387 research outputs found

    Spin Detection, Amplification, and Microwave Squeezing with Kinetic Inductance Parametric Amplifiers

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    Superconducting parametric amplifiers operating at microwave frequencies have become an essential component in circuit quantum electrodynamics experiments. They are used to amplify signals at the single-photon level, while adding only the minimum amount of noise required by quantum mechanics. To achieve gain, energy is transferred from a pump to the signal through a non-linear interaction. A common strategy to enhance this process is to place the non-linearity inside a high quality factor resonator, but so far, quantum limited amplifiers of this type have only been demonstrated from designs that utilize Josephson junctions. Here we demonstrate the Kinetic Inductance Parametric Amplifier (KIPA), a three-wave mixing resonant parametric amplifier that exploits the kinetic inductance intrinsic to thin films of disordered superconductors. We then utilize the KIPA for measurements of 209Bi spin ensembles in Si. First, we show that a KIPA can serve simultaneously as a high quality factor resonator for pulsed electron spin resonance measurements and as a low-noise parametric amplifier. Using this dual-functionality, we enhance the signal to noise ratio of our measurements by more than a factor of seven and ultimately achieve a measurement sensitivity of 2.4 x 10^3 spins. Then we show that pushed to the high-gain limit, KIPAs can serve as a `click'-detector for microwave wave packets by utilizing a hysteretic transition to a self-oscillating state. We calibrate the detector's sensitivity to be 3.7 zJ and then apply it to measurements of electron spin resonance. Finally, we demonstrate the suitability of the KIPA for generating squeezed vacuum states. Using a cryogenic noise source, we first confirm the KIPAs in our experiment to be quantum limited amplifiers. Then, using two KIPAs arranged in series, we make direct measurements of vacuum noise squeezing, where we generate itinerant squeezed states with minimum uncertainty more than 7 dB below the standard quantum limit. High quality factor resonators have also recently been used to achieve strong coupling between the spins of single electrons in gate-defined quantum dots and microwave photons. We present our efforts to achieve the equivalent goal for the 31P flip-flop qubit. In doing so, we confirm previous predictions that the superconducting material MoRe would produce magnetic field-resilient resonators and demonstrate that it has kinetic inductance equivalent to the popular material NbTiN

    Notes on Quantum Computation and Information

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    We discuss fundamentals of quantum computing and information - quantum gates, circuits, algorithms, theorems, error correction, and provide collection of QISKIT programs and exercises for the interested reader.Comment: v2: 86 pages, 97 references. Refined the text, fixed several typos, added some text on continuous variables, and added few solved example problems. v1: 72 pages, 76 references. Suggestions, comments, and corrections are very welcome

    Conformal Feynman Integrals and Correlation Functions in Fishnet Theory

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    In dieser Dissertation untersuchen wir unterschiedliche Aspekte im Zusammenhang mit Korrelationsfunktionen in der Fischnetz-Theorie. Zunächst betrachten wir einen der einfachsten Korrelatoren der Fischnetz Theorie, das konforme Box-Integral, in Minkowski Signatur. Während dieses Integral in Euklidischer Signatur eine konforme Symmetrie aufweist, wird diese Symmetrie in Minkowski-Raumzeit subtil gebrochen. Wir beschreiben die Brechung der konformen Symmetrie quantitativ, indem wir die funktionale Form des Box-Integrals in allen kinematischen Regionen untersuchen. Ausserdem untersuchen wir das Ausmass zu dem das Box integral durch seine Yangian-Symmetrie festgelegt ist. Als nächstes widmen wir uns den Basso-Dixon-Graphen, die ebenfalls konforme Vier-Punkt-Integrale sind und Verallgemeinerungen des Box-Integrals zu höheren Schleifenordnungen darstellen. Wir leiten die Yangian-Ward-Identitäten ab, die diese Klasse von Integralen erfüllen. Die Ward-Identitäten sind einhomogene Erweiterungen der partiellen Differentialgleichungen, die im homogenen Fall durch Appell-Hypergeometrische Funktionen gelöst werden. Die Ward-Identitäten können natürlicherweise auf eine Ein-Parameter-Familie von D-dimensionalen Integralen erweitert werden, die Korrelatoren in der verallgemeinerten Fischnetz-Theorie von Kazakov und Olivucci darstellen. Schliesslich untersuchen wir den Dilatationsoperator in einem Drei-Skalar-Sektor der Fischnetztheorie, der auch als Eklektisches Modell bezeichnet wird. In diesem Sektor der Dilatationsoperator nimmt nicht--diagonalisierbare Form an. Das führt dazu, dass die Zwei-Punkt-Korrelationsfunktionen eine logarithmische Abhängigkeit von der Raumzeitseparierung der Operatoren annimmt. Unter Zuhilfenahme von kombinatorischen Argumenten führen wir eine generierende Funktion ein, die das Jordan-Block-Spektrum eines verwandten Modells, der hypereklektischen Spinkette, vollständig charakterisiert.We study various aspects of correlation functions in fishnet theory. We begin with the study of the simplest correlator in theory theory, represented by the conformal box integral, in Minkowski space. While this integral is conformally invariant in Euclidean space, this symmetry is subtly broken in Minkowski space. We quantify the extent to which conformal symmetry is broken by analysing the functional form of the box in each kinematic region. We propose a new method to calculate the box integral directly in Minkowski space, by introducing a family of configurations with two points at infinity. Furthermore, we investigate the extent to which the box integral is constrained by Yangian symmetry. We constrain the functional form of the box integral in all kinematic regions up to twelve undetermined constants, which we fix by three separate analytic continuations from the Euclidean region. Next, we study the Basso-Dixon graphs, which represent higher-loop versions of the box integral. We derive and study Yangian Ward identities for this class of integrals. These take the form of inhomogeneous extensions of the partial differential equations defining the Appell hypergeometric functions. The Ward identities naturally generalise to a one-parameter family of D dimensional integrals representing correlators in a generalised fishnet theory. Finally, we study the dilatation operator in a particular three scalar sector of the fishnet theory, which has been dubbed the eclectic model. This dilatation operator is non-diagonalisable in this sector. This leads to logarithmic spacetime dependence in the corresponding two-point functions. Using combinatorial arguments, we introduce a generating function which fully characterises the Jordan block spectrum of a related model: the hypereclectic spin chain. This function is found by purely combinatorial means and can be expressed in terms of the q-binomial coefficient

