Symmetries in cavity models: Beyond the rotating wave approximation

The interaction of confined atoms with a single mode radiation field is the main subject in the theory of cavity quantum electrodynamics. The constraints imposed by the cavity on matter and radiation fields give rise to collective phenomena. One possible outcome is the enhanced and coherent spontaneous emission of photons by the atoms: the superradiance. As predicted by Dicke, conservation laws are essential in superradiance and are derived from the matter-interaction Hamiltonian. Here, we consider N two-level ultracold atoms interacting with a single mode bosonic field, in the Dicke Hamiltonian, and trapped inside a non-dissipative optical cavity. Numerical and analytical results derived from finite size regime indicate the matter–radiation coupling strength, λ, is insufficient to draw the complete picture of the system. Instead, they support the relevance of U(1)symmetry, which prompts the study of (i) particle and angular momentum conservation, (ii) the constraints imposed to correlation functions and (iii) the influence of symmetries in the system dynamics. Further exploring the U(1)and rotational symmetries permits a simple interpretation of antirotating contributions as spin–orbit operators. As application, we show two species of ultracold clouds develop interactions due to antirotating operators