We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of stat
es in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. In the 1D Bose-Hubbard model, the NEM as a function of $t/U$ changes from zero to negative on approaching the critical point of quantum phase transition.
Negative index metamaterials (NIMs) give rise to unusual and intriguing properties and phenomena, which may lead to important applications such as superlens, subwavelength cavity and slow light devices. However, the negative refractive index in metam
aterials normally requires a stringent condition of simultaneously negative permittivity and negative permeability. A new class of negative index metamaterials - chiral NIMs, have been recently proposed. In contrast to the conventional NIMs, chiral NIMs do not require the above condition, thus presenting a very robust route toward negative refraction. Here we present the first experimental demonstration of a chiral metamaterial exhibiting negative refractive index down to n=-5 at terahertz frequencies, with only a single chiral resonance. The strong chirality present in the structure lifts the degeneracy for the two circularly polarized waves and relieves the double negativity requirement. Chiral NIM are predicted to possess intriguing electromagnetic properties that go beyond the traditional NIMs, such as opposite signs of refractive indices for the two circular polarizations and negative reflection. The realization of terahertz chiral NIMs offers new opportunities for investigations of their novel electromagnetic properties, as well as important terahertz device applications.
