# AC Stark shift

1. Apr 16, 2011

### Niles

1. The problem statement, all variables and given/known data
Hi

In my book, they do calculations on a 2-level atom. After some approximations, they reach the following equation for the coefficient for the first (lower) level:

$$c_1(t)\approx c_1(0)e^{-i|\Omega|^2t/\delta}$$

where Omega is the Rabi frequency and delta is the detuning. They say that this equations is basically the AC Stark shift, since the amplitude evolves as if the state energy was shifted |Omega|2/delta. My questions are

1) How do we see that the state energy is shifted by |Omega|2/delta?
2) Is there a specific reason why we call it AC Stark shift?

Any help will be greatly appreciated.

Best,
Niles.