Quantum gate synthesis by small perturbation of a free particle in a box with electric field

A quantum unitary gate is realized in this paper by perturbing a free charged particle in a one-dimensional box with a time- and position-varying electric field. The perturbed Hamiltonian is composed of a free particle Hamiltonian plus a perturbing electric potential such that the Schr$\ddot{o}$dinger evolution in time $T$, the unitary evolution operator of the unperturbed system after truncation to a finite number of energy levels, approximates a given unitary gate such as the quantum Fourier transform gate. The idea is to truncate the half-wave Fourier sine series to $M$ terms in the spatial variable $\mathbf x$ before extending the potential as a Dyson series in the interaction picture to compute the evolution operator matrix elements up to the linear and quadratic integral functionals of $\mathbf V_n(t)'$s. As a result, we used the Dyson series with the Frobenius norm to reduce the difference between the derived gate energy and the given gate energy, and we determined the temporal performance criterion by plotting the noise-to-signal energy ratio (NSER). A mathematical explanation for a quantum gate's magnetic control has also been provided. In addition, we provide a mathematical explanation for a quantum gate that uses magnetic control.Comment: 16 page

Symmetries in Quantum Mechanics

Symmetry and quantum mechanics are two of the most fundamental probes we have of nature. This collection of eleven papers discusses new quantum phenomena in atoms, galaxies, and people (quantum cognition), which is a testimonial to the breadth of the influence of symmetry and quantum mechanics. The book represents an international effort of researchers from educational and research institutions in nine countries, including India, Finland, France, Mexico, Norway, Russia, Spain, Turkey, and the United States. The papers can be divided into four broad categories: Fundamentals of quantum systems, including a new derivation of the uncertainty principle from optimal stochastic control theory, a new model of energy transfer between atoms with no wave function collapse, a new asymmetric optical micro-device with the remarkable property of showing a current with no applied voltage, and a model of quantum cognition to predict the effect of irrelevant information on decision making. 2. Algebraic methods in quantum mechanics, describing an elegant derivation of hydrogen atom Stark effect matrix elements, and a new group theoretical method for the computation of radiative shifts. Teleportation and scattering, including a method to improve the information transfer in teleportation, and the use of permutation symmetry to compute scattering cross sections. Cosmology, including scalar-tensor theory applied to inflation, the characterization of new Levi-Cevita space-times, and a comprehensive analysis of gravitational dispersion forces

Journeys from quantum optics to quantum technology

Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research

Progress in Group Field Theory and Related Quantum Gravity Formalisms

Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research

Novel Computing Paradigms using Oscillators

This dissertation is concerned with new ways of using oscillators to perform computational tasks. Specifically, it introduces methods for building finite state machines (for general-purpose Boolean computation) as well as Ising machines (for solving combinatorial optimization problems) using coupled oscillator networks.But firstly, why oscillators? Why use them for computation?An important reason is simply that oscillators are fascinating. Coupled oscillator systems often display intriguing synchronization phenomena where spontaneous patterns arise. From the synchronous flashing of fireflies to Huygens' clocks ticking in unison, from the molecular mechanism of circadian rhythms to the phase patterns in oscillatory neural circuits, the observation and study of synchronization in coupled oscillators has a long and rich history. Engineers across many disciplines have also taken inspiration from these phenomena, e.g., to design high-performance radio frequency communication circuits and optical lasers. To be able to contribute to the study of coupled oscillators and leverage them in novel paradigms of computing is without question an interesting andfulfilling quest in and of itself.Moreover, as Moore's Law nears its limits, new computing paradigms that are different from mere conventional complementary metal–oxide–semiconductor (CMOS) scaling have become an important area of exploration. One broad direction aims to improve CMOS performance using device technology such as fin field-effect transistors (FinFET) and gate-all-around (GAA) FETs. Other new computing schemes are based on non-CMOS material and device technology, e.g., graphene, carbon nanotubes, memristive devices, optical devices, etc.. Another growing trend in both academia and industry is to build digital application-specific integrated circuits (ASIC) suitable for speeding up certain computational tasks, often leveraging the parallel nature of unconventional non-von Neumann architectures. These schemes seek to circumvent the limitations posed at the device level through innovations at the system/architecture level.Our work on oscillator-based computation represents a direction that is different from the above and features several points of novelty and attractiveness. Firstly, it makes meaningful use of nonlinear dynamical phenomena to tackle well-defined computational tasks that span analog and digital domains. It also differs from conventional computational systems at the fundamental logic encoding level, using timing/phase of oscillation as opposed to voltage levels to represent logic values. These differences bring about several advantages. The change of logic encoding scheme has several device- and system-level benefits related to noise immunity and interference resistance. The use of nonlinear oscillator dynamics allows our systems to address problems difficult for conventional digital computation. Furthermore, our schemes are amenable to realizations using almost all types of oscillators, allowing a wide variety of devices from multiple physical domains to serve as the substrate for computing. This ability to leverage emerging multiphysics devices need not put off the realization of our ideas far into the future. Instead, implementations using well-established circuit technology are already both practical and attractive.This work also differs from all past work on oscillator-based computing, which mostly focuses on specialized image preprocessing tasks, such as edge detection, image segmentation and pattern recognition. Perhaps its most unique feature is that our systems use transitions between analog and digital modes of operation --- unlike other existing schemes that simply couple oscillators and let their phases settle to a continuum of values, we use a special type of injection locking to make each oscillator settle to one of the several well-defined multistable phase-locked states, which we use to encode logic values for computation. Our schemes of oscillator-based Boolean and Ising computation are built upon this digitization of phase; they expand the scope of oscillator-based computing significantly.Our ideas are built on years of past research in the modelling, simulation and analysis of oscillators. While there is a considerable amount of literature (arguably since Christiaan Huygens wrote about his observation of synchronized pendulum clocks in the 17th century) analyzing the synchronization phenomenon from different perspectives at different levels, we have been able to further develop the theory of injection locking, connecting the dots to find a path of analysis that starts from the low-level differential equations of individual oscillators and arrives at phase-based models and energy landscapes of coupled oscillator systems. This theoretical scaffolding is able not only to explain the operation of oscillator-based systems, but also to serve as the basis for simulation and design tools. Building on this, we explore the practical design of our proposed systems, demonstrate working prototypes, as well as develop the techniques, tools and methodologies essential for the process

