Ultrahigh Purcell factors and Lamb shifts using slow-light metamaterial waveguides

TL;DR

This paper demonstrates how slow-light metamaterial waveguides can significantly enhance spontaneous emission rates and Lamb shifts of quantum emitters, providing measurable effects with potential applications in quantum optics.

Contribution

It introduces a formalism combining quantum optics and Green functions to analyze Purcell factors and Lamb shifts near metamaterial waveguides, revealing unprecedented enhancement effects.

Findings

Purcell factors of approximately 250 (p-polarized) and 100 (s-polarized) at optical frequencies.

Lamb shifts of about -1 GHz to -6 GHz predicted for quantum dots near metamaterials.

Large Purcell enhancements are achievable even with realistic metamaterial losses.

Abstract

Employing a medium-dependent quantum optics formalism and a Green function solution of Maxwell's equations, we study the enhanced spontaneous emission factors (Purcell factors) and Lamb shifts from a quantum dot or atom near the surface of a %embedded in a slow-light metamaterial waveguide. Purcell factors of approximately 250 and 100 are found at optical frequencies for $p-$polarized and $s-$polarized dipoles respectively placed 28\thinspace nm (0.02\thinspace $\lambda_{0}$) above the slab surface, including a realistic metamaterial loss factor of $\gamma /2\pi =2 \mathrm{THz}$. For smaller loss values, we demonstrate that the slow-light regime of odd metamaterial waveguide propagation modes can be observed and related to distinct resonances in the Purcell factors. Correspondingly, we predict unusually large and rich Lamb shifts of approximately -1 GHz to -6 GHz for a dipole moment of 50 Debye. We also make a direct calculation of the far field emission spectrum, which contains direct measurable access to these enhanced Purcell factors and Lamb shifts.