Observation of an exceptional point in an ultrasonic cavity

Abstract

A physical system can be described by a non-Hermitian Hamiltonian if the system is open or it has either absorptive loss or amplifying gain. One of the important properties of the non-Hermitian Hamiltonian is the existence of an exceptional point (EP). This EP condition is satisfied when the coupling strength between interacting eigenstates is the same as their differential loss. At an EP, the eigenstates are degenerate in both eigenvalue and eigenfunction, exhibiting interesting features such as branch-point topology, breakdown of adiabaticity when encircled dynamically.

In this thesis, we reveal EP's both in ultrasonic and optical cavities, both of which are non-Hermitian systems. First we report observation of an EP in an ultrasonic cavity both theoretically and experimentally. Concentric circular shell cavity is adopted as platform for the study. At first, system parameters for the EP condition is predicted by theoretical analysis. The schlieren method, which is widely used to visualize refractive index modulation in transparent media, is applied to the ultrasonic cavity when we experimentally measure the resonance spectrum and the wavefunction. Then we confirm the existence of an EP in the shell cavity by comparing the theoretical and experimental results.

We also investigate modified spontaneous emission in a deformed optical microcavity, which is known as the Petermann effect. First we establish non-Hermitian cavity quantum electrodynamics (QED) theory, deriving modified laser rate equations. Then we find out that number of spontaneously emitted photon into a mode can be enhanced by the Petermann effect near an EP, whereas total atomic spontaneous emission rate is invariant. As a consequence, it is shown that the emission power of a lasing mode can be increased at the same pump power compared to that without the Petermann effect. Finally, we also present experimental results supporting the non-Hermitian cavity-QED theory.