If I have a single mode cavity, and I drive it with an electric field (this field was created in the macroscopic world, and then attenuated down to the quantum regime), how would I model this system's dynamics?
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What do you mean by attenutating down to the quantum regime? You can model the driven (by classical field) cavity within rotating wave approximation by $\hat{H}{}^{}(t)=\omega{}^{}b_{}^{\dagger}b_{}^{}+g (b_{}^{\dagger} e_{}^{-i\omega_{c}^{}t} + b_{}^{} e_{}^{i\omega_{c}^{}t})$. – Sunyam May 04 '18 at 08:06
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@Sunyam that seems right, thank you. If you write it up as an answer, including sources, then I'll accept – psitae May 04 '18 at 09:18
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Actually, what if I want to consider the more general case outside of the rwa? – psitae May 04 '18 at 09:18
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See https://physics.stackexchange.com/questions/27425/rigorous-justification-for-rotating-wave-approximation/27426#27426. – Jon May 04 '18 at 09:20
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@psitae You can also write down Hamiltonian for a driven cavity beyond rotating wave approximation as $\hat{H}{}^{}(t) = \omega{}^{} b_{}^{\dagger} b_{}^{} + g E(t) (b_{}^{\dagger} + b_{}^{})$ (Note : Under the assumption that we have a monochromatic classical drive and further invoking rotating wave approximation you can recover the already given Hamiltonian). But, I wanted you to explain your statement : "then attenuated down to the quantum regime" – Sunyam May 04 '18 at 11:26
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@Sunyam "attenuated down to the quantum regime" was only supposed to refer to one way to make a coherent source of light, that is, with electronics, arbitrary wave generators, filters, attenuators, until the Maxwell description fails. Does that make sense? – psitae May 04 '18 at 12:28