Supplement 01:

The Mathematica code provided here is the example I gave in class for the solutions to the coupled two level problem. The code was written using Mathematica 5.2, but I think it should be backward compatible to earlier versions. (One can also develop analytical solutions for the two level problem, but the numerical approach is useful if you want to extend to more levels, as we’ll see later in the class.)

To gain intuition, play around with different detunings, Rabi frequencies (coupling strengths) and lifetimes. You can look at late time steady-state solutions (for which there are analytical solutions, see the homework) or short-time behavior.

If you want, you can modify the code to change it from the four over-determined density matrix equations to the three optical bloch equations in u, v, and w