The SLH framework for modeling quantum input-output networks

Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving correction

Predicting the statistics of wave transport through chaotic cavities by the Random Coupling Model: a review and recent progress

In this review, a model (the Random Coupling Model) that gives a statistical description of the coupling of radiation into and out of large enclosures through localized and/or distributed channels is presented. The Random Coupling Model combines both deterministic and statistical phenomena. The model makes use of wave chaos theory to extend the classical modal description of the cavity fields in the presence of boundaries that lead to chaotic ray trajectories. The model is based on a clear separation between the universal statistical behavior of the isolated chaotic system, and the deterministic coupling channel characteristics. Moreover, the ability of the random coupling model to describe interconnected cavities, aperture coupling, and the effects of short ray trajectories is discussed. A relation between the random coupling model and other formulations adopted in acoustics, optics, and statistical electromagnetics, is examined. In particular, a rigorous analogy of the random coupling model with the Statistical Energy Analysis used in acoustics is presented.Comment: 32 pages, 9 figures, submitted to 'Wave Motion', special issue 'Innovations in Wave Model

Double population cascaded lattice boltzmann method

Lattice Boltzmann Methods (LBM) are powerful numerical tools to simulate heat and mass transfer problems. Instead of directly integrating the N-S equations, LBM solves the discretized form of the Boltzmann Transport Equation (BTE), keeping track of the microscopic description of the systems. Therefore, LBM can solve fluid flows with great stability and computational efficiency, especially complex geometry fluid flows. For thermal flows, double distribution function (DDF) LBM scheme is the most popular and successful approach. But it is evident from the literature that existing double distribution function (DDF) LBM approaches, which use two collision operators, involve collision schemes which violate Galilean invariance, therefore producing instabilities for flows with high Re and Ra numbers. In this thesis, a double population cascaded lattice Boltzmann method is developed to improve the DDF LBM scheme from this drawback. The proposed method reduces the degree of violation of Galilean invariance, increasing the stability and accuracy of the LBM scheme. The scheme was implemented to simulate advection-diffusion, forced convection and natural convection heat transfer problems. The proposed scheme was also successfully tested for turbulent flow regimes and 3-D fluid flow in porous media. The results obtained from this work are in strong agreement with those available in the literature obtained through other numerical methods and experiments.Os métodos de ”Lattice”Boltzmann (LBM) são potentes ferramentas numéricas para simular problemas de transferência de massa e calor. Ao invés de integrar diretamente as equações de Navier-Stokes, o método LBM resolve, de forma discretizada, a equação de transporte de Boltzmann, acompanhando a descrição microscópica dos sistemas. O método LBM pode solucionar fluxo de fluidos com grande estabilidade e eficiência computacional, especialmente fluxos em geometrias complexas. Para fluxos térmicos, o esquema LBM de dupla função de distribuição (DDF) é a abordagem mais popular e bem sucedida. Mas é evidente, a partir da literatura, que as abordagens LBM de dupla função de distribuição (DDF), as quais utilizam dois operadores de colisão, envolvem esquemas de colisão que violam a invariância de Galileu, produzindo instabilidades para fluxos com números Re e Ra altos. Nesta tese, o método de ”Lattice”Boltzmann em cascata de dupla população em cascata é desenvolvido para corrigir o esquema DDF LBM. O método proposto reduz o grau de violação da invariância de Galileu, aumentando a estabilidade e acurácia do método LBM. O método foi implementado para simular problemas de advecção, difusão, convecções natural e forçada típicos de transferências de calor. O esquema proposto foi também bem sucedido em regimes de fluxo turbulento e em escoamentos 3-D em meios porosos. Os resultados obtidos neste trabalho estão fortemente de acordo com experimentos e métodos numéricos disponíveis na literatura

Silicon Photonic Devices and Their Applications

Silicon photonics is the study and application of photonic systems, which use silicon as an optical medium. Data is transferred in the systems by optical rays. This technology is seen as the substitutions of electric computer chips in the future and the means to keep tack on the Moore’s law. Cavity optomechanics is a rising field of silicon photonics. It focuses on the interaction between light and mechanical objects. Although it is currently at its early stage of growth, this field has attracted rising attention. Here, we present highly sensitive optical detection of acceleration using an optomechanical accelerometer. The core part of this accelerometer is a slot-type photonic crystal cavity with strong optomechanical interactions. We first discuss theoretically the optomechanical coupling in the air-slot mode-gap photonic crystal cavity. The dispersive coupling gom is numerically calculated. Dynamical parametric oscillations for both cooling and amplification, in the resolved and unresolved sideband limit, are examined numerically, along with the displacement spectral density and cooling rates for the various operating parameters. Experimental results also demonstrated that the cavity has a large optomechanical coupling rate. The optically induced spring effect, damping and amplification of the mechanical modes are observed with measurements both in air and in vacuum. Then, we propose and demonstrate our optomechanical accelerometer. It can operate with a resolution of 730 ng/Hz¹/² (or equivalently 40.1 aN/Hz¹/²) and with a transduction bandwidth of ≈ 85 kHz. We also demonstrate an integrated photonics device, an on-chip spectroscopy, in the last part of this thesis. This new type of on-chip microspectrometer is based on the Vernier effect of two cascaded micro-ring cavities. It can measure optical spectrum with a bandwidth of 74nm and a resolution of 0.22 nm in a small footprint of 1.5 mm²

