At one point I had a good reference but I don’t have it on hand.
Quartz oscillators don’t have very good long term stability (see: Allen deviation) compared to atomic oscillators. Atomic oscillators are fascinating, and have something to do with the geometry of the atomic orbitals. See the section “Electron placement on the periodic table” and the “Orbitals table” in the “atomic orbitals” wikipedia[1]. Note that rubidium and caesium are the heaviest non radioactive alkali metals, thus have the largest s valence orbital. I believe this is the key feature to them producing a stable frequency.
We can do even better though. We put a few of atomic oscillators in orbit and have them talk to each other to agree on the time and location of each other, taking into account time of flight of signals and relativistic effects. You can use the phase offset between the different satellite signals to find your position and time very accurately on the ground. This is GPS and it is the current gold standard for time on Earth, outside of NIST and other global authorities on time.
Both GPS and atomic oscillators are very stable, but require the use of a quartz oscillator. These sources discipline a quartz oscillator in a feedback circuit (phase locked loop, PLL). PLLs allow you to synchronize two clocks (in this case, the quartz oscillator is being synchronized to the more stable source). PLLs have a loop cutoff frequency at which the tracking begins. Above this cutoff frequency, no tracking occurs. It is important that the local oscillators we use do not have a lot of phase noise (aka jitter, I literally wrote my thesis on the stuff. Phase noise manifests itself as edges coming too soon or too late compared to an ideal clock, but at rates above 10 Hz (an arbitrary boundary defined between jitter and wander). Quartz oscillators, in this context, most typically run at 10 MHz. It’s a very useful frequency for a huge number of applications. This frequency can be multiplied by any integer by using PLLs, but phase noise that seemed trivially quiet at 10 MHz is the volume of a rock concert at 1 GHz. So, we use quartz oscillators for a reason: they have low phase noise. The amount of phase noise in quartz oscillators can be decreased by compensating for temperature (TCXO) or controlling the temperature (OCXO). You can put your oscillator in an oven and put that oven in an oven for the lowest phase noise oscillator that humans make: the double ovenized cystal oscillator (DOCXO). The reason temperature affects quartz oscillators is because they work by applying a constant voltage to a crystal that outputs a resonant frequency. The physical size and electrical behavior of this crystal changes with temperature. Importantly, it also has a strong electrical signal compared to the noise. Atomic oscillators have a small signal that is amplified up, and it brings a lot of noise with it. Atomic oscillators work by modulating a bright light by a small amount[2].
1. https://en.wikipedia.org/wiki/Atomic_orbital
2. https://youtu.be/ymV9LwhD0W0