    Carácter cuántico del bloqueo fotónico

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    ilustraciones, diagramasThe present thesis aims to investigate the photon blockade effect, understood as a phenomenon in which the presence of a single photon inhibits further photons, effectively transforming a system into one that emits one photon at a time. This effect can be classified into two categories: The conventional photon blockade, which relies on the nonlinearities of a system, and the unconventional photon blockade, which employs quantum interference between two paths to cancel the probability to access a particular state. In order to investigate the underlying physical mechanisms of these two forms of blockades, this thesis employs numerical solutions of master equations, complemented by the application of analytical techniques for determining optimal conditions for each type of blockade. Specifically, the study finds that the driven dissipative Jaynes-Cummings model represents an ideal scheme in which both mechanisms are exhibited simultaneously. This enables the analysis of the photon blockade mechanism in a unique and experimentally feasible setup, such as a cavity-QED scheme composed of a semiconductor quantum dot grown inside a micropillar. Additionally, intrinsic differences between both blockade mechanisms are uncovered through the utilization of the theory of frequency-filtered correlations and the integration of dissipative mechanisms such as phonon-mediated coupling. Furthermore, new criteria for the theoretical classification based on the study of higher-order correlation functions are employed to analyze the numerical solutions of the model, determining if the systems can act as single photon sources. Moreover, the research applies the aforementioned tools to study a system that consists of an elliptical microcavity with an embedded quantum dot, subject to external excitation by a laser and a magnetic field. The optimal conditions for generating conventional photon blockade in this system were identified, constituting it to act as a single photon polarization switch. This thesis, therefore, provides a comprehensive examination of the photon blockade effect, which could be used in the future for developing high-quality single photon sources, helping for the implementation of quantum technologiesLa presente tesis tiene como objetivo investigar el efecto de bloqueo de fotones, entendido como un fenómeno en el cual la presencia de un solo fotón inhibe la emisión de más fotones, transformando efectivamente un sistema en uno que emite un fotón a la vez. Este efecto se puede clasificar en dos categorías: el bloqueo de fotones convencional, que se basa en las no linealidades de un sistema, y el bloqueo de fotones no convencional, que emplea la interferencia cuántica entre dos trayectorias para cancelar la probabilidad de acceder a un estado particular. Con el fin de investigar los mecanismos físicos subyacentes de estas dos formas de bloqueo, esta tesis utiliza soluciones numéricas de ecuaciones maestras, complementadas con la aplicación de técnicas analíticas para determinar las condiciones óptimas para cada tipo de bloqueo. Específicamente, el estudio encuentra que el modelo de Jaynes-Cummings bombeado y disipativo representa un esquema ideal en el que ambos mecanismos se exhiben simultáneamente. Esto permite el análisis del mecanismo de bloqueo de fotones en una configuración única y experimentalmente factible, como un esquema de cavidad-QED compuesto por un punto cuántico semiconductor crecido dentro de un micro-pilar. Se descubren a su vez diferencias intrínsecas entre ambos mecanismos de bloqueo a través de la utilización de la teoría de correlaciones filtradas por frecuencia y la integración de mecanismos disipativos como el acoplamiento mediado por fonones. Además, se emplean nuevos criterios para la clasificación teórica basada en el estudio de funciones de correlación de orden superior para analizar las soluciones numéricas del modelo, determinando si los sistemas pueden actuar como fuentes de un solo fotón. Complementario a ello, la investigación aplica las herramientas mencionadas para estudiar un sistema que consiste en una microcavidad elíptica con un punto cuántico incrustado, sujeto a excitación externa por un láser y un campo magnético. Se identificaron las condiciones óptimas para generar un bloqueo de fotones convencional en este sistema, lo que lo convierte en un interruptor de polarización de un solo fotón. Esta tesis, por lo tanto, proporciona un examen exhaustivo del efecto de bloqueo de fotones, que podría en el futuro servir para desarrollar fuentes de fotones individuales de alta calidad, que ayuden a la implementación de tecnologías cuánticasMaestríaMagíster en Ciencias - Físic

