  Controlling the emission and interaction properties of quantum emitters (QEs)
embedded within an optical cavity is a key technique in engineering
light-matter interactions at the nanoscale, as well as in the development of
quantum information processing. State-of-the-art optical cavities are based on
high Q photonics crystals and dielectric resonators. However, wealthier
responses might be attainable with cavities carved in more exotic materials.
Here, we theoretically investigate the emission and interaction properties of
QEs embedded in open epsilon-near-zero (ENZ) cavities. Using analytical methods
and numerical simulations, it is demonstrated that open ENZ cavities present
the unique property of supporting nonradiating modes independently of the
geometry of the external boundary of the cavity (shape, size, topology...).
Moreover, the possibility of switching between radiating and nonradiating modes
enables a dynamic control of both the emission by, and the interaction between,
QEs. These phenomena provide unprecedented degrees of freedom in controlling
and trapping fields within optical cavities, as well as in the design of cavity
opto- and acousto-mechanical systems.
