On the Transmittance of Metallic Superlattices in the Optical Regime and the True Refraction Angle

Transmission of electromagnetic fields through (dielectric/metallic)n superlattices, for frequencies below the plasma frequency ωp, is a subtle and important topic that is reviewed and further developed here. Recently, an approach for metallic superlattices based on the theory of finite periodic systems was published. Unlike most, if not all, of the published approaches that are valid in the n→∞ limit, the finite periodic systems approach is valid for any value of n, allows one to determine analytical expressions for scattering amplitudes and dispersion relations. It was shown that, for frequencies below ωp, large metallic-layer thickness, and electromagnetic fields moving along the so-called “true” angle, anomalous results with an apparent parity effect appear. We show here that these results are related to the lack of unitarity and the underlying phenomena of absorption and loss of energy. To solve this problem we present two compatible approaches, both based on the theory of finite periodic systems, which is not only more accurate, but has also the ability to reveal and predict the intra-subband resonances. In the first approach we show that by keeping complex angles, above and below ωp, the principle of flux conservation is fully satisfied. The results above ωp remain the same as in Pereyra (2020). This approach, free of assumptions, where all the information of the scattering process is preserved, gives us insight to improve the formalism where the assumption of electromagnetic fields moving along the real angles is made. In fact, we show that by taking into account the induced currents and the requirement of flux conservation, we end up with an improved approach, with new Fresnel and transmission coefficients, fully compatible with those of the complex-angle approach. The improved approach also allows one to evaluate the magnitude of the induced currents and the absorbed energy, as functions of the frequency and the superlattice parameters. We show that the resonant frequencies of intra-subband plasmons, which may be of interest for applications, in particular for biosensors, can be accurately determined. We also apply the approach for the transmission of electromagnetic wave packets, defined in the optical domain, and show that the predicted space-time positions agree extremely well with the actual positions of the wave packet centroids.

Measuring outcome correlation for Bell cat state and geometric phase induced spin parity effect

In terms of quantum probability statistics, the Bell inequality (BI) and its violation are extended to spin-[Formula: see text] entangled Schrödinger cat state (called the Bell cat state) with both parallel and antiparallel spin-polarizations. Except the spin-1/2, the BI is never ever violated by the Bell cat states with the measuring outcomes including entire Hilbert space. If, on the other hand, measuring outcomes are restricted in the subspace of spin coherent state (SCS), a universal Bell-type inequality (UBI), [Formula: see text], is formulated in terms of the local realistic model. We observe a spin parity effect that the UBI can be violated only by the Bell cat states of half-integer but not the integer spins. The violation of UBI is seen to be a direct result of nontrivial Berry phase between the SCSs of south- and north-pole gauges for half-integer spin, while the geometric phase is trivial for the integer spins. A maximum violation bound of UBI is found as [Formula: see text], which is valid for arbitrary half-integer spin-[Formula: see text] states.

Spin-parity effect in violation of Bell’s inequalities for entangled states of parallel polarization

Bell’s inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while the inequality formulated by Clauser–Horne–Shimony–Holt (CHSH) remains unchanged. The violation of BIs indeed resulted from the quantum nonlocal correlation for spin-[Formula: see text] case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two spins. The spin parity effect originally demonstrated with the antiparallel spin-polarizations (Z. Song, J.-Q. Liang and L.-F. Wei, Mod. Phys. Lett. B 28 (2013) 145004) still exists for the parallel case. The quantum nonlocality does not lead to the violation for integer spins due to the cancellation of nonlocal interference effects by the quantum statistical average. Again, the violation of BIs seems to be a result of the measurement-induced nontrivial Berry phase (BP) for half-integer spins.