Potential one-forms for hyperk\"ahler structures with torsion

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperk\"ahler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion.Comment: 16 pages, Latex, no figure

Planar immersion lens with metasurfaces

The solid immersion lens is a powerful optical tool that allows light entering material from air or vacuum to focus to a spot much smaller than the free-space wavelength. Conventionally, however, they rely on semispherical topographies and are non-planar and bulky, which limits their integration in many applications. Recently, there has been considerable interest in using planar structures, referred to as metasurfaces, to construct flat optical components for manipulating light in unusual ways. Here, we propose and demonstrate the concept of a planar immersion lens based on metasurfaces. The resulting planar device, when placed near an interface between air and dielectric material, can focus electromagnetic radiation incident from air to a spot in material smaller than the free-space wavelength. As an experimental demonstration, we fabricate an ultrathin and flexible microwave lens and further show that it achieves wireless energy transfer in material mimicking biological tissue

Polarization and frequency disentanglement of photons via stochastic polarization mode dispersion

We investigate the quantum decoherence of frequency and polarization variables of photons via polarization mode dispersion in optical fibers. By observing the analogy between the propagation equation of the field and the Schr\"odinger equation, we develop a master equation under Markovian approximation and analytically solve for the field density matrix. We identify distinct decay behaviors for the polarization and frequency variables for single-photon and two-photon states. For the single photon case, purity functions indicate that complete decoherence for each variable is possible only for infinite fiber length. For entangled two-photon states passing through separate fibers, entanglement associated with each variable can be completely destroyed after characteristic finite propagation distances. In particular, we show that frequency disentanglement is independent of the initial polarization status. For propagation of two photons in a common fiber, the evolution of a polarization singlet state is addressed. We show that while complete polarization disentanglement occurs at a finite propagation distance, frequency entanglement could survive at any finite distance for gaussian states.Comment: 2 figure

Determining system Hamiltonian from eigenstate measurements without correlation functions

Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate $|\psi\rangle$ require information of nonlocal correlation functions. In this work, we develop an algorithm to determine local Hamiltonians from only local measurements on $|\psi\rangle$, by reformulating the task as an unconstrained optimization problem of certain target function of Hamiltonian parameters, with only polynomial number of parameters in terms of system size. We also develop a machine learning-based-method to solve the first-order gradient used in the algorithm. Our method is tested numerically for randomly generated local Hamiltonians and returns promising reconstruction in the desired accuracy. Our result shed light on the fundamental question on how a single eigenstate can encode the full system Hamiltonian, indicating a somewhat surprising answer that only local measurements are enough without additional assumptions, for generic cases.Comment: 11 pages, 10 figure

Relation Between First Arrival Time and Permeability in Self-Affine Fractures with Areas in Contact

We demonstrate that the first arrival time in dispersive processes in self-affine fractures are governed by the same length scale characterizing the fractures as that which controls their permeability. In one-dimensional channel flow this length scale is the aperture of the bottle neck, i.e., the region having the smallest aperture. In two dimensions, the concept of a bottle neck is generalized to that of a minimal path normal to the flow. The length scale is then the average aperture along this path. There is a linear relationship between the first arrival time and this length scale, even when there is strong overlap between the fracture surfaces creating areas with zero permeability. We express the first arrival time directly in terms of the permeability.Comment: EPL (2012)