Twofold Transition in PT-Symmetric Coupled Oscillators

TL;DR

This paper presents a theoretical analysis of PT-symmetric coupled oscillators, revealing two phase transitions as the coupling parameter varies, which explain experimental observations in optical resonator systems.

Contribution

It introduces a theoretical model showing two PT transitions in coupled oscillators with gain and loss, extending understanding of PT symmetry in optical systems.

Findings

Identification of two PT transitions depending on coupling strength

Equivalence of classical and quantum transition points

Explanation of experimental phenomena in optical resonators

Abstract

The inspiration for this theoretical paper comes from recent experiments on a PT-symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators, one with gain and the other with loss. If the coupled oscillators have a balanced loss and gain, the system is described by a Hamiltonian and the energy is conserved. This theoretical model exhibits two PT transitions depending on the size of the coupling parameter \epsilon. For small \epsilon the PT symmetry is broken and the system is not in equilibrium, but when \epsilon becomes sufficiently large, the system undergoes a transition to an equilibrium phase in which the PT symmetry is unbroken. For very large \epsilon the system undergoes a second transition and is no longer in equilibrium. The classical and the quantized versions of the system exhibit transitions at exactly the same values of \epsilon.