency. Typical laser light is oscillating at a frequency of hundreds of terahertz. To notice an interference between two different beams with our bare eyes, their frequency difference has to be smaller than few tens of Hertz (otherwise they would flicker so fast we won't notice). This would require the frequency of light emitted by the two lasers to be accurate to one fraction out of ten trillion.
Even if we could nail the laser's frequency with such accuracy, the phase of the laser's field is randomly changing due to quantum and environmental noise. Since two different lasers have uncorrelated noise, the interference might be washed out.
So how do we conduct this experiment? Electrical engineers have solved this problem in every cellphone. They simply "lock" two oscillators together using a "phase lock loop". The optical implementation of that idea is called "Optical phase lock loop". This is how it works - an electronic circuit monitors the relative frequency difference of the two lasers. If that frequency is getting too high, the electronic "feeds-back" a signal to the laser that forces it to drift back to place. Of course, implementing this circuit might not be that easy…
We were interested in this experiment because we wanted to demonstrate how control over frequency and phase can be used for beam-steering. This is how it works -
Few "slave" lasers are locked to a "master" laser using an optical-phase-lock-loop, shown in the figure above. Control of the relative phases of the lasers (using electronic phase shifters) can be used to shape the interference pattern.
Notice the very pronounced interference between the two lasers:
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So - was Dirac wrong after all? The answer is NO. How come? Well, the realm of quantum mechanics is almost magical - a single photon can exist in both laser cavities at the same time…