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

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

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

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

Optimal Ensemble Control of Matter-Wave Splitting in Bose-Einstein Condensates

We present a framework for designing optimal optical pulses for the matter-wave splitting of a Bose-Einstein Condensate (BEC) under the influence of experimental inhomogeneities, so that the sample is transferred from an initial rest position into a singular higher diffraction order. To represent the evolution of the population of atoms, the Schroedinger's equation is reinterpreted as a parameterized ensemble of dynamical units that are disparately impacted by the beam light-shift potential in a continuous manner. The derived infinite-dimensional coupled Raman-Nath equations are truncated to a finite system of diffraction levels, and we suppose that the parameter that defines the inhomogeneity in the control applied to the ensemble system is restricted to a compact interval. We first design baseline square pulse sequences for the excitation of BEC beam-splitter states following a previous study, subject to dynamic constraints for either a nominal system assuming no inhomogeneity or for several samples of the uncertain parameter. We then approximate the continuum state-space of the ensemble of dynamics using a spectral approach based on Legendre moments, which is truncated at a finite order. Control functions that steer the BEC system from an equivalent rest position to a desired final excitation are designed using a constrained optimal control approach developed for handling nonlinear dynamics. This representation results in a minimal dimension of the computational problem and is shown to be highly robust to inhomogeneity in comparison to the baseline approach. Our method accomplishes the BEC-splitting state transfer for each subsystem in the ensemble, and is promising for precise excitation in experimental settings where robustness to environmental and intrinsic noise is paramount