The possibility of creating a scaleable quantum network by interconverting photonic and atomic qubits shows great promise. The fundamental requirement for such a network is deterministic control over the emission and absorption of photons from single atoms. This thesis reports on the experi-mental construction of a photon source that can emit single-photons with arbitrary spatio-temporal shape, phase, and frequency. The photon source itself is a strongly-coupled atom cavity system based on a single ⁸⁷ Rb atom within a macroscopic high-finesse Fabry-Perot cavity. It operates intermittently for periods of up to 100µs, with single-photon repetition rates of 1.0 MHz and an efficiency of almost 80%. Atoms are loaded into the cavity using an atomic fountain, with the upper turning point near the centre of the cavity mode. This ensures long interaction times without any disturbances introduced by trapping potentials. The photons’ indistinguishability was tested, with a two-photon Hong-Ou-Mandel visibility of 87%. This ability to both generate, and control, the photons’ properties, for example producing photons with symmetric or multi-peaked spatio-temporal shapes, allows for the production of photons in an n-time-bin superposition state where each time-bin has an arbitrarily defined amplitude and phase. These photons can be used as photonic qubits, qutrits and qquads, and their properties have been tested using a small linear-optics network.

This thesis describes the duality methods used in the tensor renormalization group method and their application to quantum simulation with cold atoms in optical lattices. Here we consider specifically the O(2) and O(3) nonlinear sigma models in two dimensions, as well as the Abelian Higgs model in two dimensions. We give numerical results from the tensor renormalization group and comparisons with other numerical methods for all three models. We give proposals for possible experimental methods with which these models could be simulated using cold atoms trapped in optical lattices as is done in ongoing experiments.

<p>The blooming of quantum computer hardware provokes enormous enthusiasm seeking for applications in various fields.</p> <p>Particularly, it is always of great interest to study the chemical or physical systems with quantum enhanced learning process or quantum simulation in the NISQ era.</p> <p>Here we will present our recent research on chemical or physical systems based on quantum computing. </p> <p><br></p> <p>One main focus of this dissertation is the quantum classification algorithms development, especially for the entanglement classification.</p> <p>As a quantum mechanical property describing the correlation between quantum mechanical systems, entanglement has no classical analog.</p> <p>In the past 100 years, entanglement has been attracting enormous attentions in both the theoretical and experimental research.</p> <p>We investigate the entanglement classification in chemical reactions, generalizing the typical CHSH inequality from discrete measurement results into the continuous measurement results.</p> <p>Furthermore, we develop a quantum classification algorithm based on the typical instance-based learning algorithms, which in turn is applied into the entanglement classification problems.</p> <p>Additionally, the proposed quantum algorithm has a variety of applications, such as the prediction of phase transition. </p> <p><br></p> <p>Quantum-enhanced classification algorithm is never the only practicable application of quantum computer.</p> <p>Moreover, we propose a universal quantum circuit implementation to estimate a given one-dimensional functions with a finite Fourier expansion.</p> <p>We demonstrate the circuit implementation with the application on square wave function.</p> <p>Additionally, we present a quantum circuit for the typical time-independent perturbation theory.</p> <p>Perturbation theory is always one of the most powerful tools for physicists and chemists dealing with the eigenenergy problems in quantum mechanics.</p> <p>Though PT is quite popular today, it seems that the techniques for PT does not take a ride in the era of quantum computing.</p> <p>In this dissertation, we present a a universal quantum circuit implementation  for the time-independent PT method, which is often termed as Rayleigh–Schr\"odinger PT.</p> <p>In order to demonstrate the implementation of the proposed quantum circuit, the extended Fermi Hubbard Model is introduced as an example.</p> <p>In particular, the proposed quantum circuit shows considerable speedup comparing with the typical PT methods.</p>

Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems. This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed. The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.

