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In a two level atomic system (Rabi oscillating problem) the perturbative potential is oscillating / sinusoidal because it comes from the electric field from the laser.

Now stark effect is the phenomena of splitting of energy levels in atomic system due to electric field. Here how does the splitting takes place? What is the signature of Stark effect?

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Is your question not covered by If so can you please edit your question to be more focused on what you need. –  Michael Brown Mar 16 '13 at 13:35

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In my opinion:

The Stark effect is the splitting of atomic energy levels in external static electric field. The electric field will separate some of the the degenerate energy levels and thus create splittings.There is also the AC Stark effect, which is the splitting of energy levels in sinusoidal external electric field. To my understanding, it is the same effect as Autler-Townes splitting, in which the sinusoidal electric field is near resonant with some transitions, and thus drives the population under goes Rabi oscillation.

Consider a two level system driven by a classical electric field, and the initial population is in the ground state. In the dressed state picture, the initial state is the superposition of the two bare states, and since the dressed states are the eigenstates of the system, the time evolution is just gain of phase in the dressed states basis. Since the dressed states are separated by one Rabi frequency, transform back to bare states will give the Rabi oscillation in the population inversion. In the time domain picture, when apply a sinusoidal external field, the dipole oscillation is modified by the external filed at a rate of Rabi frequency. Frequency mixing with the natural frequency, the dipole oscillation will have two frequency response at two splitting which are one half Rabi frequency appart from the natural transition, which are the AT splitting peaks.

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