We study the optical properties of quantum dipole emitters coupled tohyperbolic metamaterial nano-resonators using a semi-analytical quasinormalmode approach. We show that coupling to metamaterial nano-resonators can leadto significant Purcell enhancements that are nearly an order of magnitudelarger than those of plasmonic resonators with comparable geometry. However,the associated single photon output $\beta$-factors are extremely low (around10$\%$), far smaller than those of comparable sized metallic resonators(70$\%$). Using a quasinormal mode expansion of the photon Green function, wedescribe how the low $\beta$-factors are due to increased Ohmic quenchingarising from redshifted resonances, larger quality factors, and strongerconfinement of light within the metal. In contrast to current wisdom, theseresults suggest that hyperbolic metamaterial nano-structures make poor choicesfor single photon sources.
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