Please gradually expain principles of atomic clocks

[Martian2020]

TL;DR Summary

I want deep fundamental understanding how atomic clock works. This is supposed to be step-by-step discussion of one principle in a time, please do not jump to next principle before I ask for next step. It could be many days thread.

Atomic clocks. I tried to read wiki, read some QAs (on stackexchange), use web search. I would spend way much time to link all together alone, so I ask your help. I'm not sure if its called top-down or bottom-up.

1) Principle 1.
Please confirm (or correct) my understanding of 1st underlining principle:
1) frequency of photons emitted by Caesium atoms when exited by electro-magnetic radiation is same.
Is it correct? Should I start here or is there even deeper principle?
Absolutely same or with margin of error of e.g. uncertainty principle etc.?
In general relativity is it (frequency of oscillation per unit of time) called proper time?

 

[hutchphd]

1) perfectly isolated Cesium atoms yes. But you can never really totally isolate so a very narrow range of frequencies, yes. It can be made ~arbitrarilly narrow using multiple measurements over longer times. Counting the wiggles will convert frequency to time. This will be the proper time for the cesium atom.
Corrections?(not an expert here...)

 

[Nugatory]

In general relativity is it (frequency of oscillation per unit of time) called proper time?

Proper time (an essential concept in special relativity as well as general relativity) is what a clock measures. We have a clock, it reads 3:45, a bit later it reads 3:47, we do some subtraction and we say that there were two minutes between the events “clock reads 3:45” and “clock reads 3:47”. The clock has measured the passage of two minutes. That two minutes is a real physical thing - if I’m sitting next to the clock while it measures two minutes I’ll age by two minutes.

There’s nothing special about atomic clocks here. Any time-dependent process can be used as a clock: count heartbeats, watch sand sliding through an hourglass, track the sun moving through the sky during the day, count swings of a pendulum in an old-fashioned grandfather clock, ... We use atomic clocks because they are very accurate, and that’s important in experiments where we’re looking for a few microseconds of difference between one event and another. Thus, I’ll suggest that you don’t need to do a deep dive into the working of atomic clocks - just accept that if we want to do very accurate measurements of time, we have a way of doing them.

Note that the clock has tobe present at both events to measure the time that has passed between them. Suppose someone calls me to say “the airliner just took off” and my clock (present at the event of me receiving the call) reads 2:00, then sometime later I get another phone call telling me that the plane just landed and I see that my clock reads 4:00. The clock has not measured the flight time; it has measured the time between me receiving two phone calls.

In casual English, we’d say that the plane took off at 2:00 and landed at 4:00, but it would be more accurate to say that the plane took off at the same time that our clock read 2:00 and it landed at the same time that our clock read 4:00. We’re attaching timestamps to distant events according to what our clock read “at the same time” that they happened. These timestamps are called “coordinate time”, and it’s important not to confuse coordinate time with proper time - one is something we measure, the other is an artifact of how we define “at the same time” for spatially separated events.

That definition is trickier than it looks. Google for “Einstein clock synchronization” and “Einstein train simultaneity” to see why.

 

[f95toli]

At the level of accuracy where a regular Cs clock (fountain) operate (around 1 part in 10^15) there are very few "funny" effects and you can understand how it works using using very conventional (Newtonian) physics. Most of the complexity of the clock has to do with the engineering rather than the physics.

Things get a bit more complicated when using more modern optical clocks since they are quite a bit (1000-100000) more precise and you can observe GR effects even when comparing to clocks in the same lab. Some of these clocks also use entangled states etc so the physics is quite a bit more complicated.

Also, do note that whereas people tend to mean Cs fountains when they talk about atomic clocks; most "atomic clocks" are actually hydrogen masers. A full metrology-grade clock system (and there aren't that many of those) consists of one Cs fountain (good long term stability) "steering" one or several hydrogen maser-based clocks (good short term stability); but it is always the latter that is outputting the time signal . One -obvious- reason for this is that fountains because of the they work don't give a continuous output.
Masers are commercially available and quite a bit cheaper (and simpler) than a Cs fountain.

There are also other types of "atomic clocks" (e.g rubidium clocks); so you need to read the fine print to see what they actually mean

 

[Martian2020]

1) perfectly isolated Cesium atoms yes. But you can never really totally isolate so a very narrow range of frequencies, yes. It can be made ~arbitrarilly narrow using multiple measurements over longer times. Counting the wiggles will convert frequency to time. This will be the proper time for the cesium atom.
Corrections?(not an expert here...)

2) Principle 2: averaging
Thank you. I recall reading measurements are that precise due to say 10,000 atoms and averaging. Photons make interference patterns. How to count wiggles in view of interference? There are thousands atoms emitting photons at slightly different times from slightly different places as I understand.

 

[hutchphd]

Roughly speaking the $10^4$ atoms should reduce the uncertainty of the mean value by $10^2$. I was talking about "counting the wiggles" in the oscillations in this (very low energy) hyperfine transition. Someone who really knows how this part is done should speak to this! I will watch an learn.

 

[f95toli]

2) Principle 2: averaging
Thank you. I recall reading measurements are that precise due to say 10,000 atoms and averaging. Photons make interference patterns. How to count wiggles in view of interference? There are thousands atoms emitting photons at slightly different times from slightly different places as I understand.

The principle is not actually that complicated. The clock operates as a "frequency closed loop" where the frequency of an an external microwave oscillator is being constantly compared to the transition frequency between the two states that are used (a hyperfine transition of Cs-133). The "comparison" can be done by irradiating the Cs atoms and seeing how much of the signal is absorbed, the frequency of the external oscillator is then adjusted slightly and you try again until you find a minima.

There is no need to think about photons for a Cs clock; the frequency is "only" 9.2 GHz which is not that much higher than the clock in the CPU of your computer. That is, the electronics that is used is just off-the-shelf microwave kit which is today is mass produced for the telecom industry.
Also, because of the loop you don't actually need to "count" anything; this can (and is) all be done using analogue electronics.

Again, you need to be careful about what you mean by an "atomic clock" here; the principle of the hydrogen maser is somewhat different and there you really do have an emitted signal (a maser is just the microwave version of a laser).

 

[Imager]

n casual English, we’d say that the plane took off at 2:00 and landed at 4:00, but it would be more accurate to say that the plane took off at the same time that our clock read 2:00 and it landed at the same time that our clock read 4:00. We’re attaching timestamps to distant events according to what our clock read “at the same time” that they happened. These timestamps are called “coordinate time”, and it’s important not to confuse coordinate time with proper time - one is something we measure, the other is an artifact of how we define “at the same time” for spatially separated events.

Thank you @Nugatory this is very helpful!