Qutip code for open Dicke model

[KINGSHUK ADHIKARY]

Hello,

I used the Qutip code for the Dicke model, but there are two different codes*(1,2) available. I'm not sure which one is best for my system.

1) piqs-open-dicke-model.ipynb

2) Lecture-3A-Dicke-model.ipynb

Besides this, I have encountered an error "Zero pivot, numerical factorization or iterative refinement problem"— during the steady state computation snd I can't figure out this.

Thanks,

Sincerely,

Kingshuk Adhikary

[KINGSHUK ADHIKARY]

I used the Qutip code for the open Dicke model, but there are two different codes*(1,2) available. I'm not sure which one is best for my system.

1) piqs-open-dicke-model.ipynb

2) Lecture-3A-Dicke-model.ipynb

Besides this, I have encountered an error "Zero pivot, numerical factorization or iterative refinement problem" during te steady state computation—I can't figure out this.

Thanks,

Regards,

Kingshuk Adhikary
Senior research fellow
School of Physical Sciences
Indian Association for the Cultivation of Science
Kolkata 700032, INDIA

[Simon Cross]

Hi Kingshuk,

There are two tutorials that feature the Dicke model, but they are quite different.

If you are new to QuTiP I recommend starting with "Lecture-3A-Dicke-model.ipynb". This covers just simulating the Dicke model itself. It is more straight forward, has more explanations and nicer plots.

The second one, "piqs-open-dicke-model.ipynb", covers the Dicke model interacting with a surrounding environment (this is what the "open" means in the title). Here the cavity "leaks" photons requiring more sophisticated simulation techniques. One has to switch from describing the system using a Hamiltonian to using a Liouvillian (which has size [N**2, N**2] if [N, N] is the size of the Hamiltonian). This bigger task also makes it useful to use a more tailored algorithm, called PIQS, for finding the steady state. PIQS stands for "permutation invariant quantum solver" and is a solver that takes advantage of the permutation symmetries of the Hamiltonian / Liouvillian (e.g. in the Dicke model, all of the spins are interchangeable).

The "Zero pivot" error likely means that your Hamiltonian is ill-conditioned somehow. I would start debugging it by write the smallest complete piece of code you can that shows the error and work from there to understand the issue. Maybe it is as simple as a typo somewhere in the construction of the Hamiltonian.

Regards,

Simon

[KINGSHUK ADHIKARY]

Dear Simon,

 Thank you so much for your advice. However, I'm not sure which code is better for the open Dicke model because both of them ("Lecture-3A-Dicke-model.ipynb" & "piqs-open-dicke-model.ipynb") can handle dissipation and provide steady-state behavior.

"The "Zero pivot" error likely means that your Hamiltonian is ill-conditioned somehow"- I don't think so because I got this error when I compiled the steady-state program in a loop of some system parameters like interaction strength, drive strength, etc. Though for a single input parameter, the output yields a finite result for me.

So, I respectfully request that you review my code, and if you agree, I will send it to you.

Sincerely,

Kingshuk Adhikary

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KINGSHUK ADHIKARY