Undergrad Rabi Hamiltonian : counter-rotating terms

[Paul159]

Hello,

I'm trying to understand the counter-rotating terms of the Rabi Hamiltonian : $a^\dagger \sigma_+$ and $a \sigma_-$.

I find these terms rather strange, in the sense that naively I would interpret them as describing an electron that gets excited by emitting a photon (and vice versa).
So how should these terms be correctly interpreted ?

Thanks.

 

[vanhees71]

I'd need a bit more context. What are the annihilation and creation operators and the "spin-ladder operators" refer to? Maybe you refer to the Jaynes-Cummings model?

https://en.wikipedia.org/wiki/Jaynes–Cummings_model

Here a two-level "atom" is formally described using spin-1/2 operators. The "counter-rotating terms" mean transitions, where a photon is emitted and the atom is excited to a higher state or a photon is absorbed and the atom relaxes to its lower state.

As explained in the Wikipedia article these rapidly oscillating contributions are often neglected, leading to the solvable "rotating-wave approximation".

 

[Paul159]

I'd need a bit more context. What are the annihilation and creation operators and the "spin-ladder operators" refer to? Maybe you refer to the Jaynes-Cummings model?

https://en.wikipedia.org/wiki/Jaynes–Cummings_model

I'm referring to the Rabi Hamiltonian model (Jaynes-Cumming model without the rotating-wave approximation).

Here a two-level "atom" is formally described using spin-1/2 operators. The "counter-rotating terms" mean transitions, where a photon is emitted and the atom is excited to a higher state or a photon is absorbed and the atom relaxes to its lower state.

Yes this is exactly what I don't understand (at least I found this terms counter-intuitive).

As explained in the Wikipedia article these rapidly oscillating contributions are often neglected, leading to the solvable "rotating-wave approximation".

Yes but for strong coupling with matter we cannot neglect them.