Taking advantage of multiplet structure for lineshape analysis in Fourier space

Lineshape analysis is a recurrent and often computationally intensive task in optics, even more so for multiple peaks in the presence of noise. We demonstrate an algorithm which takes advantage of peak multiplicity (N) to retrieve line shape information. The method is exemplified via analysis of Lorentzian and Gaussian contributions to individual lineshapes for a practical spectroscopic measurement and benefits from a linear increase in sensitivity with the number N. The robustness of the method and its benefits in terms of noise reduction and order of magnitude improvement in run-time performance are discussed.Comment: 12 pages, 6 figure

Direct and alignment-insensitive measurement of cantilever curvature

We analytically derive and experimentally demonstrate a method for the simultaneous measurement of deflection for large arrays of cantilevers. The Fresnel diffraction patterns of a cantilever independently reveals tilt, curvature, cubic and higher order bending of the cantilever. It provides a calibrated absolute measurement of the polynomial coefficients describing the cantilever shape, without careful alignment and could be applied to several cantilevers simultaneously with no added complexity. We show that the method is easily implemented, works in both liquid mediums and in air, for a broad range of displacements and is especially suited to the requirements for multi-marker biosensors.Comment: 5 Pages, 4 figures, letter forma

Optical diffraction for measurements of nano-mechanical bending

Micromechanical transducers such as cantilevers for AFM often rely on optical readout methods that require illumination of a specific region of the microstructure. Here we explore and exploit the diffraction effects that have been previously neglected when modeling cantilever bending measurement techniques. The illumination of a cantilever end causes an asymmetric diffraction pattern at the photodetector that significantly affects the calibration of the signal in the popular optical beam deflection technique (OBDT). Conditions for optimized linear signals that avoid detection artifacts conflict with small numerical aperture illumination and narrow cantilevers which are softer and therefore more sensitive. Embracing diffraction patterns as a physical measurable allows a richer detection technique that decouples measurements of tilt and curvature and simultaneously relaxes the requirements on the alignment of illumination and detector. We show analytical results, numerical simulations and physiologically relevant experimental data demonstrating the usefulness of these diffraction features. We offer experimental design guidelines and identify and quantify possible sources of systematic error of up to 10% in OBDT. We demonstrate a new nanometre resolution detection method that can replace OBDT, where Frauenhofer and Bragg diffraction effects from finite sized and patterned cantilevers are exploited. Such effects are readily generalized to arrays, and allow transmission detection of mechanical curvature, enabling in-line instruments. In particular, a cantilever with a periodic array of slots produces Bragg peaks which can be analyzed to deduce the cantilever curvature. We highlight the comparative advantages over OBDT by detecting molecular activity of antibiotic Vancomycin, with an RMS noise equivalent to less than $2.5 \mu M$ (1.5 nm), as example of possible multi-maker bio-assays.Comment: 9 pages, 8 figure

Using random testing to manage a safe exit from the COVID-19 lockdown

We argue that frequent sampling of the fraction of infected people (either by random testing or by analysis of sewage water), is central to managing the COVID-19 pandemic because it both measures in real time the key variable controlled by restrictive measures, and anticipates the load on the healthcare system due to progression of the disease. Knowledge of random testing outcomes will (i) significantly improve the predictability of the pandemic, (ii) allow informed and optimized decisions on how to modify restrictive measures, with much shorter delay times than the present ones, and (iii) enable the real-time assessment of the efficiency of new means to reduce transmission rates. Here we suggest, irrespective of the size of a suitably homogeneous population, a conservative estimate of 15000 for the number of randomly tested people per day which will suffice to obtain reliable data about the current fraction of infections and its evolution in time, thus enabling close to real-time assessment of the quantitative effect of restrictive measures. Still higher testing capacity permits detection of geographical differences in spreading rates. Furthermore and most importantly, with daily sampling in place, a reboot could be attempted while the fraction of infected people is still an order of magnitude higher than the level required for a relaxation of restrictions with testing focused on symptomatic individuals. This is demonstrated by considering a feedback and control model of mitigation where the feed-back is derived from noisy sampling data.Comment: 18 pages, 6 figures, 2 appendices. Phys. Biol. (2020

High-Frequency Spin Waves in YBa₂Cu₃O\u3csub\u3e6.15\u3e/sub\u3e

Pulsed neutron spectroscopy is used to absolute measurements of the dynamic magnetic susceptibility of insulating YBa2Cu3O6.15. Acoustic and optical modes, derived from inand out-of-phase oscillation of spins in adjacent CuO2 planes, dominate the spectra and are observed up to 250 meV. The optical modes appear first at 74±5 meV. Linear-spin-wave theory gives an excellent description of the data and yields intralayer and interlayer exchange constants of J∥=125±5 meV and J⊥=11±2 meV, respectively, and a spin-wave intensity renormalization ZΧ=0.4±0.1

Influence of oxygen pressure and aging on LaAlO3 films grown by pulsed laser deposition on SrTiO3 substrates

The crystal structures of LaAlO3 films grown by pulsed laser deposition on SrTiO3 substrates at oxygen pressure of 10-3 mbar or 10-5 mbar, where kinetics of ablated species hardly depend on oxygen background pressure, are compared. Our results show that the interface between LaAlO3 and SrTiO3 is sharper when the oxygen pressure is lower. Over time, the formation of various crystalline phases is observed while the crystalline thickness of the LaAlO3 layer remains unchanged. X-ray scattering as well as atomic force microscopy measurements indicate three-dimensional growth of such phases, which appear to be fed from an amorphous capping layer present in as-grown samples

Quantum phase transitions in transverse field spin models: from statistical physics to quantum information

We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of the spin-1/2 Ising and XY models in a transverse field. Beginning with an overview of quantum phase transitions, we introduce a number of model Hamiltonians. We provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies. We also discuss Kitaev models and some other exactly solvable spin systems. Studies of quantum phase transitions in the presence of quenched randomness and with frustrating interactions are presented in detail. We discuss novel phenomena like Griffiths-McCoy singularities. We then turn to more recent topics like information theoretic measures of the quantum phase transitions in these models such as concurrence, entanglement entropy, quantum discord and quantum fidelity. We then focus on non-equilibrium dynamics of a variety of transverse field systems across quantum critical points and lines. After mentioning rapid quenching studies, we dwell on slow dynamics and discuss the Kibble-Zurek scaling for the defect density following a quench across critical points and its modifications for quenching across critical lines, gapless regions and multicritical points. Topics like the role of different quenching schemes, local quenching, quenching of models with random interactions and quenching of a spin chain coupled to a heat bath are touched upon. The connection between non-equilibrium dynamics and quantum information theoretic measures is presented at some length. We indicate the connection between Kibble-Zurek scaling and adiabatic evolution of a state as well as the application of adiabatic dynamics as a tool of a quantum optimization technique known as quantum annealing. The final section is dedicated to a detailed discussion on recent experimental studies of transverse Ising-like systems.Comment: 106 pages, 38 figures; an expanded version has been published as a book (330 pages, 72 figures, 874 references) as A. Dutta, G. Aeppli, B. K. Chakrabarti, U. Divakaran, T. F. Rosenbaum and D. Sen, Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information (Cambridge University Press, Cambridge, 2015