# Atomic clocks and how to synchronize them

While teaching measurement precision in the class, our professor mentioned atomic clocks. I have two questions:

1. What exactly is exactly an atomic clock?

2. How do we synchronize two atomic clocks far far away, e.g. in New York and Beijing?

The Wikipedia article you cite explains how atomic clocks work, but I have to concede that all such explanations tend to be a bit confusing for the non-nerd. I'll attempt to pick out the main points.

Suppose you generate a microwave signal with a frequency of 9GHz. Then if you want to time 1 second you just count $$9 \times 10^9$$ cycles of the microwave and that gives you one second. Conversely suppose you want to time something. You start counting the microwave cycles when your event starts and stop counting when it finishes. However many cycles you count, you just divide this by $$9 \times 10^9$$ and that gives you the time in seconds.

The trouble is that this only works if you are absolutely sure your microwave is exactly 9GHz. An atomic clock uses the fact that caesium atoms absorb energy at exactly 9.192631770GHz. So what you do is shine your microwave beam through a gas of caesium atoms and adjust the frequency until the caesium atoms start absorbing it. Then you know it's frequency is exactly 9.192631770GHz and you can use it as a reliable timer.

This is what atomic clocks do, though as you can imagine the technical details can get extremely complicated. Have a look at this NIST article for a good popular level description of how it's done in practice.

Atomic clocks are synchronised with each other by using GPS and sending each other synchronisation signals. In fact, about 200 atomic clocks, all synchronised with each other, are used to define International Atomic Time.

• Can you please tell me when you say "Then if you want to time 1 second you just count 9×109 cycles of the microwave and that gives you one second. Conversely suppose you want to time something. You start counting the microwave cycles", what do you mean by microwave cycle? What kind of cycle is it? Do you mean a microwave signal? A single photon? – Árpád Szendrei Nov 9 '20 at 19:42

Sometimes a molecule's(such as NH3) inversion frequency is so sharp that it can be used as a safe information about time. Sometimes a molecule's vibration is sharp enough sometimes rotation of a tip is sharp enough so you can use that as a primary standard. You must know the temperature and pressure.

You need to know the distance when the sync signal arrives then you calculate from relativistic approach. Also think about the estimated calculation time.

Given your refernce to a 9Ghz clock, one can assume you are talking about a Caesium primary reference standard clock like the HP5071 or similar.

These clocks are based on physics discovered and made practical by Isador Rabi on magnetic resonance for which he was awarded the Nobel in 1944. This led to the Stern-Gerlach experiment that forms the core physics package of a caesium primary standard atomic clock. I mention primary standard here as there are other caesium clocks which are not primary standards and use techniques like coherent population trapping to realize their clock. Stern also received the Nobel in 1943, however it was not for the Stern-Gerlach experiment.

The Stern-Gerlach experiment basically described is a mass spectroscopy experiment which can discriminate between atoms with different spin moments. In the original experiment, Stern used silver, however caseium is better suited to a clock since there are two and only two ground states. Caseium in a vacuum is heated in an oven that produces a beam of caesium atoms escaping from the oven through a first magnet that selects (steers) them through a microwave cavity tuned to the 9192... MHz that corresponds to the "definition" of a second. This pumps the caseium atoms into the desired hyperfine state which emerge from the microwave cavity through second magnet that steers resonate atoms to a detector where they are counted. Non-resonate atoms are steered away from the detector and are not counted. By carefully varying the frequency of the 9192... MHz microwave field, and observing the intensity (count) of the Cs atoms at the detector, a feedback loop is established that directly relates the microwave frequency to the resonance of the Cs atom in the desired state. Maximizing the intensity of the detected Cs atoms by varying the microwave frequency, in effect provides a "count" of the 9192...MHz from the SI definition.

This microwave frequency source is thus locked to atoms and can be divided down to the output frequencies normally provided by a Cs reference clock (typically 10Mhz, 5MHz and 10.24 Mhz) Normally a 1PPS (once a second) pulse is also provided which is accurate to a small number of ns. The stability of a Cs primary reference clock exhibits and Allen Deviation of about 10^15. This is exceeded only by hydrogen masers at 10^17 and newer optical clocks which have even better stability. Not bad for technology that was invented in the 1920s and first realized as a clock by Louis Essen and Jack Parry in 1955. The Cs clock was predated by an NH3 clock at NIST (then NBS) in 1949 but it was less accurate than quartz at the time.

The Cs primary reference standard (eg. HP5071a) does not need calibration since it relies directly on the physics. Since it is a mechanical system however, there are a lot of systemics which must be accounted for, for example, the stability of the oven temperature, the quality of the microwave source, the ability to control the microwave frequency, the physical characteristics of the electronic components used to divide the microwave frequency to output frequencies and a host of others. In theory one properly constructed Cs clock should be the same as the next, to get an idea of how true this is, one can compare the performance of the clock ensembles at the various national labs like NIST an USNO.

