What a fascinating question which, I have to admit, I knew nothing about.
The best answer seems to be here (courtesy of 'timeanddate.com')-
"In an atomic clock, the natural oscillations of atoms act like the pendulum in a grandfather clock. However, atomic clocks are far more precise than conventional clocks because atomic oscillations have a much higher frequency and are much more stable.
There are many different types of atomic clocks, but they generally share the same basic working principle, which is described below:
1. Heat, Bundle, and Sort
First, the atoms are heated in an oven and bundled into a beam. Each atom has one of two possible energy states. They are referred to as hyperfine levels, but let's call them state A and state B.
A magnetic field then removes all atoms in state B from the beam, so only atoms in state A remain.
2. Irridate and Count
The state-A atoms are sent through a resonator where they are subjected to microwave radiation, which triggers some of the atoms to change to state B. Behind the resonator, atoms that are still in state A are removed by a second magnetic field. A detector then counts all atoms that have changed to state B.
The percentage of atoms that change their state while passing through the resonator depends on the frequency of the microwave radiation. The more it is in sync with the inherent oscillation frequency of the atoms, the more atoms change their state.
The goal is to perfectly tune the microwave frequency to the oscillation of the atoms, and then measure it. After exactly 9,192,631,770 oscillations, a second has passed." (source- https://www.timeanddate.com/time/how-do-atomic-clocks-work.html).
You can use a potato to power a clock though- http://www.wikihow.com/Make-a-Potato-Clock. Perhaps not with the accuracy you're looking for though!!)