Ramsey Spectroscopy

We want to compare the frequency of our reference oscillator ν osc   with the atomic transition frequency ν clock   using microwave pulses and measurements.

This can be done with the following 3-step algorithm (Ramsey spectroscopy):

1. Prepare the atom in |↓⟩  .
   
2. A microwave π/2  -pulse performs a 90 ∘   -rotation around the y  -axis.
   
3. Now we wait during the interrogation time τ  . During this time the state evolves and precesses around the z  -axis until φ=τΔν  .
4. After the interrogation time a second microwave π/2  -pulse is sent - but this time with a phase such that it performs a 90 ∘   -rotation around the x  -axis.
5. Finally we measure whether the atom is in the ↓−  or ↑  -state. This way - depending on whether Δν  was positive or negative - the probability find the atom in either the upper or the lower state is larger and we can adjust the frequency of the reference oscillator ν osc   accordingly.

Of course this experiment is not just performed with a single atoms but rather with about 100000  atoms simultaneously.