MCSOLVE with optional lindblad

[Giuseppe Buonaiuto]

Hi,

I'm quite new with qutip. I was wondering (maybe is a very trivial question) if, having the following Lindblad term in my master equation

  L1 = - sqrt(kappa * gamma * eta) * (

        spre(sm.dag() * a) - spre(a) * spost(sm.dag()) + 
        spost(a.dag() * sm) - spre(sm) * spost(a.dag()))

there is any way to solve this with mcsolve? I doesn't look clear to me how to put this L1 in the "standard" collapse operator form. But maybe I'm wrong.

Thanks

[Kevin Fischer]

Hi Giuseppe,

If I'm guessing this correctly, you want to use the coupling Liouvillian from Garden/Zoller's formalism for cascaded quantum systems, where you want to take the output of the cavity and feed-forward it into the atom?

[CAVITY] ----c1----> [ATOM] --------> c3

                         --

                      --

                   --

         c2 <--

Then you need:

c1 = sqrt(kappa * (1 - eta)) * a

c2 = sqrt(kappa * eta) * a + sqrt(gamma/2) * sm

c3 = sqrt(gamma/2) * sm

c_ops = [c1, c2, c3]

and

H1 = 1 / (2 * 1j) * (kappa * gamma * eta) * (a * sm.dag() -  a.dag() * sm)

Which is then in a form that you can easily put into mcsolve. My understanding is that as long as its a Lindblad term, you can always make some sort of decomposition like this, where you have a collapse operator that can represent continuous measurement. (Though it's not always super obvious to arrive at that.) An example that uses a slightly more complicated version of this form is Phys. Rev. Lett. 78, 3221 (1997).

Hope this is what you're look for!

Kevin