How Rabi frequency scales with laser intensity?

[Mark Mendl]

Homework Statement

It's not a homework, I'm just studying for the exam, but one question that I'm not sure of the answer is:
"In the semiclassical model of a two-level atom interacting with a monochromatic field, how does the Rabi frequency scale with the laser intensity"

Homework Equations

Also, V=d*E0 (I'm not sure how to put formulas here, sorry)

The Attempt at a Solution

Do I assume no damping? Still, I think something is missing...

 

[blue_leaf77]

In the semiclassical model of a two-level atom interacting with a monochromatic field, how does the Rabi frequency scale with the laser intensity

Well you can say $V^2 \propto I$ since intensity is proportional to the square modulus of the electric field amplitude $E_0$. Several approximations assumed in arriving in that expression of Rabi frequency are:
1) Two participating levels approximation: Generally in tackling problems of time-dependent Hamiltonian, one uses the eigenstates of the time-independent part of the Hamiltonian as the bases into which the true wavefunction of the system is expanded, clearly there will be an infinite number of terms. However it can be simplified in the case where the frequency of the interacting light is close to the frequency difference of certain pair of eigenstates, and we can approximate the true wavefunction as a linear combination of only those two coupled eigenstates of the time-independent part of the Hamiltonian.
2) Dipole approximation: the "size" of the participating wavefunctions from point 1) be much smaller than the wavelength of the light the atom in question is interacting with.

 

[Mark Mendl]

Thank you for the answer, but for exemple in a more specific question in this model :
"We place a two-level atom with transition energy ħ*ω₀ in a monochromatic laser field with
frequency ω. The transition dipole moment is d = 3ea₀. a₀= 5.29 x10¹¹ m.
(a) Calculate the laser intensity needed to achieve a Rabi frequency Ω₁/2π = 1MHz.
So, can I just use the formula above for Rabi frequency (ignoring damping) and the relation between the field and intensity? This would give me something like I=0.896 Js^-1m^-2

 

[blue_leaf77]

As far as I know, the Rabi oscillation frequency was originally derived in the quantum picture of light-matter interaction where only the atom is treated quantum mechanically, I have never known people incorporated the damping term in the Hamiltonian. May be you confused it with the purely classical Lorentz model.
ALso, you have to calculate the 'real' intensity, not just the square of E field. For plane wave in a medium of refractive index $n$, the time averaged intensity is $\frac{1}{2} \epsilon_0 nc |E_0|^2$.