Is your clock laser stable?

Take a tape measure for example: To be any good it should give you the same length readings today and also tomorrow. How can you verify that its length is stable over time? Easy, you go into a hardware store, get a quality measure from a respectable brand and verify that the scale of your questionable tape measure agrees and continues to agree with the known-to-be-good ruler. What if you are all alone on a far-away island and all your rulers are just sticks? Then you might be in trouble (for probably more than just this one reason). Time to get creative.

You are facing the same issue if what you want to measure is time and your ruler is a clock laser. We previously saw that the stability of a reasonably good clock laser is in the one in 10¹⁵ range. State of the art clock lasers can even reach stabilities in the 10¹⁷ to 10¹⁸ ranges. The challenge is to find a known-to-be-good reference for such a stable frequency to compare against. Because that is what it comes down to: Comparisons. Lengths used to be compared against the meter length reference "stick" (the so-called prototype that till 1960 served as the official SI reference) and masses were compared against a reference weight (another prototype, stored with great care in a vault in Paris and in use till 2019). For comparisons of time the SI defines the frequency of a specific microwave transition of cesium. This is a very precise definition. However, it can currently "only" be realized with an uncertainty in the 10⁻¹⁶ range. That is not stable enough to serve as a reference for really good clock lasers (which would be like trying to measure something with micrometer precision if all you have is a ruler with millimeter marks). In addition, more readily available time references have uncertainties in the 10⁻¹² realm, rendering practical comparisons to absolute references even less feasible.

The solution is to fight fire with fire, and to compare clock lasers against each other. This works by creating a so-called optical beat between two clock lasers of similar frequency. In this interference phenomenon the two laser lights are precisely overlapped with each other and the resulting signal recorded on a fast photodetector. If you have two tuning forks that vibrate at slightly different frequencies you will generally be able to hear in addition to the two individual tones a modulation that corresponds to their frequency difference, a beating pattern. The same is true for light, and the photodetector will give a signal that corresponds to the laser light frequency difference that will usually be in the MHz to GHz radio-frequency regime. It is this signal that can be characterized with sufficient precision by good quality equipment.

This leaves us with a bunch of optical beat recordings. If only two clock lasers are available, only a single optical beat can be generated. In case this beat signal is not stable in time, one cannot tell which laser is to blame. For this it takes more clock lasers. The more beat signals available the better one can judge the stability of each laser. Its a laborious task but for the time being our only way of reaching out to those extreme levels of stability. A similar challenge people face with the prototype kilogram. Many duplicates were made and distributed around the world. Every 40 years a selection of these is reunited for comparisons. By now, their masses have drifted apart by over 50 µg. Which one is right and which one is wrong? Nobody knows, but due to the many specimen out there at least some indications exist. That is the nature of comparisons: All is relative, but statistics is key.

Previous articles of the "Clock laser 101" series:

1. What is a clock laser?
2. How does a clock laser tick?
3. What makes a clock laser so stable?