How to model two-levle atom with vibrational sublevels?

[ustc...@gmail.com]

Hello everyone, I am rencently learning Qutip and find it very powerful in modeling quantum optics.

Now I want to use it to model an atom (or molecule) with two eletronic levels, but each electronic levels has several vibrational sublevels, this is a common model used in modeling molecular optics. The processes here involve the dipole interaction between the molecule (transition between electronic levels) and the vibrational relaxation (transitions within each electronic level). A shcematic diagram (from chemwiki) has been atatched.

I wonder how to set up such a model in Qutip to consider the vibratioanl modes?

Thanks very much and looking forward to your suggestions.

Best wished,
Gong

[Kevin Fischer]

Hi Gong,

I think the Bloch Redfield solver is the only tool in QuTiP that is directly applicable. Consider a single two level system coupled to a set of vibrational levels - this can easily be adapted to the example for the Redfield solver given in the documentation (within the markovian approximation of the phonon bath interaction). Here, you should use a sigma_X operator as your laser coupling the two states and instead you need a sigma_Z Redfield tensor to represent phonon absorption and emission. The operator density of states is the vibrational density of states modified by thermal occupancy functions. You can then create a set of the two level systems like this. Next, you need to add Redfield tensors that couple the excited states of two level systems. Note that the input operators are required to be Hermetian by implementation, so you implement a directional coupling by having the negative and positive frequency density of states being different.

Kevin