Neste dissertação apresentamos um protocolo para simular, no contexto das armadilhas iônicas, o Zitterbewegung não usual, que é o análogo, na física do semicondutores, ao movimento de tremulação de uma partícula relativística. O Zitterbewegung não usual permite trajetórias cicloidais na ausência dos campos magnéticos. Além do Zitterbewegung, mostramos como gerar figuras de Lissajou para o movimento vibracional bidimensional do íon armadilhado. Ademais, o protocolo proposto nesta tese, permite gerar interações spin-órbita dos tipos Rashba e Dresselhaus, abrindo a possibilidade de simular, no âmbito dos íons armadilhados, os acoplamentos spin-órbita dos tipos Rashba e Dresselhaus, Zitterbewegung não usual e as curvas de Lissajou. Além disso, nesta tese apresentamos protocolo para produzir engenharia de interações confinadas aos subespaços do espaço de Fock. Mostramos como engenheirar os hamitonianos dos tipos Jaynes-Cumming e anti-Jaynes-Cumming confinadados aos subespaços de Fock delimitados superiormente ou inferiormente e também as interações Jaynes-Cumming e anti-Jaynes-Cumming confinados a uma fatia do espaço Fock. Esses hamitonias delimitados superiormente (inferiormente) atuam sobre os subespaço de Fock de |0&rang; a |M&rang; (|N&rang; &alpha;&infin;), enquanto aqueles confinados a uma fatia do espaço de Fock atuam sobre os subespaço de Fock de |M&rang; a |N&rang; com M < N. Enquanto que, as interações dos tipo Jaynes-Cumming ou anti-Jaynes-Cumming demilitadas superiormente conduzem qualquer estado inicial para o estado de Fock de quase-equilíbrio |N&rang; e as interações confinadas a uma fatia do espaço de Fock conduz qualquer estado inicial a superporsição de estados de Fock de equilíbrio, que estão confinados no subespaço {|N&rang; , |N + 1&rang;}. / In this dissertation we present a protocol to simulate, with a single two-leve trapped ion, the unusual zitterbewegung: the semiconductor analog of the relativistic trembling motion of eletron, allowing cycloidal trajectories in the absence of magnetic fields. Beyon zitterbewegung, we show how to generate Lissajou curves from the vibrational motion of an ion in two dimensional trap. Morever our protocol enables us to engineerthe Rashbaand the Dresselhaus-type spin-orbit interatiction, opening the possibility to simulate with a trapped ion, spin-orbit effects other than the unusual zitterbewegung and Lissajou curves. Moreover, in this work we present a protocol to engineer interactions confined to subspaces of the Fock space: we show how to engineer upper-, lower-bounded and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) Hamiltonians. The upperbounded (lower-bounded) interaction acting upon Fock subspaces ranging from |0&rang; to |M&rang; (|N&rang; to &infin;), and the sliced one confined to Fock subspace ranging from |M&rang; to |N&rang;, whatever M < N. Whereas the upper-bounded JC or AJC interactions is shown to drive any initial state to an equilibrium Fock states |N&rang;, the sliced one is shown to produce equilibrium superpositions of Fock states confined to the sliced subspaces {|N&rang; , |N + 1&rang;}.

