# I Two-Level Atom Driven by Two Lasers?

1. Jul 27, 2017

### Twigg

Hey all,

I am looking for a reference that derives the optical Bloch equations for a two-level system driven by two near-detuned monochromatic radiation sources. Specifically, I am looking to substantiate a result I derived by following the same procedure as for a two-level atom driven by a single radiation source: $$\frac{d\vec{R}}{dt} = \vec{R} \times \vec{W}$$ where $$\vec{W} = [\Omega_1 + \Omega_2 \mathrm{cos}(\delta_2 - \delta_1),\Omega_{2}\mathrm{sin}(\delta_2 - \delta_1),\hbar \delta_1]^{\mathrm{T}}$$ in which $$\hbar \Omega_n = e \langle \vec{x} \cdot \vec{E_{n}} \rangle$$ and $\delta_n$ is the detuning of the n-th laser and $\vec{E_n}$ is the amplitude and polarization of the beam.

Edit: I don't need the spontaneous emission contribution, because I'm putting this in a Monte Carlo simulation where I handle spontaneous emission as a random process for each atom.