Ramsey Interactions What are Ramsey interactions? I am researching atomic clocks and am not sure why the atoms need to be exposed twice to an electromagnetic field in order to cause excitation.
 A: I'll talk about the Ramsey method of oscillatory field, which is a method for detecting the resonance frequency of a system. Probably this is what you mean.
Imagine you have a spin-1/2 particles ensemble (for simplicity, higher spins act in the same way under the first multipole approximation), and this spin is polarized along the z-direction. If you apply a rotating field on the xy-plane, according to Bloch equations, which govern the dynamics of magnetic moments, the spins will precess and tilt from the z-direction and will reach the xy-plane and precess around the z-axis. The longer you apply a transverse field, the more the magnetic moments of the ensemble will tilt; not to mention, that the frequency of the rotating field must match the resonance frequency of your system.
Now define a $\frac{\pi}{2}$ pulse as the pulse that makes your spins do a tilt by an anglle of $\frac{\pi}{2}$. This is called a $\frac{\pi}{2}$ flip.
In the ramsey method of oscillatory fields, you keep injecting polarized particles to the system, and apply a $\frac{\pi}{2}$ flip, and along with that, every time, you tweak the rotating field frequency, and then if the rotating frequency matches the resonance frequency, we'll achieve a full $\pi$ flip.
So:


*

*We inject polarized atoms along the plus z-direction;

*we gate in a rotating field and do a $\frac{\pi}{2}$ flip;

*we block the rotating field; and wait for the ensemble to precess on the xy-plane;

*we gate in the rotating field again to make another $\frac{\pi}{2}$ flip.
If the rotating field was synchronous with the precession of the ensemble on the xy-plane, the second $\frac{\pi}{2}$ flip will give us a full $\pi$ flip, which we measure, to know whether we are on the resonance frequency.
The pattern of the measurement of the rotating field's frequency vs ratio of polarization can be see in this plot:

Quantum Mechanically, we can't measure the polarization, and what we do is count the number of particles that are polarized along the negative z-axis, after applying two consecutive $\frac{\pi}{2}$ flips.
There are lots of simulations on this on the internet, one of them is the one by Prof. Antoine Weis from University of Fribourg, who's an authority in this field (magnetic resonance). The simulation can be found here, is made in Mathematica. Check this link out for graphs on this.
