At this level of accuracy things are pretty strange. It used to bug me when you had to tune RF circuits at a distance with non-conductive tools because your body capacitance would throw the tuning off. Having a clock that just being near it will change what time it reads, well that is a whole different ballgame of weird is it not?
On a science note, why isn't this a gravity wave detector anyway?
Gravity wave detectors get phase accuracy by comparing a photon to itself using an interferometer. SNR is improved by brightening the laser and averaging over more photons. The laser frequency is less important.
It turns out there are some ultraviolet nuclear transitions. The line widths promise to be obscenely narrow. If they can get it working in a clock, they will be able to directly measure gravitational time dilation of small masses.
Do you have a reference to the UV transitions? I'm sure the LIGO folks think of themselves as being in a race with advancing clock technology with regards to actually detecting gravity waves.
I could not find many references, but I think clocks mainly make the instrument cheaper, or possible in the case of long-baseline satellite instruments.
On a science note, why isn't this a gravity wave detector anyway?