The second is defined as
I am confused as the hyperfine transition frequency is not fixed, i.e., it has a finite linewidth. The frequency is not well defined.
Is it because the linewidth is very small? If so, why is it small?
$\begingroup$
$\endgroup$
8
-
3$\begingroup$ It is trivially sensible to just pick the middle point of the distribution, no matter which linewidth is experimentally obtained. As technology improves, the linewidth gets smaller, but this middle point should stay where it is.. $\endgroup$– naturallyInconsistentCommented Sep 11 at 11:20
-
1$\begingroup$ As I said in physics.stackexchange.com/a/677946/123208 Time is what a clock measures. [...] it doesn't actually matter that each of those oscillations have a slightly different duration. You count 9192631770 of them and you have an official SI second. That is, the variation of the Cs-133 hyperfine transition is baked into the definition of the SI second. $\endgroup$– PM 2RingCommented Sep 11 at 12:02
-
$\begingroup$ @PM2Ring, So why is International Atomic Time based on the average of hundreds of atomic clocks? Why not elect a single one of them to be the master clock, and have however many others as backups that are synchronized to the master? $\endgroup$– Ohm's LawmanCommented Sep 11 at 15:12
-
1$\begingroup$ @Ohm'sLawman Guilty as charged. ;) The SI second is defined in terms of a caesium atom in ideal conditions. No actual physical clock can achieve that ideal, so we need to use statistics to estimate that ideal behaviour. The Heisenberg uncertainty is intrinsic to the definition of the second, but we can still try to reduce the other causes of variation (like atom temperature) as much as possible. Also see en.wikipedia.org/wiki/Terrestrial_Time $\endgroup$– PM 2RingCommented Sep 11 at 22:31
-
1$\begingroup$ It's like when the inch was defined as the length of 3 barleycorns. To maximise precision, you take multiple samples from a uniform collection of barleycorns that has been cleaned of the obvious outliers. $\endgroup$– PM 2RingCommented Sep 11 at 22:32
|
Show 3 more comments
1 Answer
$\begingroup$
$\endgroup$
The energy difference between every two atomic levels is a well-defined value, as those levels represent distinctive quantum states. So there is no problem with a statement that those two hyperfine levels in Cesium are separated exactly by ~$9.2$ GHz. So, in that sense, the transition frequency is fixed.
Of course, you are correct that observed transitions have their inherent widths that limit how precise one can lock their oscillator to the center of the transition. That width is inversely proportionate to the lifetime of a given state. However, in the case of magnetic dipole transitions (like the one in Cesium), the decay rate is extremely slow. I could not find an estimate for Cs, however, the other well-known similar transition - Hydrogen 21cm line has a lifetime of more than $10$ mln years. Assuming that the Cs is similar enough to the H, one can estimate that the lifetime of the clock transition is more than $10^4$ years (the decay rate is proportional to $\omega_0^3$) which corresponds to the linewidth of the order of $10^{-12}$ Hz. In that case, you are correct and the width of this transition is so small that it can be neglected.
In real applications, the width of the Cesium clock transition is mostly limited by technical difficulties and is below 10 Hz. Clocks are limited not only by the precision of their electronics or mechanical stability but also by background thermal radiation that disturbs atomic samples and also by the limited time that the sample can interact with interrogating fields.
The quality of a clock can be described by a $Q$ factor, which is a resonance frequency divided by its resonance width. Reducing observed linewidth in Cs further is very challenging. For this reason, right now the clock community is trying to use different transitions having significantly higher, optical frequencies (jump from GHz to hundreds of THz) to further improve our atomic clocks.
