Topological Transitions in Metamaterials

The ideas of mathematical topology play an important role in many aspects of modern physics - from phase transitions to field theory to nonlinear dynamics (Nakahara M (2003) in Geometry, Topology and Physics, ed Brewer DF (IOP Publishing Ltd, Bristol and Philadelphia), Monastryskiy M (1987) in Riemann Topology and Physics, (Birkhauser Verlag AG)). An important example of this is the Lifshitz transition (Lifshitz IM (1960) Anomalies of electron characteristics of a metal in the high-pressure region, Sov Phys JETP 11: 1130-1135), where the transformation of the Fermi surface of a metal from a closed to an open geometry (due to e.g. external pressure) leads to a dramatic effect on the electron magneto-transport (Kosevich AM (2004) Topology and solid-state physics. Low Temp Phys 30: 97-118). Here, we present the optical equivalent of the Lifshitz transition in strongly anisotropic metamaterials. When one of the components of the dielectric permittivity tensor of such a composite changes sign, the corresponding iso-frequency surface transforms from an ellipsoid to a hyperboloid. Since the photonic density of states can be related to the volume enclosed by the iso-frequency surface, such a topological transition in a metamaterial leads to a dramatic change in the photonic density of states, with a resulting effect on every single physical parameter related to the metamaterial - from thermodynamic quantities such as its equilibrium electromagnetic energy to the nonlinear optical response to quantum-electrodynamic effects such as spontaneous emission. In the present paper, we demonstrate the modification of spontaneous light emission from quantum dots placed near the surface of the metamaterial undergoing the topological Lifshitz transition, and present the theoretical description of the effect

The Computational Power of Minkowski Spacetime

The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.Comment: 6 pages, LaTeX, feedback welcom

Distributed Quantum Computation Based-on Small Quantum Registers

We describe and analyze an efficient register-based hybrid quantum computation scheme. Our scheme is based on probabilistic, heralded optical connection among local five-qubit quantum registers. We assume high fidelity local unitary operations within each register, but the error probability for initialization, measurement, and entanglement generation can be very high (~5%). We demonstrate that with a reasonable time overhead our scheme can achieve deterministic non-local coupling gates between arbitrary two registers with very high fidelity, limited only by the imperfections from the local unitary operation. We estimate the clock cycle and the effective error probability for implementation of quantum registers with ion-traps or nitrogen-vacancy (NV) centers. Our new scheme capitalizes on a new efficient two-level pumping scheme that in principle can create Bell pairs with arbitrarily high fidelity. We introduce a Markov chain model to study the stochastic process of entanglement pumping and map it to a deterministic process. Finally we discuss requirements for achieving fault-tolerant operation with our register-based hybrid scheme, and also present an alternative approach to fault-tolerant preparation of GHZ states.Comment: 22 Pages, 23 Figures and 1 Table (updated references

Towards Understanding Photodegradation Pathways in Lignins:The Role of Intramolecular Hydrogen Bonding in Excited States

The photoinduced dynamics of the lignin building blocks syringol, guaiacol, and phenol were studied using time-resolved ion yield spectroscopy and velocity map ion imaging. Following irradiation of syringol and guaiacol with a broad-band femtosecond ultraviolet laser pulse, a coherent superposition of out-of-plane OH torsion and/or OMe torsion/flapping motions is created in the first excited 1ππ* (S1) state, resulting in a vibrational wavepacket, which is probed by virtue of a dramatic nonplanar → planar geometry change upon photoionization from S1 to the ground state of the cation (D0). Any similar quantum beat pattern is absent in phenol. In syringol, the nonplanar geometry in S1 is pronounced enough to reduce the degree of intramolecular H bonding (between OH and OMe groups), enabling H atom elimination from the OH group. For guaiacol, H bonding is preserved after excitation, despite the nonplanar geometry in S1, and prevents O–H bond fission. This behavior affects the propensities for forming undesired phenoxyl radical sites in these three lignin chromophores and provides important insight into their relative “photostabilities” within the larger biopolymer

Boolean Models of Bistable Biological Systems

This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex differential equations models. The motivation for this work comes from mathematical systems biology. While Boolean mechanisms do not provide information about exact concentration rates or time scales, they are often sufficient to capture steady states and other key dynamics. Due to their intuitive nature, such models are very appealing to researchers in the life sciences. This paper is focused on dynamical systems that exhibit bistability and are desc ribedby delay equations. It is shown that if a certain motif including a feedback loop is present in the wiring diagram of the system, the Boolean model captures the bistability of molecular switches. The method is appl ied to two examples from biology, the lac operon and the phage lambda lysis/lysogeny switch

Multiscale Random-Walk Algorithm for Simulating Interfacial Pattern Formation

We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can be used to simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance.Comment: 4 pages RevTex, 6 eps figures; substantial changes in presentation, but results and conclusions remain the sam

Charge Solitons in 1-D Arrays of Serially Coupled Josephson Junctions

We study a 1-D array of Josephson coupled superconducting grains with kinetic inductance which dominates over the Josephson inductance. In this limit the dynamics of excess Cooper pairs in the array is described in terms of charge solitons, created by polarization of the grains. We analyze the dynamics of these topological excitations, which are dual to the fluxons in a long Josephson junction, using the continuum sine-Gordon model. We find that their classical relativistic motion leads to saturation branches in the I-V characteristic of the array. We then discuss the semi-classical quantization of the charge soliton, and show that it is consistent with the large kinetic inductance of the array. We study the dynamics of a quantum charge soliton in a ring-shaped array biased by an external flux through its center. If the dephasing length of the quantum charge soliton is larger than the circumference of the array, quantum phenomena like persistent current and coherent current oscillations are expected. As the characteristic width of the charge soliton is of the order of 100 microns, it is a macroscopic quantum object. We discuss the dephasing mechanisms which can suppress the quantum behaviour of the charge soliton.Comment: 26 pages, LaTex, 7 Postscript figure

The 3D Geometry of Reflection Nebulae IC 59 and IC 63 with their illuminating Star Gamma Cas

The early-type star $\gamma$ Cas illuminates the reflection nebulae IC 59 and IC 63, creating two photo-dissociation regions (PDRs). Uncertainties about the distances to the nebulae and the resulting uncertainty about the density of the radiation fields incident on their surfaces have hampered the study of these PDRs during the past three decades. We employed far-UV -- optical nebula -- star colour differences of dust-scattered light to infer the locations of the nebulae relative to the plane of the sky containing $\gamma$ Cas, finding IC 63 to be positioned behind the star and IC 59 in front of the star. To obtain the linear distances of the nebulae relative to $\gamma$ Cas, we fit far-infrared archival $\textit{Herschel}$ flux data for IC 59 and IC 63 with modified blackbody (MBB) curves and relate the resulting dust temperatures with the luminosity of $\gamma$ Cas, yielding approximate distances of 4.15 pc for IC 59 and 2.3 pc for IC 63. With these distances, using updated far-UV flux data in the 6 eV - 13.6 eV range for $\gamma$ Cas with two recent determinations of the interstellar extinction for $\gamma$ Cas, we estimate that the far-UV radiation density at the surface of IC 63 takes on values of $G_0$ = 58 or $G_0$ = 38 with respective values for E(B-V) for $\gamma$ Cas of 0.08 and 0.04 mag. This is a substantial reduction from the range 150 $\le$ $G_0$ $\le$ 650 used for IC 63 during the past three decades. The corresponding, even lower new values for IC 59 are $G_0$ = 18 and $G_0$ = 12.Comment: Accepted for publication on January 4th, 2024 by the Monthly Notices of the Royal Astronomical Societ