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

We introduce the complex band structure and a medium-dependent (Green's function) quantum-optics formalism to study the enhanced spontaneous emission factors and Lamb shifts from a quantum dot or atom near the surface of a slow-light metamaterial waveguide. Using a realistic loss factor of gamma/2 pi=2 THz, Purcell factors of approximately 250 and 100 are found at optical frequencies for p-polarized and s-polarized dipoles, respectively, placed 28 nm (0.02 lambda(0)) above the slab surface. 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 to -6 GHz for a dipole moment of 50 Debye. We also make a direct calculation of the far-field-emission spectra which contains direct measurable access to these enhanced Purcell factors and Lamb shifts.