Comment by Xpol | Hacker News Reader

Comment by Xpol | Hacker News Reader

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Yes, in fact, the current state-of-the-art atomic clocks are hitting a limit called the standard quantum limit (SQL) of the quantum projection noise (QPN). Basically, atomic clocks operate by probing atoms with an accurate local oscillator, in this case, the laser, to drive the clock transition (here, 698.446nm or 429.228 THz). In this two-level system (a ground state, g and excited state, e), you can think of the measurement yields a "pointer" that points the state of the system (which is a superposition of g and e, which is related the the fraction of atoms in the ensemble being excited, i.e. the excitation fraction), however, such measurement is not certain, hence QPN.

However, there're workarounds to beat this SQL. One approach people are working on is called the "spin squeezing", which, one can think of the uncertainties of a measurement mapped onto a 2D plane, for simplicity, a circle. Spin squeezing is used to improve the uncertainty in one axis while sacrificing the other, like squeezing the circle into an eclipse. There's a group in MIT which attempted to show metrological gain from spin squeezing in 2020, which they failed.

A super fascinating journal would be mit failed experiments. And what happened.

One semi-famous example from MIT would be Jerrold Zacharias's attempt to build a cesium fountain clock ( https://en.wikipedia.org/wiki/Atomic_fountain ). It took decades of additional research before anyone managed to make fountain clocks work.

Norman Ramsey's biography of Zacharias at http://www.nasonline.org/publications/biographical-memoirs/m... (.pdf link) talks a little about it:

Zacharias at this time became interested in developing atomic clocks and pursued two versions concurrently. One was a cesium atomic beam clock using my (Ramsey's) separated oscillatory field method, well engineered for reliability and commercial applications, including a source and vacuum system that could be operated for years rather than hours. He cooperated with the National Company in developing a commercial clock known as the Atomichron. The availability of this highly successful cesium atomic beam clock contributed greatly to the adoption of atomic time and to the international definition of the second as 9,192,631,770 oscillations of the cesium atom.

His other version had the potential for much greater accuracy but the risk of total failure. A very slow beam of atomic cesium was directed upward and allowed to fall as a fountain, with separated oscillatory field excitation on the way up and down. The half second required for the roundtrip in the fountain was approximately fifty times greater than that for an atom to traverse the oscillatory field region of a conventional atomic beam apparatus, so the resonance width, by the Heisenberg uncertainty principle, would be fifty times narrower with correspondingly increased clock accuracy. Despite valiant efforts by Zacharias and his associates, the fountain experiment failed because the numbers of ultraslow atoms in the beam were far below theoretical predictions, probably due to scattering in the nonequilibrium region between the slits. It is of interest to note that thirty years later, in 1989, Steven Chu succeeded in making an atomic fountain by using the new laser cooling techniques to produce ultra-slow atoms. The atomic fountain with laser cooling is now one of the most promising prospects for increasing the accuracy of clocks and frequency standards.

What the MIT group achieved was implementing spin-squeezing to clock operation, but their results are not QPN-limited (in fact, they made it above the SQL, so they actually make things worse instead of making it better) [1].

They attributed their major obstacle as their laser phase noise, and they claimed if they subtract the estimated laser noise from the result they would get sub-SQL. But hey, that's not how things work. If you think you can make it, you just make it.

[1] : https://www.nature.com/articles/s41586-020-3006-1

IIRC LIGO/VIRGO use squeezed light to lower the uncertainty in the ~~frequency~~ phase[1] of the laser they're using to improve the sensitivity of their measurements.

[1] https://www.optica-opn.org/home/newsroom/2019/december/squee...

Yes, LIGO has already implemented squeezed states in their measurements. What I'm referring to is making a spin-squeezed atomic clock with enhanced metrological gain compared to QPN limit. There're several groups working on it and so far no one has succeed.

If you are limited by the number of atoms then just add more atoms!

Usually other systematic errors are the problem though.

There're problems with increasing atom number. It is true that more atoms will allow one to resolve QPN easier, more atoms make clock rotations (along the Bloch sphere) much harder, as for a spin-squeezed clock doing Ramsey sequence, you need at least two pi/2 rotations to rotate the squeezed state.

Stupid question: what you're describing looks very similar to NMR (using RF to shape ensembles of magnetic spins, often shifting them around the bloch sphere).

You're right, the techniques in NMR like Rabi and Ramsey spectroscopy, spin echoes are all used in atomic clock experiments too.

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