Building a Better Clock

I see no progress in this industry. These clocks are no faster than the ones they made a hundred years ago.
– Henry Ford

I really hope he was kidding, but assuming he was it’s pretty funny to a timing geek like me. The way you make clocks better is by making them more precise and accurate, and the levers for this are hidden in the equation for “counting the ticks”. If our ability to count precisely is somehow limited, e.g. if we had an oscillator — like a wheel — and we could measure its angle to a precision of 3.6º, then letting it go for one oscillation represents a 1% measurement, but that same absolute error for 100 oscillations is 0.01%, and we can get there either by integrating longer or by having an oscillator with a higher frequency. So “more ticks” is better … if we don’t have a noisy oscillator. Certain noise processes don’t integrate down, so another lever is to improve the noise, or possibly the noise characterization, of our clock.

Better clocks came in the form of Harrison’s chronometer which could be put to sea, and which included advances like using multiple kinds of metals to reduce temperature effects, and a spring which maintained constant tension. On land, improvements came in the form of better pendulum clocks, culminating in Riefler and Shortt clocks in the early 1900’s, with temperature compensated pendula (to inhibit the length from changing), kept under moderate vacuum to reduce drag and possible humidity effects, and were capable of performing at a precision of around a millisecond per day, and are examples of going to a higher frequency (a period of a second rather than a day) and minimizing the noise effects. Going into the 1930’s-1940’s, quartz oscillators, using much higher frequencies (many kHz rather than 1 Hz) became the best clocks.

Up to this point, the length of the second was defined in terms of a fraction of the tropical year in 1900, which was close but not identical to 86,400 seconds per day (being off by a few milliseconds), but atomic standards were investigated and in 1967 the definition of 9,192,631,770 oscillations of Cs-133 hyperfine transition was adopted, and atomic timekeeping defined Coordinated Universal Time (UTC) starting in 1972. This also marked the start of inserting whole leap seconds to match atomic time with earth rotation time; prior to that it was done by adjusting clock frequencies or inserting fraction-of-a-second steps in time.

Which brings us to atomic clocks. How do you build one? Your atomic system is a filter, giving you a feedback signal by measuring the atomic response of the atoms to some input; the basic layout of an atomic clock is to send a hot atomic beam through two microwave cavities, which is the Ramsey method of separated oscillatory fields. The input signal is usually a radiofrequency signal (e.g. 5 MHz) that is multiplied up to the resonance frequency of the atoms. As the atoms pass through the first microwave cavity, the absorbed radiation causes them to oscillate between the two ground states of the atom. (In QM parlance we have put them in a superposition of the states with a pi/2 pulse) These atoms oscillate for some time, which depends on their speed and the distance to the second cavity. The second cavity completes the interaction — if the microwaves were exactly on resonance all of the atoms will end up in one state, but if they are off resonance, some atoms will be left in the other state, and the numbers depend on the frequency offset. So counting the atoms in each state gives you information about the frequency of your source, as measured by the atoms. An important point here is that all of these measurements are all frequency comparisons of two oscillators — this is true of all clock measurements: one clock as measured by another.

The best atoms to use are the alkali atoms, which have a simple structure, and Cs-133 has the largest hyperfine splitting, plus the technological advantage of being the only stable isotope of Cs. It also turns out that alkali atoms’ simple electronic structure makes them easy to laser cool, trap and otherwise manipulate with radiation pressure, which is important because there are limitations of an atomic-beam-based device — the interaction time is short. You can’t separate the microwave cavities very far without the deflections from gravity and other effects give you significant measurement errors. Fountains turn the clocks 90 degrees to use a vertical beam, but the atoms must be slow and cold for this to work. But an atom tossed a meter in a vacuum will take about a second to return to is starting point, vs several milliseconds of transit time for a beam clock — you get an improvement of around 100 in the number of oscillations you are counting.