Adding term to mesolve to solve Linblad equation with feedback

[Félix Desrochers]

Hi,

Hi am new to Qutip and I am trying to solve Linblad equation with feedback. So basically I am trying to solve this equation: 

The last two terms with the lambda are the feedback terms. If there is no feedback (lambda=0) I just use mesolve and everything works fine. But if there is feedback, I don't know if there is a simple way to add terms to mesolve to deal with a modified version of the lindblad equation or if there is another function that can help me with that problem. Sorry if the question is trivial or if it has already been answered but I haven't found anything on the subject. 

Best regards,

Félix

[Kevin Fischer]

Hi Felix,

mesolve can also take a custom Liouvillian instead of the the default form. An example is given in this notebook for a time-dependent case.

I believe the following snippet will help, but I recommend double checking what I wrote out. The idea is to use the qutip.spre / qutip.spost / qutip.sprepost to construct your own custom Liouvillian

n = a.dag() * a

L0 = qutip.liouvillian(H, c_ops=[np.sqrt(gamma) * a])

L1 = - lamda ** 2 / (2 * eta) *  (qutip.spre(n ** 2) + qutip.spost(n ** 2) - 2 * qutip.sprepost(n, n))

L2 = 1j * lamda * (qutip.sprepost(n, a.dag()) - qutip.sprepost(a, n) + qutip.spre(n*a) - qutip.spost(a.dag()*n))

result = qutip.mesolve(L0+L1+L2, rho0, tlist, c_ops=[], ... )

 

Regards,

Kevin