Laser and excited state linewidths in Rabi oscillations

[Malamala]

Hello! I want to simulate (numerically if analytically is not possible) the behavior of a 2 level system, when driven by a laser (basically transition probability vs laser frequency for fixed pulsed time) accounting for the laser and atomic linewidth (in my case I can assume they are comparable). What is the best way to proceed? Thank you!

 

[f95toli]

Jaynes-Cummings Hamiltonian solved numerically using Qutip

 

[Malamala]

Jaynes-Cummings Hamiltonian solved numerically using Qutip

Thank you for this! I never used Qutip before, but it looks great! Do they give details about the physics behind it, too? In particular, I would like to know how to include the laser linewidth in the Hamiltonian/density matrix approach, even if I am not able to solve it analytically.