DispersiveCavityQED Processor to Model Tavis-Cummings Hamiltonian

[Arianna Meinking]

Hello QuTIP Team!

I have been working on a Tavis-Cummings model simulation using the DispersiveCavityQED processor. My goal is to simulate a system with two qubits coupled to one cavity, investigating qubit crosstalk through direct qubit-qubit coupling. To do this, I want to tweak qubit-cavity detuning and coupling to affect qubit-qubit dynamics.

I have consulted the documentation on the CavityQEDModel, and it does not make sense to me. Why does the CavityQEDModel use qubit-cavity detuning when computing the qubit-qubit coupling, rather than calculating J for the qubit-cavity interaction? Additionally, changing the DispersiveCavityQED eps, delta, and g parameters does not change the simulation outputs at all. I was wondering if you could help me figure out why that is, or if I’m missing something about the Processor simulation method? The segment in question is this:

Thank you so much for your help! I have attached the problematic code just in case. Let me know if there is any need for clarification.

Arianna Meinking

[Boxi Li]

Hello Arianna,

First thing first, I would suggest being consistent, either using only `qutip.qip` or only `qutip_qip`. The latter has lots of features that are not available in the `qutip.qip` module. Mixing them as in your ipynb may cause some hidden bugs. (You might see a difference of 2*pi in the coeff values. That is just because the convention has been changed, no worry.)

In your example, you are trying to generate an RX rotation, so you need to change the parameter `deltamax`. There is a typo in the equation of the documentation (above the one you posted), delta^max should be the control pulse for sigmax, not sigmaz, sorry for that. The parameter documentation below is correct:

• deltamax: float or list, optional

  The pulse strength of sigma-x control, , default 1.0.

If you change `deltamax`, you will see that the compiled `coeff` changes accordingly .

> Why does the CavityQEDModel use qubit-cavity detuning when computing the qubit-qubit coupling, rather than calculating J for the qubit-cavity interaction?

In the equation you posted, `g` is the qubit-cavity interaction and `Delta` is the qubit-cavity detuning. So both of them are used. This is the result of the standard first-order perturbation. The effective qubit-qubit interaction is mediated by the cavity and described by `J`

I don't use the cavity QED model that much in my daily work though. So if you find any inaccuracy or anything that could be improved in the code or docs. You are very welcome :)

Hope this help.

Best wishes

Boxi