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Quantum noise in atomic clocks

Optical atomic clocks based on neutral atoms are about to become the most precise measurement instruments ever constructed. Their "tick" is based on measuring the frequency of light that drives a high-frequency transition in an ensemble of cold atoms with a long coherence time. While future optical time standards probably might work with Strontium atoms in our laboratory we use the two hyperfine ground states that form the current basis for the SI-definition of the second.

We can describe the relevant physics of such a clock using the quantum theory for the most elementary quantum system with only two possible energy states $|\downarrow\rangle$ and $|\uparrow\rangle$. In our Cesium atoms these states have an energy difference of $\Delta E = h \nu_{clock} = h \cdot 9.192631770$ GHz. In an atomic clock the goal is to stabilize an electronic reference oscillator with frequency $\nu_{osc}$ to this atomic frequency.

To see how quantum mechanical effects limit the precision of such clocks we have to understand how they work.