As for the synchronization aspect of your question, as explained to me by Judah Lavine at NIST, the time scale ensembles like NIST and USNO are not in fact steered (synchronized). The clocks all run at their natural frequency, some faster, some slower than the theoretical. These measurements are then combined to produce weighted average paper time-scale that is then used to steer a physical device that realizes the paper-time scale. This second seered physical device is then used as the reference and distributed by the time services. By using a sufficiently large number of clocks in your ensemble, the variation across clocks is effective averaged out and the weighted average tends to the true paper-time scale.

For users of the timescale however, the situation is different. A timescale user (for instance a far flung observatory, or someone trying to use GPS navigation) their clocks need to be ticking at the same rate (syntonous (same frequency or tone)) and synchronous (displaying the same time) - for a primary reference standard clock like a Cs clock or Hg maser - the assumption is that the physics package will cover the syntonous requirement - it's why they are call primary. The synchronous aspect is managed by a variety of services, for example common-view GPS, Two way satellite time transfer (TWSTT) (pronounced "twist"), or physical time transfer by using a traveling clock.

Originally, the only mechanism for time transfer was the traveling clock. The traveler was set to the master clock at the start, was left undisturbed until arriving at the destination clock and the destination clock was "set" to the time displayed on the traveling clock. The frequency of update was limited by the speed at which the traveling clock could be moved and the constraint of cost of travel.

From the 1930s thru the 1950s, Western Union offered a time service to provide automatically synchronizing clocks, using signal transmitted over telegraph lines. The time source was the US Naval Observatory and synchronized once an hour, when a pulse was transmitted to the clock that would reset the clock to the hour. This keep the observers clock accurate to a few seconds of the pendulum clocks then in use at the USNO (later replaced by Quartz).

As timing tracability became more of a requirement (for example for testing labs to verify that their clocks matched a known standard when calibrating instruments) NBS - now NIST introduced into the WWV, WWVB and WwVH broadcasts modulations which enable a user to synchronize their clock to within a few miliseconds of the national standard clock. In fact, during the time period of "stretchy seconds" (1960 (start of atomic time) to 1972 (introduction of leap seconds) the nominal 10MHz frequency of WWV was steered to reflect the proper frequency of oscillation for a clock - and lets not start the leap second discussion.

As timing requirements became more demanding, and atomic clocks more available, WWV while still useful, could not satisfy the most stringent applications (like precise navigation and astronomy applications like VLBI). The initial solutions were to use traveling atomic clocks, and this works well (TWSTT verification still uses this today) the limitations of traveling clocks still applied. In addition, since most Cs atomic clocks were transported by aircraft, the most demanding users ran afoul of the revativistic effects introduced by flying a atomic clock near mach 0.6.

The solution was TWSTT, but this requires expensive hardware on both ends of the link and a dedicated satelite channel between the synchronizing station and the master station. The solution was extremely precise, in one installation that I personally know about, the time delta after 1 year was only 300ps - yes picoseconds.

Common view GPS also is a satellite transfer mechanism but relies on the stability of the GPS constelation to be effective. The idea is that if two ground stations can be certain they are observing the same subset of GPS satellites, then this subset can be used to determing the true time at the two stations. This assumes that the ionospheric effects are considered by each of the station. Without the stablity of the GPS system being assured by the GPS operations center (GPSOC) this mechanism would be less effective.

Optical cable transfer is also possible and may have resulted in one of the largest oops of all time when some reserchers at CERN anounced they had observed faster than light neutrinos, only to find that a faulty optical connector was the cause of the timing discrepancy.

Several other mechanisms for the transfer of time have been developed, LORAN which operated from the 1940s to the 1980s is probably the most notable.

References (web based to be easy to find): Appendix A describes most of the time transfer services used today and in the recent past. http://www.allanstime.com/Publications/DWA/Science_Timekeeping/TheScienceOfTimekeeping.pdf

The Western Union time service description (not an easy google search) https://www.kensclockclinic.com/pdf/SWCC%20Historical%20Docs/Western%20Union%20Time%20Service%20Bulletin%2046-B.pdf

Timekeeping at the US Naval Observatory TWSTT - https://www.usno.navy.mil/USNO/time/twstt/what-is-twstt

https://www.nist.gov/pml/time-and-frequency-division/time-services the NIST Time and Frequency Division in Boulder

A media treatment of the same subjects: http://www2.unb.ca/gge/Resources/gpsworld.nov-dec91.corr.pdf

LeapSecond.com - a resource for time-nuts - some links are broken :-(

bipm.org - all things weights and measures

• Thank you very much for such a thorough and comprehensive answer! – Goodarz Mehr Nov 9 '20 at 20:50