Dicke model for quantum Hall systems

In GaAs quantum Hall (QH) systems, electrons are coupled with nuclear spins through the hyperfine interaction, which is normally not strong enough to change the dynamics of electrons and nuclear spins. The dynamics of the QH systems, however, may drastically change when the nuclear spins interact with low-energy collective excitation modes of the electron spins. We theoretically investigate the nuclear-electron spin interaction in the QH systems as hybrid quantum systems driven by the hyperfine interaction. In particular, we study the interaction between the nuclear spins and the Nambu-Goldstone (NG) mode with the linear dispersion relation associated with the U(1) spin rotational symmetry breaking. We show that such an interaction is described as nuclear spins collectively coupled to the NG mode, and can be effectively described by the Dicke model. Based on the model we suggest that various collective spin phenomena realized in quantum optical systems can also emerge in the QH systems.