Elementary modes of coupled oscillators as whispering-gallery microresonators (Q2809102)

The authors analyze a system of two linear coupled oscillators, one with loss (dissipation) and the other with gain (negative dissipation). The study is motivated by experiments on so-called whispering-gallery microresonators (WGMR). In previous experiments it has been shown that in the case when loss and gain are equal, the system becomes parity-time (PT) symmetric. The theoretical analysis in this paper is based on construction of the Lagrangian for the system and on the study of elementary modes. In such way, the energy is understood in terms of energy sharing between modes. This theoretical analysis explains phase transition from PT-symmetry-breaking phase to PT-symmetric phase observed experimentally. The analysis is further extended to the case when the system of coupled oscillators is driven by a weak external force.