Thursday, April 19, 2012

The Russian Solution to the quantum Rabi Model

There's a frightful phrase in physics that goes "a Russian solved it a while ago."

A while ago a very nice paper of D. Braak appeared discussing the integrability of the quantum Rabi Model in Physical Review Letters. This is a nice elegant paper using a discrete symmetry to show that the model is  integrable and gives an exact spectrum for the model [Phys. Rev. Lett. 107, 100401 (2011)].  

The one interesting thing is that the spectrum for the quantum Rabi model was shown by É. A. Tur by resolvent theory eleven years before [Optics and Srectoscopy 89, 574-588 (2000) (English) Optika i Spektroskopiya 89, 628-642 (2000) (Russian)]. If someone can find a pdf file please email it to me, I could only get a bad scan of a battered photocopy.

And don't get me wrong, Braak's paper contribution goes beyond the spectrum. He explores the implications that symmetries has on integrability for models that doesn't have a classical limit/analogue.

Also, a little bit further in time, J. Casanova et. al. analyzed the spectra and dynamics of the quantum Rabi model in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 (2010)] and presented an approximated spectra for the model and the curious collapse and full revival of the ground state of the positive parity chain.

Again, that particular oscillatory behavior for the same state was discussed by É. A. Tur but for weak coupling in [Optics and Spectoscopy 89, 574-588 (2000) (English) Optika i Spektroskopiya 89, 628-642 (2000) (Russian)] and an elegant approximation to the spectra leading to their result in [arXiv: 0211055 [math-ph]].

And don't get me wrong again, Casanova et. al. study the deep ultrastrong coupling and delve in the analysis they are presenting by adding a phase space analysis and some numerical analysis on the topic.

My point is that some of the results in both Physical Review Letters has been known for ten years already and nobody cited the work of É. A. Tur. A simple Google search of "Jaynes-Cummings model  without rotating wave approximation" brings Tur's paper in the second place, did the editors or reviewers even bother?

Now, surely there's a dozen papers in the review queue that are working on the topic and citing Braak and Casanova—which is the right honest thing to do—but is someone citing Tur? Show the guy some love, his work is nice, clean and elegant.


Edit: I forgot to mention that Tur's result was for weak coupling, g=0.5.



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