Query Regarding time dependent collapse operator while solving master equation by "mesolve"

[SHISHIRA MAHUNTA]

Dear All,

I want to solve the lindblad master equation for a time dependent two level system (Please see the attached file). Both Hamiltonian, H(t) and collapse operators are time dependent, but the collapse operators has the following form,

L_{+-} = f(t) * |+> < -| and L_{-+} = g(t)* |-> <+| where |+> and |-> are time dependent instantaneous eigen states of the H(t). I know how to solve the master equation when the collapse operator has the following form : L_{+-} = time dependent function f(t)  * constant operator . But in my case the operator part also has the time dependency.  I tried doing it with a loop  but I am getting error as " Incorrect Q_object specification" 

Could anybody please help me out regarding this ? It will be a great help, Thanks in advance.

[Paul Menczel]

Hi,

There are various ways of specifying time-dependent operators in QuTiP. A full overview can be found in the documentation here: https://qutip.readthedocs.io/en/latest/apidoc/classes.html#qobjevo

One of the options -- the one that you have been using so far -- is to provide a pair [Qobj, Coefficient] (where "Coefficient" can be a list of numbers, interpreted as a time-dependent prefactor for the Qobj). However, this format does not allow the "Qobj" to be time-dependent itself.

The two easiest ways I can see to solve your problem is

(1) Manually multiply your projectors with the prefactors, and just provide a list of Qobjs to the solver. That is, something like `[op * coeff for op, coeff in zip(Collapse_op1, coefficient_op1)]` etc.

(2) Write Python functions `def cop1(t): ...`, `def cop2(t): ...` that return the full collapse operators (coefficient times projector) at the given time t, and provide those to the solver: `c_ops=[cop1, cop2]`.

Kind regards,

Paul