Optical response of an active medium can substantially be modified when coherent superpositions of states are excited, that is, when systems display quantum coherence and interference. This has led to fascinating applications in atomic and molecular systems. Examples include coherent population trapping, lasing without inversion, electromagnetically induced transparency, cooperative spontaneous emission, and quantum entanglement. We study quantum coherence effects in several quantum optical systems and find interesting applications. We show that quantum coherence can lead to transient Raman lasing and lasing without inversion in short wavelength spectral regions--extreme ultraviolet and x-ray--without the requirement of incoherent pumping. For example, we demonstrate transient Raman lasing at 58.4 nm in Helium atom and transient lasing without inversion at 6.1 nm in Helium-like Boron (triply-ionized Boron). We also investigate dynamical properties of a collective superradiant state prepared by absorption of a single photon when the size of the sample is larger than the radiation wavelength. We show that for large number of atoms such a state, to a good approximation, decays exponentially with a rate proportional to the number of atoms. We also find that the collective frequency shift resulting from repeated emission and reabsorption of short-lived virtual photons is proportional to the number of species in the sample. Furthermore, we examine how a position-dependent excitation phase affects the evolution of entanglement between two dipole-coupled qubits. It turns out that the coherence induced by position-dependent excitation phase slows down the otherwise fast decay of the two-qubit entanglement. We also show that it is possible to entangle two spatially separated and uncoupled qubits via interaction with correlated photons in a cavity quantum electrodynamics setup. Finally, we analyze how quantum coherence can be used to generate continuous-variable entanglement in quantum-beat lasers in steady state and propose possible implementation in quantum lithography.

Στην συγκεκριμένη εργασία ασχολούμαστε με την μελέτη θερμικά σύμπλεκτων (entangled) καταστάσεων πολλών κβαντικών bit (qubit) σε διάφορα μοντέλα Heisenberg με την μέθοδο Monte Carlo (MC). Αρχικά χρησιμοποιώντας τον μετασχηματισμό Suzuki-Trotter μετατρέπουμε την κβαντική μονοδιάστατη αλυσίδα των spin (μοντέλα Ising, Heisenberg με και χωρίς μαγνητικό πεδίο στις διευθύνσεις x,y,z) σε κλασικό δισδιάστατο πλέγμα. Εξετάζουμε την συμπεριφορά του συγκεκριμένου μετασχηματισμού για το αντισιδηρομαγνητικό Heisenberg ΧΧΧ μοντέλο, για το σιδηρομαγνητικό Heisenberg μοντέλο (ΧΧΧ και ΧΥΖ) χωρίς και με μαγνητικό πεδίο στις διευθύνσεις x,y,z για διάφορα μήκη της αλυσίδας, διαφορετικές διαστάσεις Trotter και διαφορετικό αριθμό Monte Carlo βημάτων (MCΒήματα). Μελετάμε την συμπεριφορά της θερμοχωρητικότητας, της ενέργειας, της μαγνητικής επιδεκτικότητας και της μαγνήτισης στις διευθύνσεις x,y,z. Επιβεβαιώνουμε την σωστή συμπεριφορά τους με βάση τα αναλυτικά αποτελέσματα. Τέλος γνωρίζοντας, ότι η κλασική συσχέτιση είναι το κάτω όριο της ποσότητας Localizable Entanglement, και ότι η ποσότητα Entanglement of Assistance είναι το πάνω όριο, εκτιμούμε για τα ίδια μοντέλα τη συμπεριφορά των ορίων και προσπαθούμε να εκτιμήσουμε το μήκος σύμπλεξης (Entanglement Length) για διάφορες θερμοκρασίες. / In the present Master Thesis we study the thermal entangled states of many qubits in a variety of Heisenberg models with the deployment of the Monte Carlo(MC) method. Initially we are using the Suzuki-Trotter decomposition in order to convert the one dimensional spin chain(models Ising, Heisenberg with and without magnetic field in the x,y,z axis) into a classical two dimensional lattice. We examine the behavior of the latter decomposition for the antiferromagnetic Heisenberg XXX model, the ferromagnetic Heisenberg model (XXX and XYZ) with or without magnetic field in the axis x,y,z for different chain lengths, Trotter dimensions and number of Monte Carlo Steps (MCSteps). We investigate the behavior of the following quantities: specific heat, energy, susceptibility and magnetization in the axis x,y,z. We confirm their proper behavior comparing to analytical and arithmetic results. Finally knowing that the maximum classical correlation function is the lower limit of the quantity Localizable Entanglement (LE) and that the quantity Entanglement of Assistance is the upper limit, we evaluate for the same models the behavior of the limits and we try to evaluate the Entanglement Length for a variety of temperatures.

