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Physics
Atomic and Condensed Matter
The sign of coupling Hamiltonian in CQED
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[QUOTE="thariya, post: 6027566, member: 648545"] Hi all, I've always regarded the coupling Hamiltonian for a bosonic cavity mode coupled to a two-level fermionic gain medium chromophore to be of the form, $$H_{coupling}=\hbar g(\sigma_{10}+\sigma_{01})(b+b^{\dagger})$$, where ##b## and ##b^{\dagger}## and annihilation and creation operators for the bosonic cavity mode and ##\sigma_{ij}## are the raising and lowering operators for a two level atom. ##g## is the coupling constant. Using the rotating wave approximation, this sometimes is simplified to, $$H_{coupling}=\hbar g(\sigma_{10}b+\sigma_{01}b^{\dagger})$$. I've recently come across some texts that seems to use an alternate form(under the rotating wave approximation) to describe (what I perceive is) the exact same system, $$H_{coupling}=\hbar g(\sigma_{10}b-\sigma_{01}b^{\dagger})$$, the main difference being the negative sign. Would you be able to explain why this difference occurs and what the significance of the negative sign is? Thanks! [/QUOTE]
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Physics
Atomic and Condensed Matter
The sign of coupling Hamiltonian in CQED
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