# How to calculate the resonant florescent spectrum of 2-level

1. Aug 5, 2015

### zzihuai

I am working on calculating the interaction between 2-level atoms and an coherent laser field. I can calculate the radiation intensity versus time from the atoms. I want to calculate the spectrum now. I know the spectrum can be calculated as the fourier transform of ⟨$\langle \sigma^\dagger (t)\sigma (t+\tau)\rangle$,where σ(t)=|0><1| is the lower operator of the atom. I am not sure how to calculate the expectation value containing 2 different time. I heard that it is possible to do so by using the quantum regression theorem. But I don't really understand it, could someone tell me how to use quantum regression theorem using computer explicitly? I am using matlab and treating the operators as matrix. Thank you.

2. Aug 10, 2015