Space Communications: Theory and Applications. Volume 3: Information Processing and Advanced Techniques. A Bibliography, 1958 - 1963

Annotated bibliography on information processing and advanced communication techniques - theory and applications of space communication

Cold and Ultracold Molecules: Science, Technology, and Applications

This article presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the Special Issue of the New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography, and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field.Comment: 82 pages, 9 figures, review article to appear in New Journal of Physics Special Issue on Cold and Ultracold Molecule

On inter-satellite laser ranging, clock synchronization and gravitational wave data analysis

[no abstract

The magnetic quadrupole transition in neutral strontium

Analog quantum simulators enable the experimental investigation of strongly interacting quantum many-body systems, for which numerical calculations are often out of reach for classical computers. One remarkably successful invention in the development of these simulators is the quantum gas microscope. These high-numerical-aperture microscopes enable the detection of ultracold atoms in optical lattices and can resolve individual lattice sites. Until now, most quantum gas microscope experiments use alkali atoms, but recent experiments aim to make use of the special properties of alkaline earth atoms. Alkaline earth atoms possess two valence electrons, giving rise to a rich electronic-level structure featuring singlet and metastable triplet states. This internal structure results in ultranarrow optical intercombination transitions, opening up numerous applications in quantum sciences. The most prominent application of strontium is the optical lattice clock based on the 1S0-3P0 transition. Based on this success story, there has been a recent effort to use the metastable states and the achieved second-scale coherence time for quantum computing and quantum simulation. Our approach is to implement highly state-dependent optical lattices for the ground and metastable triplet states and to study the emerging quantum many-body phenomena using a quantum gas microscope. Working with alkaline earth atoms under a quantum gas microscope requires developing local readout and manipulation of atoms or qubits. This addressing can be realized by focusing an optical beam through the microscope. However, the diffraction-limited resolution results in cross-talk between adjacent lattice sites. The addressing resolution can be enhanced beyond the diffraction limit by ap- plying magnetic field gradients in combination with magnetic-field-sensitive transitions. Doing so allows controlling the atoms’ spin or electronic state on dedicated lattice sites within a larger sample of hundreds of atoms. Implementing local addressability for strontium atoms is technically challenging since most magnetic-field-sensitive transitions are too broad. A promising solution is to use the millihertz-wide and magnetically-sensitive 1S0-3P2 magnetic quadrupole transition, which features excellent frequency discrimination for even moderate magnetic field gradients due to its narrow linewidth. Although this transition opens up unique applications, many of the key features of the transition, such as the exact transition frequency, or the 3P2 state’s trapping potential have not been investigated prior to the work described in this thesis. This thesis reports on the first high-resolution and Doppler-free laser spectroscopy of the 1S0-3P2 transition with kilohertz precision in a light-shift-compensated optical lattice. We engineer the light-shift-free lattice by tuning the vector and tensor polarizability of the excited 3P2 state. We measure the absolute transition frequency with an improvement of three orders of magnitude compared to previously reported values. Finally, we demonstrate local addressing on the 1S0-3P2 transition in the optical lattice, a first crucial step towards single-particle control under the quantum gas microscope. In the near future, the addressing will allow us to isolate a single layer of the optical lattice in the focus of the first strontium quantum