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In the Jaynes-Cummings model (JCM) https://www.tandfonline.com/doi/abs/10.1080/09500349314551321, you have a model for a single cavity where you have two bosonic state operators coupled to a photon operator which describes the radiation that happens when the bosonic fields go from the excited state to the ground state. My question is, would it be possible from a quantum mechanics point of view as well as from an experimental point of view to have a lattice of cavities with a single possible state with different energy levels so that you get a spatial JCM where you hop from one site to another and this gives radiation with the frequency given by the energy difference between the two sites?

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I don't understand what you want to ask.You mean we put different JCMs which contain atoms with different energy levels in different sites?The frequency of photons hopped between sites are only related to the natural cavity frequency,so I don't think there's a inevitable connection between hopping and radiation.

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  • $\begingroup$ Okay I guess what you understood is precisely what I meant. So in the JCM the natural cavity frequencies are tuned so that they match the differences in the energy levels in the cavity, but what if you have a fixed decrease in energy levels for the cavities in one direction in a chain lattice and all the cavities have natural frequencies corresponding to that difference? I guess it would be possible that then hopping would be able to excite a photon in a cavity? Since in this paper nature.com/articles/nphys466 they also talk about photon hopping in a JCM. $\endgroup$ – Zach Jacobs Oct 17 '20 at 9:32
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    $\begingroup$ You mean we coupled cavities whose natural frequencies are different.Assuming the system is 1-D,the i-th cavity hopped a photon with frequency omega_i.I think this photon was most likely to pass through the next cavity(the i+1 th cavity) with natural frequency omega_i+1,because the hopping photon could not form a standing wave due to the frequency difference in linear optics regime. $\endgroup$ – Guoqing Oct 18 '20 at 2:42

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