Proper way to couple two lasers to the same transition?

[SoraUmika]

Hi there,

So I am trying to couple state |a> to |b> with two lasers, the ultimate goal is to do some kind of wave mixing scheme in a ladder system. However, I am having trouble achieving this in rydiqule.

The first thing I attempted was to add two couplings independently, so we have Add_Coupling((a,b), laser_1 parameters) Add_Coupling((a,b)laser_2 parameters). The problem with this is that if you check the Hamiltonian before and after the second coupling, what the second coupling will do is simply overwrite the first coupling, so laser1's parameter will be replaced by the laser2 parameter.

The other thing I've tried was instead of solving in steady state, I solve it in the time domain, such that I only need 1 coupling statement. The way this works (or at least what I believe to be) is that since laser1 and laser2 couple the same state, then in a suitable rotating frame, we can have the off-diagonal element be written as O1+O2e^(-iDt )|a><b| where O1,O2 is the rabi frequency corresponding to laser1 and laser2 and D is the detuning of laser2. Now, I'm not sure if the time-dependent scaler function just effectively multiplies it by the rabi frequencies so that you'll see a change in the off-diagonal element but what I have done was I defined f to be f(t)=1+(O2/O1)e^(iDt ) and using this then solving it at large time scale, I did get a sensible answer but have no way of verifying the validity. Also, this method is extremely slow for my purpose and I would avoid it if possible and do a steady solution instead.