Caltech Authors

    Recent progress in weak value amplification and direct measurement

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    The ability to manipulate light has allowed scientists to verify fundamental theories of physics and to develop a new generation of technologies that use photons as a primary resource. Recent developments in quantum measurement theory have offered new alternatives to approach some of the most remarkable problems in quantum physics. Consequently, the principles of quantum mechanics have been exploited in the development of quantum technologies such as optical metrology, quantum communication, and quantum information. In recent years, weak measurements and two of its most remarkable variants: weak value amplification and direct measurement, have been developed and are considered important resources for quantum applications. In this paper, we discuss weak measurements and some significant applications of weak values. We elaborate on how distinct forms of weak values are used to observe and amplify small effects or to directly measure the quantum wave function of photons, a crucial task for schemes for quantum communication and quantum information. We also review some of the most recent methods for weak value amplification and direct measurement that our group has developed

    Performance analysis of d-dimensional quantum cryptography with mode-dependent diffraction

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    We analyze the degraded performance of QKD that results from mode-dependent diffraction in spatial-mode-encoded QKD systems. A pre-compensation method is proposed to solve this problem without sacrificing the security

    Influence of thick atmospheric turbulence on the propagation of quantum states of light using spatial mode encoding

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    The effects of thick turbulence on transverse modes of light carrying orbital angular momentum are studied theoretically and experimentally. These results have potentially important implications for free-space quantum communications systems

    PALM-3000: visible light AO on the 5.1-meter Telescope

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    PALM-3000 is proposed to be the first visible-light sodium laser guide star astronomical adaptive optics system. Deployed as a multi-user shared facility on the 5.1 meter Hale Telescope at Palomar Mountain, this state-of-the-art upgrade to the successful Palomar Adaptive Optics System will have the unique capability to open the visible light spectrum to diffraction-limited scientific access from the ground, providing angular imaging resolution as fine as 16 milliarcsec with modest sky coverage fraction

    Temporal-Harmonic Specific POD Mode Extraction

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    While POD / PCA / KL approximations are statistically energetically optimal, statistical optimality is indeed the sole consideration these (equivalent) methods invoke. This type of approximation is neither geared for, nor is it optimized to extract modes based on their significance to an underlying system dynamics. Furthermore, as computational considerations limit the size of empirical ensembles used for mode extraction, the resulting mode set is significantly effected by the arbitrariness of the ensemble selection. System theoretic model reductions methods aim to home on dynamically significant modes by direct interrogation of the underlying equation, such as the linearized Navier-Stokes equations. An alternative / complimentary approach is to impose a priori knowledge of structural properties, such as symmetry and periodicity, on the mode-extraction procedure. The idea is that these conditions will force the selection of physically meaningful modes, and thus enables an effective appeal to first principles. Here we focus on systems known to be periodically dominant, and describe a simple method to extract modes associated with temporal harmonics. The method accommodates time variations in the dominant frequency(ies) and exploits a preliminary data compression, such as by the standard POD procedure

    Astro2020: Astrophotonics White Paper

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    Astrophotonics is the application of versatile photonic technologies to channel, manipulate, and disperse guided light from one or more telescopes to achieve scientific objectives in astronomy in an efficient and cost-effective way. The developments and demands from the telecommunication industry have driven a major boost in photonic technology and vice versa in the last 40 years. The photonic platform of guided light in fibers and waveguides has opened the doors to next-generation instrumentation for both ground- and space-based telescopes in optical and near/mid-IR bands, particularly for the upcoming extremely large telescopes (ELTs). The large telescopes are pushing the limits of adaptive optics to reach close to a near-diffraction-limited performance. The photonic devices are ideally suited for capturing this AO-corrected light and enabling new and exciting science such as characterizing exoplanet atmospheres. The purpose of this white paper is to summarize the current landscape of astrophotonic devices and their scientific impact, highlight the key issues, and outline specific technological and organizational approaches to address these issues in the coming decade and thereby enable new discoveries as we embark on the era of extremely large telescopes

    Viewpoints: Approaches to defining and investigating fear

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    There is disagreement on how best to define and investigate fear. Nature Neuroscience asked Dean Mobbs to lead experts from the fields of human and animal affective neuroscience to discuss their viewpoints on how to define fear and how to move forward with the study of fear

    Analysis Of Momentum Methods

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    Gradient decent-based optimization methods underpin the parameter training which results in the impressive results now found when testing neural networks. Introducing stochasticity is key to their success in practical problems, and there is some understanding of the role of stochastic gradient decent in this context. Momentum modifications of gradient decent such as Polyak's Heavy Ball method (HB) and Nesterov's method of accelerated gradients (NAG), are widely adopted. In this work, our focus is on understanding the role of momentum in the training of neural networks, concentrating on the common situation in which the momentum contribution is fixed at each step of the algorithm; to expose the ideas simply we work in the deterministic setting. We show that, contrary to popular belief, standard implementations of fixed momentum methods do no more than act to rescale the learning rate. We achieve this by showing that the momentum method converges to a gradient flow, with a momentum-dependent time-rescaling, using the method of modified equations from numerical analysis. Further we show that the momentum method admits an exponentially attractive invariant manifold on which the dynamic reduces to a gradient flow with respect to a modified loss function, equal to the original one plus a small perturbation

    Extracting Knowledge from Massive Astronomical Data Sets

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    The exponential growth of astronomical data collected by both ground-based and spaceborne instruments has fostered the growth of astroinformatics: a new discipline lying at the intersection between astronomy, applied computer science, and information and computation technologies. At the very heart of astroinformatics is a complex set of methodologies usually called data mining (DM) or knowledge discovery in databases (KDD). In the astronomical domain, DM/KDD are still in a very early usage stage, even though new methods and tools are being continuously deployed to cope with the massive data sets (MDSs) that can only grow in the future. In this paper, we briefly outline some general problems encountered when applying DM/KDD methods to astrophysical problems and describe the DAME (Data Mining and Exploration) Web application. While specifically tailored to work on MDSs, DAME can be effectively applied also to smaller data sets. As an illustration, we describe two applications of DAME to two different problems: the identification of candidate GCs in external galaxies and the classification of active Galactic nuclei (AGN). We believe that tools and services of this nature will become increasingly necessary for data-intensive astronomy (and indeed all sciences) in the twenty-first century
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