Dicke Phase Transition with Multiple Superradiant States in Quantum Chaotic Resonators
Physical Review X
We experimentally investigate the Dicke phase transition in chaotic optical resonators realized with two-dimensional photonics crystals. This setup circumvents the constraints of the system originally investigated by Dicke and allows a detailed study of the various properties of the superradiant transition. Our experimental results, analytical prediction, and numerical modeling based on random-matrix theory demonstrate that the probability density PðΓÞ of the resonance widths provides a new
... provides a new criterion to test the occurrence of the Dicke transition. Superradiance is an emergent property of quantum systems that has stirred a large interest in scientific research       . Initially predicted by Dicke in the context of twolevel atoms , superradiance has been investigated in a wide range of systems including gases , plasmas , semiconductors [10-12], free-electron lasers [13,14], Bose-Einstein condensates [15-19], superconductors , quantum systems with impurities , and quantum dots [10, 22, 23] . In two-level media, a superradiant state results from the spontaneous synchronization of different atoms immersed in a common radiation field, whose wavelength is larger than the volume occupied by the material. When this condition is met, a quantum phase transition occurs and atoms radiate energy with a quadratic dependence on their population (∝ N 2 ), much higher than the rate predicted by incoherent spontaneous emission (∝ N)     . The consequence of such a superradiant behavior is recognized in the spatiotemporal domain, where a directional, shortlived energy burst is generated due to the enhanced radiation rate, while in the case of incoherent emission, only exponentially decaying intensity is observed  .