Roadmap on quantum nanotechnologies

Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano- and opto-mechanical systems, low-dimensional systems, molecular devices, nano-plasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon

Quantum dots for quantum information processing

Electron spins confined in quantum dots (QDs) are among the leading contenders for implementing quantum information processing. In this Thesis we address two of the most significant technological challenges towards developing a scalable quantum information processor based on spins in quantum dots: (i) decoherence of the electronic spin qubit due to the surrounding nuclear spin bath, and (ii) long-range spin-spin coupling between remote qubits. To this end, we develop novel strategies that turn the unavoidable coupling to the solid-state environment (in particular, nuclear spins and phonons) into a valuable asset rather than a liability. In the first part of this Thesis, we investigate electron transport through single and double QDs, with the aim of harnessing the (dissipative) coupling to the electronic degrees of freedom for the creation of coherence in both the transient and steady-state behaviour of the ambient nuclear spins. First, we theoretically show that intriguing features of coherent many-body physics can be observed in electron transport through a single QD. To this end, we first develop a master-equation-based formalism for electron transport in the Coulomb-blockade regime assisted by hyperfine (HF) interaction with the nuclear spin ensemble in the QD. This general tool is then used to study the leakage current through a single QD in a transport setting. When starting from an initially uncorrelated, highly polarized state, the nuclear system experiences a strong correlation buildup, due to the collective nature of the coupling to the central electron spin. We demonstrate that this results in a sudden intensity burst in the electronic tunneling current emitted from the QD system, which exceeds the maximal current of a corresponding classical system by several orders of magnitude. This gives rise to the new paradigm of electronic superradiance. Second, building upon the insight that the nuclear spin dynamics are governed by collective interactions giving rise to coherent effects such as superradiance, we propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics is shown to lead to intriguing effects such as multistability and criticality in the steady-state solutions. In the second part of this Thesis, our focus turns towards the realization of long-range spin-spin coupling between remote qubits. We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezo-active materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range, can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitations can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits. In summary, this thesis provides contributions towards developing a scalable quantum information processor based on spins in quantum dots in two different aspects. The first part is dedicated to a deeper understanding of the nuclear spin dynamics in quantum dots. In the second part we put forward a novel sound-based strategy to realize long-range spin-spin coupling between remote qubits. This completes a broad picture of spin-based quantum information processing which integrates different perspectives, ranging from the single-qubit level to a broader quantum network level.Elektronenspins in Quantenpunkten gehören zu den vielversprechendsten Ansätzen für die erfolgreiche Implementierung von Quanteninformationsverarbeitung. Diese Arbeit behandelt zwei der größten Herausforderungen für die Entwicklung eines skalierbaren Quanteninformationsprozessors auf Basis von Spins in Quantenpunkten: (i) die Kontrolle der Dekohärenz des elektronischen Spins aufgrund der Wechselwirkung mit dem umliegenden Kernspin-Bad, und (ii) die Realisierung einer langreichweitigen Spin-Spin Kopplung zwischen entfernt liegenden Qubits. Zu diesem Zweck entwickeln wir neue Strategien, die die unvermeidliche Kopplung an die Festkörperumgebung (insbesondere Kernspins und Phononen) zu ihrem Vorteil ausnutzen. Im ersten Teil dieser Arbeit untersuchen wir den Elektronentransport durch Einzel- und Doppel-Quantenpunkte, mit dem Ziel die dissipative Kopplung an die elektronischen Freiheitsgrade zur Erzeugung von kohärenter Kernspindynamik auszunutzen. Dies gilt sowohl für das kurzfristige wie auch das langfristige Verhalten der Kernspins. Zunächst zeigen wir theoretisch, dass faszinierende Eigenschaften kohärenter Vielteilchenphysik im Elektronen-transport durch einen einzelnen Quantenpunkt beobachtet werden können. Dazu entwickeln wir zunächst einen auf Master-Gleichungen basierenden Formalismus für den Elektronentransport im Coulomb-Blockade Regime, der die Hyperfeinwechselwirkung mit dem Kernspin-Ensemble im Quantenpunkt berücksichtigt. Dieses allgemeine theoretische Werkzeug wird anschließend verwendet, um den Strom durch einen einzelnen Quantenpunkt in einem Transportszenario zu studieren. Sind die Kernspins anfänglich in einem unkorrelierten, hoch polarisierten Zustand, so bauen sich aufgrund der kollektiven Wechselwirkung mit dem zentralen Elektronenspin starke Korrelationen zwischen den Kernspins auf. Wir zeigen, dass dies zu einem plötzlichen, starken Anstieg im Tunnelstrom durch den Quantenpunkt führt, welcher den maximalen Strom in einem analogen klassischen System um mehrere Größenordnungen übersteigt. Dieses Verhalten begründet das neue Paradigma von elektronischer Superradianz. Ausgehend von der Einsicht, dass die Kernspindynamik von kollektiven Wechselwirkungen bestimmt wird, welche wiederum zu kohärenten Effekten wie Superradianz führen können, schlagen wir im nächsten Schritt ein Modell zur deterministischen Verschränkungserzeugung zwischen den beiden Kernspinensembles in einem elektrisch definierten Doppelquantenpunkt vor. Aufgrund von Quanteninterferenz in der kollektiven Kopplung an die elektronischen Freiheitsgrade wird das Kernspinsystem aktiv in einen gequetschten zwei-Moden Zustand gepumpt. Der Aufbau von Verschränkung wird durch einen Polarisationsprozess der Kernspins hin zu großen Overhauser-Feldern begleitet. Darüber hinaus wird gezeigt, dass die Rückkopplung zwischen elektronischen und Kernspin-Freiheitsgraden zu interessanten Effekten wie zum Beispiel Multistabilität und kritischem Verhalten in den stationären Lösungen führt. Im zweiten Teil der Arbeit wenden wir uns der langreichweitigen Spin-Spin Kopplung zwischen entfernt liegenden Qubits zu. Dazu schlagen wir einen universellen Quanten-Transducer vor, der auf akustischen Oberflächenwellen in piezo-aktiven Materialen beruht und direkt auf Chips aufgebracht werden kann. Aufgrund der piezo-elektrischen (und/oder magnetostriktiven) Eigenschaften des Materials bietet unser Ansatz eine universelle Platform für eine ganze Reihe von Qubits; dazu gehören Quantenpunkte, Ionen, Stickstoff-Fehlstellen-Zentren (NV-Zentren) oder auch supraleitende Qubits. Die quantisierten Moden der akustischen Oberflächenwellen haben typische Frequenzen im Gigahertz-Bereich, können stark in der Nähe der Oberfläche in phononischen Resonatoren lokalisiert werden und entlang akustischer Wellenleiter geleitet werden. Wir zeigen, dass diese Art der akustischen Oberflächenanregung effizient als Quanten-Bus verwendet werden kann, der als mechanisches Analogon zu Mikrowellen-Photonen in der Resonator-Quanten-Elektrodynamik fungiert und langreichweitige Kopplung zwischen entfernt liegenden Qubits ermöglicht. Zusammenfassend liefert diese Arbeit einen Beitrag zur Entwicklung eines skalierbaren, auf Spins in Quantenpunkten beruhenden Quanteninformationsprozessors aus zwei verschiedenen Perspektiven. Der erste Teil widmet sich eines tiefgehenderen Verständnisses der Kernspin-dynamik in Quantenpunkten. Im zweiten Teil schlagen wir eine neue, auf Schall basierende Strategie zur Erzeugung von langreichweitiger Spin-Spin Kopplung zwischen entfernt liegenden Qubits vor. Dies vervollständigt ein breites Bild von Spin-basierter Quanteninformationsverarbeitung, welches verschiedene Perspektiven vereinigt, von der Ebene einzelner Qubits bis hinzu einer umfassenderen Ebene eines Quanten-Netzwerks