    Wigner negativity on the sphere

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    The rise of quantum information theory has largely vindicated the long-held belief that Wigner negativity is an indicator of genuine nonclassicality in quantum systems. This thesis explores its manifestation in spin-j systems using the spherical Wigner function. Common symmetric multi-qubit states are studied and compared. Spin coherent states are shown to never have vanishing Wigner negativity. Pure states that maximize negativity are determined and analyzed using the Majorana stellar representation. The relationship between negativity and state mixedness is discussed, and polytopes characterizing unitary orbits of lower-bounded Wigner functions are studied. Results throughout are contrasted with similar works on symmetric state entanglement and other forms of phase-space nonclassicality

    Simplicial Lattice Study of the 2d Ising CFT

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    I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a well-defined continuum limit. I perform Monte Carlo simulations of the critical Ising model on discretizations of several non-trivial manifolds including a twisted torus and a 2-sphere and I show that the simulations are in agreement with the 2d Ising CFT in the continuum limit. I discuss the inherent benefits of using non-uniform simplicial lattices to study quantum field theory and how the methods developed here can potentially be generalized for use with other theories.Comment: PhD Thesis, Boston University 2023, 61 page

    Technical Matter Wave Optics - Imaging devices for Bose condensed matter waves - an aberration analysis in space and time

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    Cold atomic gases are the ultimate quantum sensors. Embedded in a matter-wave interferometer, they provide a platform for high-precision sensing of accelerations and rotations probing fundamental physical questions. As in all optical instruments, these devices require careful modeling. Sources of possible aberrations need to be quantified and optimized to guarantee the best possible performance. This applies in particular to high-demanding experiments in microgravity with low repetition rates. In this thesis, we present a theoretical (3+1)d aberration analysis of expanded Bose-Einstein condensates. We demonstrate that the Bogoliubov modes of the scaled mean-field equation serve as good basis states to obtain the corresponding aberration coefficients. Introducing the Stringari polynomials, we describe density and phase variations in terms of a multipole decomposition analogous to the Zernike wavefront analysis in classical optics. We apply our aberration analysis to Bose-Einstein condensates on magnetic chip traps. We obtain the trapping potential using magnetic field simulations with finite wire elements. Using the multipole expansion, we characterize the anharmonic contributions of the Ioffe-Pritchard type Zeeman potential. Used as a matter-wave lens for delta-kick collimation, we determine the wavefront aberrations in terms of \say{Seidel-diagrams}. Supported by (3+1)d Gross-Pitaevskii simulations we study mean-field interactions during long expansion times. Matter-wave interferometry with Bose-Einstein condensates can also be performed in guiding potentials. One of the building blocks are toroidal condensates in a ring-shaped geometry. The required light field patterns are obtained by using the effect of conical refraction or with programmable digital micromirror devices. For the former, we study equilibrium properties and compare them with experimental data. We investigate the collective excitations in the two-dimensional ring-shaped condensate. Our result is compared to the numerical results of the Bogoliubov-de Gennes equations. The latter is used to find signatures in the excitation spectrum during the topological transition from simply connected harmonic to multiply connected ring traps. Changing the topology dynamically leads to radial excitations of the condensate. We propose a damping mechanism based on feedback measurements to control the motion within the toroidal ring

