Density Matrix evolution as a function of the detuning

[Vishal Narnaulia]

Hi,

I am getting the wrong plots for a 2 level atom when I tried to get the solutions for the density matrix elements as a function of the detuning which is giving the same dynamics as got in the time domain. But we know that the imaginary parts of the density matrix elements should be symmetric around 0 detuning. And my result is not coming like that.

Actually, I have given detuning as the variable instead of t_list in the arguments of mesolve() and run a loop in delta for Hamiltonian. But the output is not correct.

Here, I'm attaching my both programs for the density matrix of a 2 level atom in time domain and in delta (detuning ) domain.

I hope you'll help to guide me through this problem.

Thanks,

Regards,

Vishal Narnaulia

[nwla...@gmail.com]

hi vishal,

I had a quick look at your examples. The second one, as a function of detuning seems to have a couple of issues.. firstly you repeatedly construct H as a function of Delta in a for loop, but that only retains the final H (i.e., @ Delta = 0.5).  Secondly, sending the list of Deltas to mesolve(), in place of the t_range, will still just calculate the dynamics using the list of Deltas as time steps instead of changing anything in the model. The mesolve() function doesn't know that what you want to do is change delta in H (unless you are purposefully doing this for some reason I dont quite understand), it just assumes whatever list is sent is a list of timesteps to solve the evolution for.

Perhaps what you want to do there is include both mesolve() and the changes to H in a for loop, and run a separate solution for each value of Delta and for a given time interval?  Or, if you just care about the steadystate response, you can use steadystate() instead of mesolve()?

hope this helps

All the best

neill

[Vishal Narnaulia]

Thank you for your reply. 

Actually I want to get the plots w.r.t. delta here instead of time (keeping the time as a constant number because one variable has to be constant if we need to find the dynamics of the system w.r.t. some other variable i.e. delta). And the steadystate() function gives only a single constant matrix but I want to get the all the steadystate() values at all the values of the time. Isn't there any other solver except mesolve() which can provide us the dynamics w.r.t. delta?