The nuclear spin in the vicinity of a nitrogen-vacancy (NV) center possesses of long coherence time and convenient manipulation assisted by the strong hyperfine interaction with the NV center. It is suggested for the subsequent quantum information storage and processing after appropriate initialization. However, current experimental schemes are either sensitive to the inclination and magnitude of the magnetic field or require thousands of repetitions to achieve successful realization. Here, we propose polarizing a 13 C nuclear spin in the vicinity of an NV center via a dark state. We demonstrate theoretically that it is robust to polarize various nuclear spins with different hyperfine couplings and noise strengths.

We theoretically investigate the intra-band transitions in Möbius molecules. Due to the weak magnetic response, the relative permittivity is significantly modified by the presence of the medium while the relative permeability is not.We show that there is hyperbolic dispersion relation induced by the intra-band transitions because one of the eigen-values of permittivity possesses a different sign from the other two, while all three eigen-values of permeability are positive. We further demonstrate that the bandwidth of negative refraction is 0.1952 eV for the H -polarized incident light, which is broader than the ones for inter-band transitions by 3 orders of magnitude. Moreover, the frequency domain has been shifted from ultra-violet to visible domain. Although there is negative refraction for the Epolarized incident light, the bandwidth is much narrower and depends on the incident angle.

The potential applications of metamaterials with negative refraction are limited by their narrow bandwidth and difficulty in fabrication. In order to broaden the bandwidth, we analyze different factors which influence the negative refraction in solids and multi-atom molecules. We find that this negative refraction can be significantly enhanced by simultaneous multi-electron transitions with the same transition frequency and dipole redistribution over different eigenstates. We show that these simultaneous multi-electron transitions and enhanced transition dipole broaden the bandwidth of the negative refraction by at least one order of magnitude. Furthermore, we show the possible application of this scheme in hyperbolic metamaterials using diamonds with NV centers.