Understanding the AC Stark Shift in a 2-Level Atom

[Niles]

Homework Statement

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.


Niles.

 

[NateD]

Homework Equations c_1(t)\approx c_1(0)e^{-i|\Omega|^2t/\delta}The Attempt at a Solution1) The equation for the coefficient for the first (lower) level can be written in terms of the state energy as follows:c_1(t)\approx c_1(0)e^{-i E_1 t/\hbar}where E_1 is the energy of the first (lower) level. We can then see that the energy is shifted by |Omega|2/delta by rewriting the equation in the following form:c_1(t)\approx c_1(0)e^{-i (E_1 + |\Omega|^2/\delta) t/\hbar}2) The AC Stark shift is named after the physicist Johannes Stark, who studied the effect of electric fields on atomic spectra. The AC Stark shift is a shift in the energy levels of an atom due to the presence of an alternating electric field. This shift is caused by the interaction of the electric field with the electron's dipole moment and is hence referred to as the AC Stark shift.