How atomic clock works? I came across to atomic clocks when I was learning special theory of relativity  in part Time dilation  i simply want know how atomic clock defer from normal clocks.
 A: Basic Principle of Atomic Clock:
To make the Atomic Clock, scientists used Cesium atom (133^Cs) in its lowest energy state we can call it (V1). 
When they bombarded Cesium atom by the micro-wave of precisely the proper frequency of actually 9,192,631,770 cycles per this period of time, the outermost electron of Cesium atom reversed its spin direction, this makes Cesium atom move to the second state i.e (V2). 
This transition took place in a certain interval of the time which was the difference between the two states.
ΔVcs= V2 - V1
This ΔVcs represents the time electron takes to reverse its spin direction which can be defined as One Second abbreviated (s).


So, Why using the Cesium atom in the Atomic Clock?


*

*It's not affected by the effect of time on atoms.

*It has a fairly stable atomic radioactivity and can stay like that for many years compared to other atoms.
Hope this can answer your question!
A: 
The big difference between a standard clock in your home and an atomic clock is that the oscillation in an atomic clock is between the nucleus of an atom and the surrounding electrons. This oscillation is not exactly a parallel to the balance wheel and hairspring of a clockwork watch, but the fact is that both use oscillations to keep track of passing time. The oscillation frequencies within the atom are determined by the mass of the nucleus and the gravity and electrostatic "spring" between the positive charge on the nucleus and the electron cloud surrounding it.

In a pendulum clock the oscillations of the pendulum are "counted" ( in analogue) by the turning of the hands of the clock.
Atomic clocks depend on much higher  oscillations, as described above, than the pendulum, and thus are more accurate, In a given time interval more counts occur and the error in counting time is much smaller.
See also this video .
A: I'm going to dump some notes of interest as I learn more and more about it here.
https://www.youtube.com/watch?v=eOti3kKWX-c Inside the HP 5061A Cesium Clock by CuriousMarc has some good information.
Launched in 1964, the HP 5061A is a very portable atomic clock similar to the ones that were taken on the plane relativity experiments such as the Hafele-Keating experiment.
Being so compact also carries the educational advantage that we can have a good snapshot of the entire system. Being mass manufactured also means it is well documented. The manual of the closely related 5061A can be downloaded from https://www.manualslib.com/download/1501827/Hp-5061b.html
https://youtu.be/eOti3kKWX-c?t=250 shows the lid open:

The manual contains a more perpendicular although ultra blurry/low res shot with some key elements labelled:

Table 5-1. HP 5061B Assembly Designations lists the parts some of which are labelled in the picture, some which I can more or less understand:

*

*A10 Quartz Oscillator Assembly

*A12: (big cylinder at the bottom) Cesium Beam Tube is the Cesium oven. Marc mentions that this is a disposable part, as after some use, the whole cesium evaporates, and then you have to get a new cylinder, 40k USD a pop, now from Agilent, HP spin-off.

*A18: +3500 Vdc Power Supply Assembly. So we understand that high voltages are needed at some point.

*A19: -2500 Vdc Power Supply Assembly. Idem.

contains a schematic which is also highlighted in Marc's video:

to which we can add some comments:

*

*first to the left there is the Caesium oven, which produces a stream of Caesium atoms flying out of it. The cylinder is well sealed and there is a vacuum inside of it, otherwise the Caesium would crash into air molecules all the time. Markings say it operates at 129 Celcius, so a slight hazard, but not insane either.


*the "A" magnet selects only caesium atoms with the low energy state. This happens because the spin  acts like a little magnet, and so the "A" magnet makes atoms with different spins turn in slightly different directions


*the "C" field is the microwave cavity, i.e. a specially shaped piece of metal that given some input voltage produces microwaves of a certain frequency, more or less like in your microwave oven. But this one seems to be shaped like a C instead.
This microwave frequency is tuned to excite the caesium atoms. Such cavities were first created in WW2 for radar systems, and were a revolutionary technology, as we didn't have a very efficient way to produce microwaves before them.


