PT\mathcal{PT}-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states

Aubry-Andre Harper (AAH) lattice models, characterized by reflection-asymmetric, sinusoidally varying nearest-neighbor tunneling profile, are well-known for their topological properties. We consider the fate of such models in the presence of balanced gain and loss potentials $\pm i\gamma$ located at reflection-symmetric sites. We predict that these models have a finite $\mathcal{PT}$ breaking threshold only for {\it specific locations} of the gain-loss potential, and uncover a hidden symmetry that is instrumental to the finite threshold strength. We also show that the topological edge-states remain robust in the $\mathcal{PT}$-symmetry broken phase. Our predictions substantially broaden the possible realizations of a $\mathcal{PT}$-symmetric system.Comment: 8 pages, 5 figure

Assessment of fish populations and habitat on Oculina Bank, a deep-sea coral marine protected area off eastern Florida

A portion of the Oculina Bank located off eastern Florida is a marine protected area (MPA) preserved for its dense populations of the ivory tree coral (Oculina varicosa), which provides important habitat for fish. Surveys of fish assemblages and benthic habitat were conducted inside and outside the MPA in 2003 and 2005 by using remotely operated vehicle video transects and digital still imagery. Fish species composition, biodiversity, and grouper densities were used to determine whether O. varicosa forms an essential habitat compared to other structure-forming habitats and to examine the effectiveness of the MPA. Multivariate analyses indicated no differences in fish assemblages or biodiversity among hardbottom habitat types and grouper densities were highest among the most complex habitats; however the higher densities were not exclusive to coral habitat. Therefore, we conclude that O. varicosa was functionally equivalent to other hardbottom habitats. Even though fish assemblages were not different among management areas, biodiversity and grouper densities were higher inside the MPA compared to outside. The percentage of intact coral was also higher inside the MPA. These results provide initial evidence demonstrating effectiveness of the MPA for restoring reef fish and their habitat. This is the first study to compare reef fish populations on O. varicosa with other structure-forming reef habitats and also the first to examine the effectiveness of the MPA for restoring fish populations and live reef cover

Sublattice signatures of transitions in a PT -symmetric dimer lattice

Lattice models with non-hermitian, parity and time-reversal (PTPT) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A PTPT-symmetric dimer lattice consists of dimers with intra-dimer coupling νν, inter-dimer coupling ν′ν′, and balanced gain and loss potentials ±iγ±iγ within each dimer. This model undergoes two independent transitions, namely a PTPT-breaking transition and a topological transition. We numerically and analytically investigate the signatures of these transitions in the time-evolution of states that are initially localized on the gain-site or the loss-site

Passive parity-time-symmetry-breaking transitions without exceptional points in dissipative photonic systems

Over the past decade, parity-time (PT)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the PT-symmetry-breaking transition occurs at the exceptional point of the non-Hermitian Hamiltonian, where its eigenvalues and the corresponding eigenvectors both coincide. Here, we show that in lossy systems, the PT transition is a phenomenon that broadly occurs without an attendant exceptional point, and is driven by the potential asymmetry between the neutral and the lossy regions. With experimentally realizable quantum models in mind, we investigate dimer and trimer waveguide configurations with one lossy waveguide. We validate the tight-binding model results by using the beam-propagation-method analysis. Our results pave a robust way toward studying the interplay between passive PT transitions and quantum effects in dissipative photonic configurations

Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks

Quantum walks often provide telling insights about the structure of the system on which they are performed. In PT-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models. We find that the transition is sensitive to the initial state of the walker on the Bloch sphere, and the resultant mean displacement has a robust topological component and a quasiclassical component. In PT symmetric dimer lattices, we also show that the transition is smeared by nonlinear effects that become important in the PT-symmetry broken region. By carrying out consistency checks via analytical calculations, tight-binding results, and beam-propagation-method simulations, we show that our predictions are easily testable in today’s experimental systems

PT symmetry breaking in the presence of random, periodic, long-range hopping

Over the past five years, open systems with balanced gain and loss have been investigated for extraordinary properties that are not shared by their closed counterparts. Non-Hermitian, Parity-Time (PT ) symmetric Hamiltonians faithfully model such systems. Such a Hamiltonian typically consists of a reflection-symmetric, Hermitian, nearest-neighbor hopping profile and a PT-symmetric, non-Hermitian, gain and loss potential, and has a robust PT -symmetric phase. Here we investigate the robustness of this phase in the presence of long-range hopping disorder that is not PT-symmetric, but is periodic. We find that the PT-symmetric phase remains robust in the presence of such disorder, and characterize the configurations where that happens. Our results are found using a tight-binding model, and we validate our predictions through the beam-propagation method

Nonlinear and time-resolved optical study of the 112-type iron-based superconductor parent Ca_(1−x)La_xFeAs_2 across its structural phase transition

The newly discovered 112-type ferropnictide superconductors contain chains of As atoms that break the tetragonal symmetry between the ɑ and b axes. This feature eliminates the need for uniaxial strain that is usually required to stabilize large single domains in the electronic nematic state that exists in the vicinity of magnetic order in the iron-based superconductors. We report detailed structural symmetry measurements of 112-type Ca_(0.73)La_(0.27)FeAs_2 using rotational anisotropy optical second-harmonic generation. This technique is complementary to diffraction experiments and enables a precise determination of the point-group symmetry of a crystal. By combining our measurements with density functional theory calculations, we uncover a strong optical second-harmonic response of bulk electric dipole origin from the Fe and Ca 3d-derived states that enables us to assign C_2 as the crystallographic point group. This makes the 112-type materials high-temperature superconductors without a center of inversion, allowing for the possible mixing of singlet and triplet Cooper pairs in the superconducting state. We also perform pump-probe transient reflectivity experiments that reveal a 4.6-THz phonon mode associated with the out-of-plane motion of As atoms in the FeAs layers. We do not observe any suppression of the optical second-harmonic response or shift in the phonon frequency upon cooling through the reported monoclinic-to-triclinic transition at 58 K. This allows us to identify C_1 as the low-temperature crystallographic point group but suggests that structural changes induced by long-range magnetic order are subtle and do not significantly affect electronic states near the Fermi level

From Spectators of Public Affairs to Agents of Social Change: Engaging Students in the Basic Course through Service-Learning

Much literature bemoans the attitudes of Generation X (and their successors) toward civic participation (e.g., Putnam, 2000) and indeed education itself (e.g., Sacks, 1996). However, we have found students to be highly engaged when they have opportunities for active learning, such as those found in well designed service learning projects. We see this pedagogy as a small antidote to the sense of powerlessness that often pervades our culture. Drawing on diverse literatures, we explore theoretical reasons for using service-learning and illustrate its usefulness in speech communication basic course. Our discussion is organized around two key themes: (a) connection of self to subject matter, and (b) the connection of self to community. After discussing service learning exemplars in the basic course, we close with cautions about the use of service-learning