    A Quaternionic Version Theory related to Spheroidal Functions

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    In dieser Arbeit wird eine neue Theorie der quaternionischen Funktionen vorgestellt, welche das Problem der Bestapproximation von Familien prolater und oblater sphäroidalen Funktionen im Hilberträumen behandelt. Die allgemeine Theorie beginnt mit der expliziten Konstruktion von orthogonalen Basen für Räume, definiert auf sphäroidalen Gebieten mit beliebiger Exzentrizität, deren Elemente harmonische, monogene und kontragene Funktionen sind und durch die Form der Gebiete parametrisiert werden. Eine detaillierte Studie dieser grundlegenden Elemente wird in dieser Arbeit durchgeführt. Der Begriff der kontragenen Funktion hängt vom Definitionsbereich ab und ist daher keine lokale Eigenschaft, während die Begriffe der harmonischen und monogenen Funktionen lokal sind. Es werden verschiedene Umwandlungsformeln vorgestellt, die Systeme harmonischer, monogener und kontragener Funktionen auf Sphäroiden unterschiedlicher Exzentrizität in Beziehung setzen. Darüber hinaus wird die Existenz gemeinsamer nichttrivialer kontragener Funktionen für Sphäroide jeglicher Exzentrizität gezeigt. Der zweite wichtige Beitrag dieser Arbeit betrifft eine quaternionische Raumfrequenztheorie für bandbegrenzte quaternionische Funktionen. Es wird eine neue Art von quaternionischen Signalen vorgeschlagen, deren Energiekonzentration im Raum und in den Frequenzbereichen unter der quaternionischen Fourier-Transformation maximal ist. Darüber hinaus werden diese Signale im Kontext der Spektralkonzentration als Eigenfunktionen eines kompakten und selbstadjungierteren quaternionischen Integraloperators untersucht und die grundlegenden Eigenschaften ihrer zugehörigen Eigenwerte werden detailliert beschrieben. Wenn die Konzentrationsgebiete beider Räume kugelförmig sind, kann der Winkelanteil dieser Signale explizit gefunden werden, was zur Lösung von mehreren eindimensionalen radialen Integralgleichungen führt. Wir nutzen die theoretischen Ergebnisse und harmonische Konjugierten um Klassen monogener Funktionen in verschiedenen Räumen zu konstruieren. Zur Charakterisierung der monogenen gewichteten Hardy- und Bergman-Räume in der Einheitskugel werden zwei konstruktive Algorithmen vorgeschlagen. Für eine reelle harmonische Funktion, die zu einem gewichteten Hardy- und Bergman-Raum gehört, werden die harmonischen Konjugiert in den gleichen Räumen gefunden. Die Beschränktheit der zugrundeliegenden harmonischen Konjugationsoperatoren wird in den angegebenen gewichteten Räumen bewiesen. Zusätzlich wird ein quaternionisches Gegenstück zum Satz von Bloch für monogene Funktionen bewiesen.This work presents a novel Quaternionic Function Theory associated with the best approximation problem in the setting of Hilbert spaces concerning families of prolate and oblate spheroidal functions. The general theory begins with the explicit construction of orthogonal bases for the spaces of harmonic, monogenic, and contragenic functions defined in spheroidal domains of arbitrary eccentricity, whose elements are parametrized by the shape of the corresponding spheroids. A detailed study regarding the elements that constitute these bases is carried out in this thesis. The notion of a contragenic function depends on the domain, and, therefore, it is not a local property in contrast to the concepts of harmonic and monogenic functions. Various conversion formulas that relate systems of harmonic, monogenic, and contragenic functions associated with spheroids of differing eccentricity are presented. Furthermore, the existence of standard nontrivial contragenic functions is shown for spheroids of any eccentricity. The second significant contribution presented in this work pertains to a quaternionic space-frequency theory for band-limited quaternionic functions. A new class of quaternionic signals is proposed, whose energy concentration in the space and the frequency domains are maximal under the quaternion Fourier transform. These signals are studied in the context of spatial-frequency concentration as eigenfunctions of a compact and self-adjoint quaternion integral operator. The fundamental properties of their associated eigenvalues are described in detail. When the concentration domains are spherical in both spaces, the angular part of these signals can be found explicitly, leading to a set of one-dimensional radial integral equations. The theoretical framework described in this work is applied to the construction of classes of monogenic functions in different spaces via harmonic conjugates. Two constructive algorithms are proposed to characterize the monogenic weighted Hardy and Bergman spaces in the Euclidean unit ball. For a real-valued harmonic function belonging to a Hardy and a weighted Bergman space, the harmonic conjugates in the same spaces are found. The boundedness of the underlying harmonic conjugation operators is proven in the given weighted spaces. Additionally, a quaternionic counterpart of Bloch’s Theorem is established for monogenic functions