Neste dissertação apresentamos um protocolo para simular, no contexto das armadilhas iônicas, o Zitterbewegung não usual, que é o análogo, na física do semicondutores, ao movimento de tremulação de uma partícula relativística. O Zitterbewegung não usual permite trajetórias cicloidais na ausência dos campos magnéticos. Além do Zitterbewegung, mostramos como gerar figuras de Lissajou para o movimento vibracional bidimensional do íon armadilhado. Ademais, o protocolo proposto nesta tese, permite gerar interações spin-órbita dos tipos Rashba e Dresselhaus, abrindo a possibilidade de simular, no âmbito dos íons armadilhados, os acoplamentos spin-órbita dos tipos Rashba e Dresselhaus, Zitterbewegung não usual e as curvas de Lissajou. Além disso, nesta tese apresentamos protocolo para produzir engenharia de interações confinadas aos subespaços do espaço de Fock. Mostramos como engenheirar os hamitonianos dos tipos Jaynes-Cumming e anti-Jaynes-Cumming confinadados aos subespaços de Fock delimitados superiormente ou inferiormente e também as interações Jaynes-Cumming e anti-Jaynes-Cumming confinados a uma fatia do espaço Fock. Esses hamitonias delimitados superiormente (inferiormente) atuam sobre os subespaço de Fock de |0&rang; a |M&rang; (|N&rang; &alpha;&infin;), enquanto aqueles confinados a uma fatia do espaço de Fock atuam sobre os subespaço de Fock de |M&rang; a |N&rang; com M < N. Enquanto que, as interações dos tipo Jaynes-Cumming ou anti-Jaynes-Cumming demilitadas superiormente conduzem qualquer estado inicial para o estado de Fock de quase-equilíbrio |N&rang; e as interações confinadas a uma fatia do espaço de Fock conduz qualquer estado inicial a superporsição de estados de Fock de equilíbrio, que estão confinados no subespaço {|N&rang; , |N + 1&rang;}. / In this dissertation we present a protocol to simulate, with a single two-leve trapped ion, the unusual zitterbewegung: the semiconductor analog of the relativistic trembling motion of eletron, allowing cycloidal trajectories in the absence of magnetic fields. Beyon zitterbewegung, we show how to generate Lissajou curves from the vibrational motion of an ion in two dimensional trap. Morever our protocol enables us to engineerthe Rashbaand the Dresselhaus-type spin-orbit interatiction, opening the possibility to simulate with a trapped ion, spin-orbit effects other than the unusual zitterbewegung and Lissajou curves. Moreover, in this work we present a protocol to engineer interactions confined to subspaces of the Fock space: we show how to engineer upper-, lower-bounded and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) Hamiltonians. The upperbounded (lower-bounded) interaction acting upon Fock subspaces ranging from |0&rang; to |M&rang; (|N&rang; to &infin;), and the sliced one confined to Fock subspace ranging from |M&rang; to |N&rang;, whatever M < N. Whereas the upper-bounded JC or AJC interactions is shown to drive any initial state to an equilibrium Fock states |N&rang;, the sliced one is shown to produce equilibrium superpositions of Fock states confined to the sliced subspaces {|N&rang; , |N + 1&rang;}.

In this thesis, I present experiments on making and probing strongly correlated gases of ultracold atoms in an optical lattice with engineered potentials and dynamics. The quantum gas microscope first developed in our lab enables single-site resolution imaging and manipulation of atoms in a two-dimensional lattice, offering an ideal platform for quantum simulation of condensed matter systems. Here we demonstrate our abilities to generate optical potential with high precision and high resolution, and engineer coherent dynamics using photon assisted tunneling. We also create a system of bilayer quantum gases that brings new imaging capabilities and extends the possible range of our quantum simulation. / Physics

