Three Level Atom

Overview

Calculations

Consider an atom with three levels in the typical $\Lambda$ configuration. This atom then has two ground states, which we denoted $|g_1⟩,|g_2⟩$ and an excited state $|e⟩$. The energy difference between the two ground states and the excited states are given by $\hslash {\omega }_{g1}$ and $\hslash {\omega }_{g2}$. Typically we will have two beams with frequencies ${\omega }_1,{\omega }_2$ addressing two legs respectively.

We start by first writing the Hamiltonian of the system