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I'm a bit confused about the application of the Jaynes Cummings model and what exactly is meant by "one single mode":

Usually, it is said that the Jaynes Cummings model describes a single atom in a high Q cavity. The atom then only interacts with a single mode of the light field and the Hamiltonian is written as:

$$ H=H_0+H_I=\hbar \omega\sigma_+\sigma_-+\hbar\omega_La^{\dagger}a+\hbar g(\sigma_+a+\sigma_- a^{\dagger}) $$

Question 1: Why does this Hamiltonian only describe cavity QED and not e.g. an atom in free space?

Question 2: Is it correct that this description is not valid for interaction with a laser field, since the coherent state is not an eigenstate of $a^{\dagger}a$, i.e. the above Hamiltonian describes interaction with a photon Fock state?

I would appreciate some help, I'm a bit confused about these different models...

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You need a cavity so that the modes are well separated in frequency.In free space there are arbitrarily close-in-frequency modes, and so it is impossible to let the atom interact with only one of them.

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  • $\begingroup$ mmh, I'm not quite sure if I understand that argument. I can also have an arbitrarily narrow laser in free space right? $\endgroup$ – CPE Jun 30 '18 at 23:15
  • $\begingroup$ @CPE narrow in frequency yes, but it can radiate in any direction, so the atom is not coupling to a single mode. Also a laser beam is not closed quantum system, so I don't think that the model is applicable there -- but I might be wrong in this. $\endgroup$ – mike stone Jul 2 '18 at 12:14

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