Microstrip Superconducting Quantum Interference Devices for Quantum Information Science

Quantum-limited amplification in the microwave frequency range is of both practical and fundamental importance. The weak signals corresponding to single microwave photons require substantial amplification to resolve. When probing quantum excitations of the electromagnetic field, the substantial noise produced by standard amplifiers dominates the signal, therefore, several averages must be accumulated to achieve even a modest signal-to-noise ratio. Even worse, the back-action on the system due to amplifier noise can hasten the decay of the quantum state. In recent years, low-noise microwave-frequency amplification has been advancing rapidly and one field that would benefit greatly from this is circuit quantum electrodynamics (cQED). The development of circuit quantum electrodynamics---which implements techniques of quantum optics at microwave frequencies---has led to revolutionary progress in the field of quantum information science. cQED employs quantum bits (qubits) and superconducting microwave resonators in place of the atoms and cavities used in quantum optics permitting preparation and control of low energy photon states in macroscopic superconducting circuits at millikelvin temperatures. We have developed a microstrip superconducting quantum interference device (SQUID) amplifier (MSA) to provide the first stage of amplification for these systems. Employing sub-micron Josephson tunnel junctions for enhanced gain, these MSAs operate at microwave frequencies and are optimized to perform with near quantum-limited noise characteristics. Our MSA is utilized as the first stage of amplification to probe the dynamics of a SQUID oscillator. The SQUID oscillator is a flux-tunable microwave resonator formed by a capacitively shunted dc SQUID. Josephson plasma oscillations are induced by pulsed microwave excitations at the resonant frequency of the oscillator. Once pulsed, decaying plasma oscillations are observed in the time domain. By measuring with pulse amplitudes approaching the critical current of the SQUID, it is possible to probe the free evolution of a highly nonlinear oscillator