Optimal measurement under cost constraints for estimation of propagating wave fields

We give a precise mathematical formulation of some measurement problems arising in optics, which is also applicable in a wide variety of other contexts. In essence the measurement problem is an estimation problem in which data collected by a number of noisy measurement probes arc combined to reconstruct an unknown realization of a random process f(x) indexed by a spatial variable x ε ℝk for some k ≥ 1. We wish to optimally choose and position the probes given the statistical characterization of the process f(x) and of the measurement noise processes. We use a model in which we define a cost function for measurement probes depending on their resolving power. The estimation problem is then set up as an optimization problem in which we wish to minimize the mean-square estimation error summed over the entire domain of f subject to a total cost constraint for the probes. The decision variables are the number of probes, their positions and qualities. We are unable to offer a solution to this problem in such generality; however, for the metrical problem in which the number and locations or the probes are fixed, we give complete solutions Tor some special cases and an efficient numerical algorithm for computing the best trade-off between measurement cost and mean-square estimation error. A novel aspect of our formulation is its close connection with information theory; as we argue in the paper, the mutual information function is the natural cost function for a measurement device. The use of information as a cost measure for noisy measurements opens up several direct analogies between the measurement problem and classical problems of information theory, which are pointed out in the paper. ©2007 IEEE

On the possibility of Vacuum-QED measurements with gravitational wave detectors

Quantum electro dynamics (QED) comprises virtual particle production and thus gives rise to a refractive index of the vacuum larger than unity in the presence of a magnetic field. This predicted effect has not been measured to date, even after considerable effort of a number of experiments. It has been proposed by other authors to possibly use gravitational wave detectors for such vacuum QED measurements, and we give this proposal some new consideration in this paper. In particular we look at possible source field magnet designs and further constraints on the implementation at a gravitational wave detector. We conclude that such an experiment seems to be feasible with permanent magnets, yet still challenging in its implementation.Comment: 11 pages, 10 figure

Holographic particle localization under multiple scattering

We introduce a novel framework that incorporates multiple scattering for large-scale 3D particle-localization using single-shot in-line holography. Traditional holographic techniques rely on single-scattering models which become inaccurate under high particle-density. We demonstrate that by exploiting multiple-scattering, localization is significantly improved. Both forward and back-scattering are computed by our method under a tractable recursive framework, in which each recursion estimates the next higher-order field within the volume. The inverse scattering is presented as a nonlinear optimization that promotes sparsity, and can be implemented efficiently. We experimentally reconstruct 100 million object voxels from a single 1-megapixel hologram. Our work promises utilization of multiple scattering for versatile large-scale applications

Rotated Spectral Principal Component Analysis (rsPCA) for Identifying Dynamical Modes of Variability in Climate Systems.

Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3-60-day periods) in both GPH and SST and El Niño-Southern Oscillation (ENSO) at low frequencies (2-7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics

Coherent storage and manipulation of broadband photons via dynamically controlled Autler-Townes splitting

The coherent control of light with matter, enabling storage and manipulation of optical signals, was revolutionized by electromagnetically induced transparency (EIT), which is a quantum interference effect. For strong electromagnetic fields that induce a wide transparency band, this quantum interference vanishes, giving rise to the well-known phenomenon of Autler-Townes splitting (ATS). To date, it is an open question whether ATS can be directly leveraged for coherent control as more than just a case of "bad" EIT. Here, we establish a protocol showing that dynamically controlled absorption of light in the ATS regime mediates coherent storage and manipulation that is inherently suitable for efficient broadband quantum memory and processing devices. We experimentally demonstrate this protocol by storing and manipulating nanoseconds-long optical pulses through a collective spin state of laser-cooled Rb atoms for up to a microsecond. Furthermore, we show that our approach substantially relaxes the technical requirements intrinsic to established memory schemes, rendering it suitable for broad range of platforms with applications to quantum information processing, high-precision spectroscopy, and metrology.Comment: 14 pages with 6 figures; 3 pages supplementary info with 2 supplementary figure

Generation and characterization of microwave quantum states

Quantum mechanics is the branch of physics that describes the properties and behavior of systems on the atomic and subatomic level. Over the past decades there has also been considerable progress in engineering larger-scale quantum systems. In this day and age, quantum information and quantum technology are rapidly developing areas of research where quantum effects are harnessed to improve sensitivity in measurements, encrypt secure communications, and enhance the performance of information processing and computing. Specific types of quantum states are needed for these purposes, and they can be challenging to generate in practice. This thesis describes methods to generate and characterize microwave states that could be useful for quantum computing protocols based on quantum states of light