    Accelerating gravitational-wave inference with machine learning

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    The future for gravitational-wave astronomy is bright, with improvements for existing ground-based interferometers of the LIGO-Virgo-KAGRA Collaboration (LVK) and new ground- and space-based interferometers planned for the near future. As a result, there will imminently be an abundance of data to analyse from these detectors, which will bring with it the chances to probe new regimes. However, this will also bring with it new challenges to address, such as the volume of data and need for new analysis techniques. Leveraging this data hinges on our ability to determine the characteristics of the sources that produce the observed gravitational-wave signals, and Bayesian inference is the method of choice. The main algorithms that have been used in these analyses are Markov Chain Monte Carlo and Nested Sampling. Each have their own advantages and disadvantages. However, both are computationally expensive when applied to gravitational-wave inference, typically taking of order days to weeks for shorter signals and up to months for longer signals, such as those from binary neutron star mergers. Furthermore, the cost of these analyses increases as additional physics is included, such as higher-order modes, precession and eccentricity. These factors, combined with the previously mentioned increase in data, and therefore number of signals, pose a significant challenge. As such, there is a need for faster and more efficient algorithms for gravitational-wave inference. In this work, we present novel algorithms that serve as drop-in replacements for existing approaches but can accelerate inference by an order of magnitude. Our initial approach is to incorporate machine learning into an existing algorithm, namely nested sampling, with the aim of accelerating it whilst leaving the underlying algorithm unchanged. To this end, we introduce nessai, a nested sampling algorithm that includes a novel method for sampling from the likelihood-constrained prior that leverages normalizing flows, a type of machine learning algorithm. Normalizing flows can approximate the distribution of live points during a nested sampling run, and allow for new points to be drawn from it. They are also flexible and can learn complex correlations, thus eliminating the need to use a random walk to propose new samples. We validate nessai for gravitational-wave inference by analysing a population of simulated binary black holes (BBHs) and demonstrate that it produces statistically consistent results. We also compare nessai to dynesty, the standard nested sampling algorithm used by the LVK, and find that, after some improvements, it is on average ∼ 6 times more efficient and enables inference in time scales of order 10 hours on a single core. We also highlight other advantages of nessai, such as the included diagnostics and simple parallelization of the likelihood evaluation. However, we also find that the rejection sampling step necessary to ensure new samples are distributed according to the prior can be a significant computational bottleneck. We then take the opposite approach and design a custom nested sampling algorithm tailored to normalizing flows, which we call i-nessai. This algorithm is based on importance nested sampling and incorporates elements from existing variants of nested sampling. In contrast to the standard algorithm, samples no longer have to be ordered by increasing likelihood nor distributed according to the prior, thus addressing the aforementioned bottleneck in nessai. Furthermore, the formulation of the evidence allows for it to be updated with batches of samples rather than one-by-one. The algorithm we design is centred around constructing a meta-proposal that approximates the posterior distribution, which is achieved by iteratively adding normalizing flows until a stopping criterion is met. We validate i-nessai on a range of toy test problems which allows us to verify the algorithm is consistent with both nessai and, when available, the analytic results. We then repeat a similar analysis to that performed previously, and analyse a population of simulated BBH signals with i-nessai. The results show that i-nessai produces consistent results, but is up to 3 times more efficient than nessai and more than an order of magnitude more efficient (13 times) than dynesty. We also apply i-nessai to a binary neutron star (BNS) analysis and find that it can yield results in less than 30 minutes whilst only requiring O(106 ) likelihood evaluations. Having developed tools to accelerate parameter estimation, we then apply them to real data from LVK observing runs. We choose to analyse all 11 events from O1 and small selection of events from O2 and O3 and find good agreement between our results and those published by the LVK This demonstrates that nessai can be used to analyse real gravitational-wave data. However, it also highlights aspects that could be improved to further accelerate the algorithm, such as how the orbital phase and multimodal likelihood surfaces are handled. We also show how i-nessai can be applied to real data, but ultimately conclude that further work is required to determine if the settings used are robust. Finally, we consider nessai in the context of next generation ground-based interferometers and highlight some of the challenges such analyses present. As a whole, the algorithms introduced in this work pave the way for faster gravitational wave inference, offering speed-ups of up to an order of magnitude compared to existing approaches. Furthermore, they demonstrate how machine learning can be incorporated into existing analyses to accelerate them, which has the additional benefit of providing drop-in replacements for existing tools
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