*the "B" magnet acts like the "A" magnet, but we then select the excited beam


*the hot wire ionizer and electron multiplier together detect incoming atoms crashing into them:

*

*when the atom hits the hot wire ionizer, it loses an electron  and becomes charged (ionized)


*the electron multiplier amplifies individual charged particles to a measureable signal. It is made of a sequence of negatively charged plates, each one of which emits more and more electrons when an incoming electron hits, thus producing an electron avalanche from a single input electron. The diagram from Wikipedia is a bit clearer:

The first paragraph of the manual gives an overview of the working procedure that is worth quoting and trying to fully understand:

1-3 In the beam tube, a state-selected beam of Cesium
133 atoms passes through a microwave cavity. When the
frequency of the applied microwave magnetic field,
derived by multiplying the quartz crystal oscillator
frequency, is near the hyperfine transition frequency of
Cesium 133 (9,192,631,770.0 Hz.), the microwave signal
induces transitions from one hyperfine energy level to
another. Those atoms which have undergone such a
transition are detected by a hot wire ionizer and electron
multiplier. The microwave field is frequency modulated
at a low frequency of 137 Hz. When the microwave
frequency deviates from the center of the atomic
resonance, the current from the electron multiplier
contains a frequency component which is the same as
the modulation frequency. The magnitude of this component is proportional to the frequency deviation, and
the phase indicates whether the microwave signal is
above or below the transition frequency. This component
is filtered, amplified, and synchronously detected to
provide a dc voltage proportional to the frequency
deviaton. The integral of this dc voltage automatically
corrects the quartz oscillator frequency.

From this we can break out some stuff:
Caesium 133
Caesium 133 is used.
This is the stable isotope.
It has nothing to with the more notorious and highly radioactive (but also very useful) Cesium 137 isotope, so it is not a choice related to radioactive properties of Cesium, but mostly electronic properties.
Reasons to choose caesium:

*

*it evaporates at relatively low temperatures to produce our beam

*its hyperfine transition has a good energy to work with. See section below.

Hyperfine transition
The hyperfine transition is a difference of energies between spin up and down of the outermost electron of Caesium.
This difference exists due to interaction between the electron spin and the nuclear spin, and as you might imagine the interaction energy is small, that's why it is hyperfine.
It can be contrasted with much higher energies such as:

*

*gross structure: jumping between two different orbitals with different N

*fine structure
All of this types of structures were first observed as line splits in spectroscopy experiments on hot samples of atoms.
Our transition energy corresponds to light with frequency 9,192,631,770.0 Hz which means that we have a wave of length of about 3 cm, which is in the microwave range. This type of centimeter wide wavelength is very convenient, as it is a convenient size for us to make metallic objects out of, which can be used to efficiently produce such frequencies.
Quartz crystal
Crystal oscillators are what keep time in modern electric watches. They are quite precise (TODO how much), but still have some variability because they are a piece of mechanical material, and are therefore affected by temperature and pressure differences.
The Caesium transition is used in a feedback control loop with the crystal oscillator to overcome such variations. This works a a fundamental level because the Caesium transition frequency is absolutely fixed for different temperatures and pressures.
Modulation frequency
TODO understand that part better. I should have paid more attention to my EE undergrad. And the should have taught me cool stuff like this ;-)
Marc tries to explain a bit more at: https://youtu.be/eOti3kKWX-c?t=903 over another block diagram from the manual but it is still not dumbed down enough for me.
What seems to happen is:

*

*an approximate frequency close to the target 9,192 MHz is synthesized

*a small frequency of 137 Hz is added on top of that frequency

The corrections then appears to depend only on this 137 Hz modulation.

Ion pump vacuum system
At https://youtu.be/eOti3kKWX-c?t=1077 Marc highlights the ion pump, some crazy ingenuous vacuum system. I think you have to keep pumping even though the tube is sealed in part or mailny because stuff inside the tube evaporates little by little.
Large more precise systems
https://youtu.be/Tc_tDVbjCQk?t=359 shows a Caesium font from the National Physical Laboratory (British NIST). It is huge. He explains that the Caesium is laser cooled in that system for greater precision for some reason.