La miniaturisation des MOSFET a permis une forte diminution des transistors et des puces, ainsi qu’une augmentation exponentielle des capacités de calcul. Cette miniaturisation ne peut néanmoins continuer ainsi: de nos jours, un microprocesseur peut contenir des dizaines de milliards de transistors et la chaleur dégagée par ces composants peut fortement détériorer ses performances. De plus, du fait de leur principe même de fonctionnement, la tension d’alimentation des MOSFET ne peut être réduite sans en impacter les performances. De nouvelles architectures telles que le TFET -basé sur l’effet tunnel bande-à-bande et pouvant fonctionner à des tensions d’alimentation très basses- ainsi que de nouveaux matériaux pourraient donc apporter une alternative au MOSFET silicium. Les monocouches de dichalcogènures de métaux de transitions (TMDs) -des semiconducteurs à bande interdite directe d’environ 1 à 2 eV- possèdent un fort potentiel pour l’électronique et la photonique. De plus, dans le cas de contraintes appropriées, ils peuvent conduire un alignement de bandes présentant un broken-gap; cette configuration permet de surpasser les limites habituelles du TFETs, à savoir de faibles courants dus à l’effet tunnel sur lequel ces dispositifs reposent. Dans ce travail de thèse, des hétérojonctions planaires de TMD sont modélisées via une approche atomistique de liaisons fortes, et une configuration broken-gap est observée dans deux d’entre elles (MoTe2/MoS2 et WTe2/MoS2). Leur potentiel dans le cadre de transistors à effet tunnel (TFETs) est évalué au moyen de simulations de transport quantique basées sur un modèle TB atomistique ainsi que la théorie des fonctions de Green hors-équilibre. Des TFETs type-p et type-n basés sur ces hétérojonctions sont simulés et présentent des courants ON élevés (ION > 103 µA/µm) ainsi que des pentes sous-seuil extrêmement raides (SS < 5 mV/dec) à des tensions d’alimentation très faibles (VDD = 0.3 V). Plusieurs architectures novatrices basées sur ces TFETs et découlant de la nature 2D des matériaux utilisés sont également présentées, et permettent d’atteindre des performances encore plus élevées. / Nowadays, microprocessors can contain tens of billions of transistors and as a result, heat dissipation and its impact on device performance has increasingly become a hindrance to further scaling. Due to their working mechanism, the power supply of MOSFETs cannot be reduced without deteriorating overall performance, and Si-MOSFETs scaling therefore seems to be reaching its end. New architectures such as the TFET, which can perform at low supply voltages thanks to its reliance on band-to-band tunneling, and new materials could solve this issue. Transition metal dichalcogenide monolayers (TMDs) are 2D semiconductors with direct band gaps ranging from 1 to 2 eV, and therefore hold potential in electronics and photonics. Moreover, when under appropriate strains, their band alignment can result in broken-gap configurations which can circumvent the traditionally low currents observed in TFETs due to the tunneling mechanism they rely upon. In this work, in-plane TMD heterojunctions are investigated using an atomistic tight-binding approach, two of which lead to a broken-gap configuration (MoTe2/MoS2 and WTe2/MoS2). The potential of these heterojunctions for use in tunnel field-effect transistors (TFETs) is evaluated via quantum transport computations based on an atomistic tight-binding model and the non-equilibrium Green’s function theory. Both p-type and n-type TFETs based on these in-plane TMD heterojunctions are shownto yield high ON currents (ION > 103 µA/µm) and extremely low subthreshold swings (SS < 5 mV/dec) at low supply voltages (VDD = 0.3 V). Innovative device architectures allowed by the 2D nature of these materials are also proposed, and shown to enhance performance even further.

<div>Atoms trapped in close proximity to optical resonators provides a powerful tool for exploring atom light interactions and their quantum applications. In this work I will describe the development of a neutral atom quantum simulator that implements trapped cesium atoms which have been localized via optical tweezers in close proximity to the surface of a micro-ring resonator fabricated on the surface of an optical chip. The small separation between the cavity and the atom allows for relatively large atom photon coupling strength g on the order of a few hundred MHz. Coupling multiple atoms to a common nanophotonic mode provides a channel through which atoms can exchange virtual photons for the study of long range spin exchange and other quantum many body models.</div><div></div><div>This platform has proven to be extremely versatile. We have thus far successfully demonstrated our ability to trap and image individual atoms directly above the surface of our photonic chips as well as the ability to extend trapping and imaging to arrays of tweezer traps which can be loaded with one or more atoms with high probability. Due to the simplified fabrication process of our planar geometry photonic chips we have been able to rapidly prototype and evolve our system to facilitate new and improved methods of trapping atoms near the surface of our nanophotonic structure. In the following I will discuss the development of our apparatus, our current progress observing signatures of atom-cavity coupling, and some of our future goals we are approaching.</div>

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