Abstract
It is shown that the phenomenon of Dicke superradiance essentially occurs due to spontaneous symmetry breaking. Two generalised versions of the Dicke model are studied, and compared with a model that describes photonic Bose-Einstein condensate, which was experimentally realised sometime back. In all the models, it is seen that the occurrence of spontaneous symmetry breaking is responsible for coherent radiation emission.
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Notes
Here the fact that \(K = a^{\dag } a + S_{z}\) is conserved, that is \([H,K]=0\), is utilised.
One can indeed show that the photon number states and the coherent states are orthogonal to each other. It follows from the fact that \(|\alpha \rangle = e^{\alpha a^{\dag } - \alpha ^{*} a} |0\rangle \), where \(|\alpha |^{2} \propto N\), which implies that \(\langle 0 | \alpha \rangle \rightarrow 0\) as \(N \rightarrow \infty \).
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Vyas, V.M., Panigrahi, P.K. & Srinivasan, V. Dicke superradiance, Bose-Einstein condensation of photons and spontaneous symmetry breaking. Eur. Phys. J. Plus 137, 815 (2022). https://doi.org/10.1140/epjp/s13360-022-03047-1
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DOI: https://doi.org/10.1140/epjp/s13360-022-03047-1