gas microscope. The demonstrated experimental control over the 1S0-3P2 transition paves the way to use the corresponding optical qubit for neutral atom quantum computation, where single qubits can be locally manipulated and read out.Analoge Quantensimulatoren ermöglichen die experimentelle Untersuchung von stark wechselwirkenden Quantenvielteilchensystemen, die auf klassischen Computern nicht mehr numerisch berechnet werden können. Eine bemerkenswert erfolgreiche Erfindung bei der Entwicklung dieser Simulatoren ist das Quantengasmikroskop. Diese Mikroskope mit hoher numerischer Apertur ermöglichen es ultrakalte Atome in optischen Gittern zu detektieren und können dabei einzelne Gitterplätze auflösen. Bisher verwenden die meisten Experimente mit Quantengasmikroskopen Alkaliatome, jedoch zielen kürzlich realisierte Experimente darauf ab, die besonderen Eigenschaften von Erdalkaliatomen zu nutzen. Erdalkaliatome besitzen zwei Valenzelektronen, was zu einer vielfältigen Struktur atom- arer Zustände mit Singulett- und metastabilen Tripletzuständen führt. Diese Atomstruktur beinhaltet ultraschmale Interkombinationsübergänge im optischen Bereich, die zahlreiche Anwendungen in den Quantenwissenschaften finden. Die bekannteste An- wendung von Strontium ist die optische Gitteruhr, die auf dem 1S0-3P0-Übergang basiert. Diese Erfolgsgeschichte trieb kürzlich Entwicklungen im Bereich der Quantensimulation und Quantencomputer voran, die die metastabilen Zustände und die im Sekundenbere- ich liegenden Kohärenzzeiten nutzen. Unser Ansatz besteht darin, stark zustandsabhängige optische Gitter für die Grund- und metastabilen Triplettzustände zu erzeugen und die darin auftretenden Quantenviel- teilchenphänomene mit einem Quantengasmikroskop zu untersuchen. Erdalkaliatome unter einem Quantengasmikroskop zu verwenden, erfordert es Atome oder Qubits lokal auslesen oder manipulieren zu können. Dieses Adressieren kann man dadurch erre- ichen, dass ein optischer Strahl mit dem Mikroskop fokussiert wird. Die beugungsbegren- zte Auflösung führt jedoch dazu, dass benachbarte Gitterplätze ebenfalls angesprochen werden. Durch die Verwendung von Magnetfeldgradienten in Kombination mit mag- netfeldempfindlichen Übergängen kann die Auflösung über die Beugungsgrenze hinaus gesteigert werden. Dadurch können der Spin oder der elektronische Zustand der Atome auf den gewünschten Gitterplätzen innerhalb eines größeren Systems von Hunderten von Atomen verändert werden. Lokales Adressieren von Strontiumatomen zu realisieren ist technisch anspruchsvoll, da die meisten magnetfeldempfindlichen Übergänge zu breit sind. Eine vielversprechende Lösung ist den Millihertz breiten und magnetisch sensitiven 1S0-3P2 magnetischen Quadrupolübergang zu verwenden, der durch seine schmale Lin- ienbreite eine hervorragende Frequenzdiskriminierung selbst bei moderate Magnetfeld- gradienten aufweist. Obwohl dieser Übergang einzigartige Anwendungen ermöglicht, wurden viele Eigenschaften des Übergangs, wie die exakte Übergangsfrequenz oder das Fallenpotential des 3P2-Zustands, vor der in dieser Dissertation beschriebenen Arbeit nicht untersucht. Diese Arbeit berichtet über die erste hochauflösende und dopplerfreie Laserspektros- kopie des 1S0-3P2-Übergangs mit Kilohertz-Präzision in einem optischen Gitter frei von Linienverschiebungen durch das Lichtfeld. Wir unterdrücken die Linienverschiebung, in- dem wir die Vektor- und Tensorpolarisierbarkeit des angeregten 3P2-Zustands einstellen. Wir messen die absolute Übergangsfrequenz mit drei Größenordnungen kleineren Fehler- balken als alle Messungen zuvor. Abschließend zeigen wir lokales Adressieren im optis- chen Gitter unter Verwendung des 1S0-3P2-Übergangs. Dies ist ein erster entscheidender Schritt auf dem Weg zur Kontrolle einzelner Atome unter dem Quantengasmikroskop. Das Adressieren wird es uns in naher Zukunft ermöglichen, eine einzelne Ebene des op- tischen Gitters im Fokus des ersten Strontium-Quantengasmikroskops zu isolieren. Die demonstrierte experimentelle Kontrolle über den 1S0-3P2-Übergang ebnet den Weg, das entsprechende optische Qubit in Quantencomputern mit neutralen Atomen zu ver- wenden, bei denen einzelne Qubits lokal manipuliert und ausgelesen werden können