Spherical harmonic based noise rejection and neuronal sampling with multi-axis OPMs

In this study we explore the interference rejection and spatial sampling properties of multi-axis Optically Pumped Magnetometer (OPM) data. We use both vector spherical harmonics and eigenspectra to quantify how well an array can separate neuronal signal from environmental interference while adequately sampling the entire cortex. We found that triaxial OPMs have superb noise rejection properties allowing for very high orders of interference (L=6) to be accounted for while minimally affecting the neural space (2dB attenuation for a 60-sensor triaxial system). To adequately model the signals arising from the cortex, we show that at least 11th order (143 spatial degrees of freedom) irregular solid harmonics or 95 eigenvectors of the lead field are needed to model the neural space for OPM data (regardless of number of axes measured). This can be adequately sampled with 75-100 equidistant triaxial sensors (225-300 channels) or 200 equidistant radial channels. In other words, ordering the same number of channels in triaxial (rather than purely radial) configuration gives significant advantages not only in terms of external noise rejection but also minimizes cost, weight and cross-talk.

Spin structures of the ground states of four body bound systems with spin 3 cold atoms

We consider the case that four spin-3 atoms are confined in an optical trap. The temperature is so low that the spatial degrees of freedom have been frozen. Exact numerical and analytical solutions for the spin-states have been both obtained. Two kinds of phase-diagrams for the ground states (g.s.) have been plotted. In general, the eigen-states with the total-spin S (a good quantum number) can be expanded in terms of a few basis-states $$f_{S,i}$$ f S , i . Let $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ be the probability of a pair of spins coupled to $$\lambda =0, 2, 4$$ λ = 0 , 2 , 4 , and 6 in the $$f_{S,i}$$ f S , i state. Obviously, when the strength $$g_{\lambda }$$ g λ of the $$\lambda $$ λ -channel is more negative, the basis-state with the largest $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ would be more preferred by the g.s.. When two strengths are more negative, the two basis-states with the two largest probabilities would be more important components. Thus, based on the probabilities, the spin-structures (described via the basis-states) can be understood. Furthermore, all the details in the phase-diagrams, say, the critical points of transition, can also be explained. Note that, for $$f_{S,i}$$ f S , i , $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ is completely determined by symmetry. Thus, symmetry plays a very important role in determining the spin-structure of the g.s..

Frequency-dependent estimation of effective spatial degrees of freedom

Climate variability occurs over wide ranges of spatial and temporal scales. It exhibits a complex spatial covariance structure, which depends on geographic location (e.g., tropics vs. extratropics), and also consists of a superposition of: (a) components with gradually decaying positive correlation functions, and (b) teleconnections that often involve anti-correlations. In addition, there are indications that the spatial covariance structure depends on frequency. Thus, a comprehensive assessment of the spatio-temporal covariance structure of climate variability would require an extensive set of statistical diagnostics. Therefore, it is often desirable to characterize the covariance structure by a simple summarizing metric that is easy to compute from datasets. Such summarizing metrics are useful, for example, in the context of comparisons between climate models or between models and observations. Here we introduce a frequency-dependent version of a simple measure of the effective spatial degrees of freedom. The measure is based on the temporal variance of the global average of some climate variable, and its novel aspect consists in its frequency-dependence. We also provide a clear geometric interpretation of the measure. Its easy applicability is demonstrated using near-surface temperature and precipitation fields obtained from a paleoclimate model simulation. This application reveals a distinct scaling behavior of the spatial degrees of freedom as a function of frequency, ranging from monthly to millennial scales.

Higher-dimensional supersymmetric microlaser arrays

The nonlinear scaling of complexity with the increased number of components in integrated photonics is a major obstacle impeding large-scale, phase-locked laser arrays. Here, we develop a higher-dimensional supersymmetry formalism for precise mode control and nonlinear power scaling. Our supersymmetric microlaser arrays feature phase-locked coherence and synchronization of all of the evanescently coupled microring lasers—collectively oscillating in the fundamental transverse supermode—which enables high-radiance, small-divergence, and single-frequency laser emission with a two-orders-of-magnitude enhancement in energy density. We also demonstrate the feasibility of structuring high-radiance vortex laser beams, which enhance the laser performance by taking full advantage of spatial degrees of freedom of light. Our approach provides a route for designing large-scale integrated photonic systems in both classical and quantum regimes.

Power-law frequency scaling of surface temperature spatial degrees of freedom – estimated from instrumental data, reanalysis and climate model simulations

<p>What is the spatial scale of climate fluctuations, and how does this scale depend on the timescale under consideration? To answer this question, the spatio-temporal correlation structure of global surface temperature fields is characterized, for the period 1850-present, by estimating frequency spectra of the effective spatial degrees of freedom (ESDOF). These ESDOF spectra serve as a simple summarizing metric of the frequency-dependent spatial auto-correlation function. ESDOF spectra are estimated from: (a) the HadCRUT global gridded temperature anomaly dataset, based exclusively on instrumental measurements, and including detailed error variance estimates; (b) the NOAA 20th Century Reanalysis; and (c) a large ensemble of CMIP historical climate model simulations. When comparing (i) error corrected ESDOF spectra from the instrumental data to (ii) those obtained from the reanalysis and the model simulations, with HadCRUT data gaps imposed, results are found to be highly consistent among the three data sources. When the analysis is applied to the entire globe, the ESDOF spectra exhibit an almost uniform power-law frequency scaling with about 100 ESDOFs at monthly timescales and only about 2 ESDOFs at multidecadal timescales. Second-order differences in this scaling behaviour are found when the analysis is restricted to various spatial subdomains of the globe, namely, the tropics, extra-tropics, land areas, and ocean areas. A few implications of the diagnosed ESDOF reduction towards the longer timescales are briefly discussed.</p>

Directional Elastic Pseudospin and Nonseparability of Directional and Spatial Degrees of Freedom in Parallel Arrays of Coupled Waveguides

We experimentally and numerically investigated elastic waves in parallel arrays of elastically coupled one-dimensional acoustic waveguides composed of aluminum rods coupled along their length with epoxy. The elastic waves in each waveguide take the form of superpositions of states in the space of direction of propagation. The direction of propagation degrees of freedom is analogous to the polarization of a quantum spin; hence, these elastic waves behave as pseudospins. The amplitude in the different rods of a coupled array of waveguides (i.e., the spatial mode of the waveguide array) refer to the spatial degrees of freedom. The elastic waves in a parallel array of coupled waveguides are subsequently represented as tensor products of the elastic pseudospin and spatial degrees of freedom. We demonstrate the existence of elastic waves that are nonseparable linear combinations of tensor products states of pseudospin/ spatial degrees of freedom. These elastic waves are analogous to the so-called Bell states of quantum mechanics. The amplitude coefficients of the nonseparable linear combination of states are complex due to the Lorentzian character of the elastic resonances associated with these waves. By tuning through the amplitudes, we are able to navigate both experimentally and numerically a portion of the Bell state Hilbert space.