The permutation symmetry of the atoms gives the col- lective parts of the master equation an SU(3) group structure, and this allows the default exponential scaling of the Liouville state space, 32^N , to be reduced to a polynomial scaling, N^4 [51].
The best optical atomic clocks provide only a correct average frequency. That means that if you have such an optical atomic clock you know with an extremely small uncertainty which is the frequency averaged over a long time interval, of days or weeks, but you know much less about the value of the frequency averaged over a short time, e.g. a second.
The instantaneous frequency and the frequency averaged over short time intervals are not determined by atomic properties, but they are determined by the length of a resonant cavity. That length varies due to vibrations from the environment and due to temperature fluctuations. To minimize these length variations great care is taken for damping vibrations and for stabilizing the temperature, usually in a cryostat, but the accuracy required for an atomic clock is so great that even extremely small residual vibrations and temperature variations limit the performance of the atomic clock.
TFA describes a way to make a laser whose frequency is determined by the atoms whose stimulated emission is used, not by the resonant cavity where they are placed. A resonant cavity is always needed in a laser, to provide the positive feedback that is required for converting an amplifier by stimulated emission into an oscillator that provides a continuous output signal, without an input.
Because the frequency of such a laser is determined by atomic properties, e.g. of barium atoms in the example given in TFA, it is no longer necessary to have a system that tunes the resonance frequency of the laser cavity by measuring atomic resonances in some separate absorption cells, where such a tuning system can only ensure a correct value for the averaged laser frequency.
Nevertheless, this paragraph from the phys.org article is misleading: "Following early theoretical ideas emerged in the 1990s, the concept didn't gain concrete traction until 2008, when researchers at the University of Colorado proposed that superradiant lasers could serve as a new kind of atomic clock.".
This paragraph implies that Reilly at al. from the University of Colorado were the only ones pursuing this idea.
First of all, making this kind of laser has always been a theoretical goal for anyone thinking how to improve atomic clocks, but nobody has succeeded to make a good one. For now, even the authors of this article do not report any conclusive experimental results, so it remains to be seen how this idea will work in practice.
Besides this research of Reilly et al., there have been several research articles published both before 2008 and after 2008, most of them by Chinese authors. The most recent of them, from a few years ago, proposed a plausible way to make such a laser using rubidium atoms or cesium atoms.
However, the main problem with such lasers is the difficulty of obtaining an output signal that is powerful enough to have an acceptable signal-to-noise ratio. IIRC, the Chinese proposal was less likely to ensure a signal-to-noise ratio as good as what seems achievable by the technique proposed by Reilly & al. in the parent article.
So what is described in the parent article seems more likely to be successful than the earlier proposals, but it certainly is not unique.
In order to tune the resonant cavity, one generates a signal that is proportional with the frequency difference between the current frequency of the laser and the frequency of an absorption line from the spectrum of some reference atoms. There are various methods for the generation of such frequency difference signals, by modulating the laser signal and passing it through some space where the reference atoms or ions are held by various methods, e.g. an optical lattice of neutral atoms, an ion trap or just a cell with metal vapor.
By tuning the cavity, the frequency locked loop ensures that the integral of the frequency difference signal over a long integration time is approximately null, which guarantees that the average frequency of the laser is equal to the frequency of the spectral line of the reference atoms.
If instead of using a laser whose frequency is determined by the resonant cavity, you use one whose frequency is determined by the stimulated emission spectral line of the laser medium, like in the parent article, you no longer need a system of control of the laser frequency. The laser frequency is itself the reference frequency.
Unfortunately, such a laser will have a very low output power. This means that if you detect the output signal of the laser it will have a very low signal-to-noise ratio. Because of this you will still have to average the laser frequency, to filter the noise. Hopefully, for filtering the noise shorter integration times will be sufficient, in comparison with those needed for the existing optical clocks.
While shorter averaging times are a possible advantage, more important is that the frequency should be less sensitive to environmental factors, like vibrations and temperature. This could enable such optical atomic clocks to be used e.g. in vehicles. Nowadays the optical atomic clocks that can be used in vehicles are many orders of magnitude less accurate than those that are restricted to a well protected laboratory environment.
If anyone is wondering, we aren't yet to the point of having an atomic clock in the dashboard of your Toyota. But they have been reduced to ~suitcase size. Example if one being tested in a Navy ship:
https://www.geoconnexion.com/in-depth/scientists-create-new-...
They are orders of magnitude less accurate than even portable optical atomic clocks and the difference is much greater in comparison with SOTA laboratory cesium clocks or hydrogen masers, which are again orders of magnitude less stable than the best laboratory optical atomic clocks.
However, these miniature atomic clocks are much smaller and cheaper than better atomic clocks and there are applications where something better than an OCXO-based quartz clock is desired.
The best laboratory optical clocks, which use ion traps or optical lattices with neutral atoms, have a higher accuracy by up to 6 orders of magnitude, which makes much harder for the system that stabilizes the length of the laser cavity to keep up with it.
Minute length changes that would not matter for a less accurate iodine clock would cause unacceptable frequency shifts in a SOTA optical clock. Therefore such optical clocks are much more sensitive to their environment.