This is truly an excellent natural language description modern atomic clocks but it contains a lot of possible lies just in the story (causation) it implies. I understand a bit of the math of this, which is where the real explanation, such as it is, exists. But in natural language lies exist everywhere...always.
But here are questions that come to mind out of the natural language description. This is where my Ph.D. lives. You can see this using just the verbs (natural language predicates) you used. But it is the story you weave that contains a lot of lies.
Note, each implied causation below also implies that something happened before something else, which takes time.
"energey levels allowed" caused by who or what agent in nature? You seem to know.. Does it take time for the allowed message to each electron to reach it and the electron to then to follow orders?
This causes quantum mechanical effects " since you use the word "effects". Again, do these take time?
Which cause "electron transitions from higher to lower levels". ibid.
Which cause the emission of a photon of a specific frequency. ibid.
For atoms also "properly prepared" by who and how? This introduces more causation and time lag.
That very specific frequency presumably in cycles per second is inverted to read off a number telling some fraction of a second? Does it lie somehow, since this is quantum mechanics?
With the story resolution that we now have some people who know how to cause a new article of human causal practice which is an "implementation of modern atomic clocks"
For each of those causations, there are time delays unless there is none. Usually agents take time to decide and to do things. So in fact the frequency number is somehow the count of time? But how? And not for example the time it takes to "allow" or "transition" or "prepare" or "effect".
This description is so good that it would be wonderful to have the longer backstory on just this story.
Also it could include how Maxwell, for example had this "atomic clock" concept without even having our model of atoms. What did he say? What story did he weave that makes this his original idea?
On the other hand, physicists have a trick to how to avoid such lies suggested by natural language. And it is, of course, a great trick, also of our apparatus for natural language communication. Namely logic and truth.
How can we use natural language to communicate what natural language seems to "not allow" in how we 'naturally' think about time as something that we all share as the same? It seems we don't know. But there is a nice resolution of this meta-story: