Most clocks and oscillators work by having a resonator that has little loss (lower = better) and then building a negative resistor to compensate for the little loss that is there. (Incidentally, this results in the interesting contradiction that a lower phase noise LC or xtal oscillator will usually also use less power, since you need to add less energy to compensate for the losses of the resonator).
Atomic clocks and their close family of molecular clocks don't use this principle: To my understanding, they instead use a material in very, very low concentrations (lower = better to get increased sharpness of the peak) in a vacuum. This atom or molecule will then have a set of resonances at which it will absorb the EM power very well, and has almost no absorption at any other frequencies. In other words it is kinda like the opposite of a resonator used in aforementioned oscillators. As the extent of this absorption is, to my knowledge, very low (as you want very few molecules to be resonating, to keep the energy levels nice and discrete). So you can, I think, kinda think of it as having a low SNR - you have only a small difference between the loss at the notch frequency vs the loss at other frequencies.
Is there any good starting point to look at the relationship between this SNR and phase noise? I think most atomic clocks in-and-of-themselves have poor phasenoise, and get good phasenoise by using them to tune the frequency of a low-phase noise OCXO or such.