This paper introduces a theoretical framework for understanding the accumulation of non-Abelian geometric phases in rotating nitrogen-vacancy centers in diamond. Specifically, we consider how degenerate states can be achieved and demonstrate that the
resulting geometric phase for multiple paths is non-Abelian. We find that the non-Abelian nature of the phase is robust to fluctuations in the path and magnetic field. In contrast to previous studies of the accumulation of Abelian geometric phases for nitrogen-vacancy centers under rotation we find that the limiting time-scale is $T_{1}$. As such a non-Abelian geometric phase accumulation in nitrogen-vacancy centers has potential advantages for applications as gyroscopes.
We derive a governing equation for a Kelvin wave supported on a vortex line in a Bose-Einstein condensate, in a rotating cylindrically symmetric parabolic trap. From this solution the Kelvin wave dispersion relation is determined. In the limit of an
oblate trap and in the absence of longitudinal trapping our results are consistent with previous work. We show that the derived Kelvin wave dispersion in the general case is in quantitative agreement with numerical calculations of the Bogoliubov spectrum and offer a significant improvement upon previous analytical work.
Quantum graphity offers the intriguing notion that space emerges in the low energy states of the spatial degrees of freedom of a dynamical lattice. Here we investigate metastable domain structures which are likely to exist in the low energy phase of
lattice evolution. Through an annealing process we explore the formation of metastable defects at domain boundaries and the effects of domain structures on the propagation of bosons. We show that these structures should have observable background independent consequences including scattering, double imaging, and gravitational lensing-like effects.
By coupling controllable quantum systems into larger structures we introduce the concept of a quantum metamaterial. Conventional meta-materials represent one of the most important frontiers in optical design, with applications in diverse fields rangi
ng from medicine to aerospace. Up until now however, metamaterials have themselves been classical structures and interact only with the classical properties of light. Here we describe a class of dynamic metamaterials, based on the quantum properties of coupled atom-cavity arrays, which are intrinsically lossless, reconfigurable, and operate fundamentally at the quantum level. We show how this new class of metamaterial could be used to create a reconfigurable quantum superlens possessing a negative index gradient for single photon imaging. With the inherent features of quantum superposition and entanglement of metamaterial properties, this new class of dynamic quantum metamaterial, opens a new vista for quantum science and technology.
