I Rabi Hamiltonian : counter-rotating terms

  • I
  • Thread starter Thread starter Paul159
  • Start date Start date
  • Tags Tags
    Hamiltonian Terms
Paul159
Messages
15
Reaction score
4
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.
 
Physics news on Phys.org
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".
 
vanhees71 said:
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).

vanhees71 said:
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).

vanhees71 said:
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.
 
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...

Similar threads

Replies
0
Views
1K
Replies
0
Views
3K
Replies
12
Views
1K
Replies
4
Views
1K
Replies
1
Views
1K
Replies
21
Views
2K
Replies
156
Views
10K
Back
Top