Ce travail de thèse porte sur l’étude fondamentale de systèmes nano-électroniques,mesurés à très basse température. Nous avons réalisé des interféromètres électroniques àdeux chemins à partir d’électrons balistiques obtenus dans un gaz 2D d’électrons d’unehétéro-structure GaAs/AlGaAs. Nous montrons que la phase des électrons, et ainsileur état quantique,peut être contrôlée par des grilles électrostatiques. Ces dispositifsse révèlent être des candidats prometteurs pour la réalisation d’un qubit volant. Nousavons développé une simulation numérique évoluée d’un modèle de liaisons fortes à partirde transport quantique ballistique qui décrit toutes les découvertes expérimentales etnous apporte une connaissance approfondie sur les signatures expérimentales de cesdispositifs particuliers. Nous proposons des mesures complémentaires de ce système dequbit volants. Pour atteindre le but ultime, à savoir un qubit volant à un électron unique,nous avons assemblé la source à électron unique précédemment développée dans notreéquipe à un beam splitter électronique. Les électrons sont alors injectés depuis une boîtequantique à un train de boîte quantiques en mouvement. Ce potentiel électrostatique enmouvement est généré par des ondes acoustiques de surface créées par des transducteursinter-digités sur le substrat GaAs piézo-électrique. Nous avons étudié et optimisé chacunde ces composants fondamentaux nécessaires à la réalisation d’un beam splitter à électronunique et développé un procédé local et fiable de fabrication. Ce dispositif nous permet d’étudier les interactions électroniques pour des électrons isolés et pourra servir de basede mesure pour des expériences d’optique quantiques sur un système électronique del’état condensé. Enfin, nous avons développé un outil puissant de simulation du potentielélectrostatique à partir de la géométrie des grilles. Ceci permet d’optimiser la conceptiondes échantillons avant même leur réalisation. Nous proposons ainsi un prototype optimiséde beam splitter à électron unique. / This thesis contains the fundamental study of nano-electronic systems at cryogenictemperatures. We made use of ballistic electrons in a two-dimensional electron gasin a GaAs/AlGaAs heterostructure to form a real two-path electronic interferometerand showed how the phase of the electrons and hence their quantum state can becontrolled by means of electrostatic gates. The device represents a promising candidateof a flying qubit. We developed a sophisticated numerical tight-binding model based onballistic quantum transport, which reproduces all experimental findings and allows togain profound knowledge about the subtle experimental features of this particular device.We proposed further measurements with this flying qubit system. With the ultimate goalof building a single electron flying qubit, we combined the single electron source that hasbeen developed in our lab prior to this manuscript with an electronic beam splitter. Theelectrons are injected from static quantum dots into a train of moving quantum dots.This moving potential landscape is induced in the piezoelectric substrate of GaAs bysurface acoustic waves from interdigial transducers. We studied and optimized all keycomponents, which are necessary to build a single electron beam splitter and built up areliable local fabrication process. The device is capable of studying electron interactionson the single electron level and can serve as a measurement platform for quantum opticsexperiments in electronic solid state systems. Finally, we developed a powerful toolcapable of calculating the potential landscapes of any surface gate geometry, which canbe used as a fast feedback optimization tool for device design and proposed an optimizedprototype for the single electron beam splitter.

Nous proposons, par voie théorique, une sonde ayant la capacité de détecter et de caractériser les états de surface d'une chaîne Su-Schrieffer-Heeger (SSH). Cette sonde consiste d’un qubit interagissant avec un environnement, et exploite le phénomène de la décohérence afin de retirer de l’information sur l’environnement. Une approximation de faible couplage permet de démontrer analytiquement que le taux de décohérence du qubit est proportionnel à la densité d’états locale de l’environnement. Dans le cas d’un environnement possédant des états discrets, une mesure de la densité d’états locale peut être équivalente à une mesure de l’amplitude d’un état, permettant donc une caractérisation spatiale des états de l’environnement. Un système tripartite consistant d'un qubit couplé à une chaîne SSH discrète muni de canaux conducteurs aux extrémités est étudié afin de valider l’utilité de la sonde pour inférer et caractériser les états de surface. L’espace des paramètres de la sonde est discuté en détail. En étudiant l’impact du couplage des canaux conducteurs, nous notons l’émergence d’états de type-surface sur des sites interdits ainsi que dans des phases topologiques ne supportant pas d’états de surface dans le modèle SSH isolé. Ces excitations, que nous appelons états fantômes, apparaissent dû à un décalage des frontières de la chaîne SSH. / We propose a novel probe with the ability to detect topological edge states in lowdimensional materials. This probe, consisting of a qubit interacting with a system of interest, utilizes the dynamics of decoherence to study the qubit’s environment. We show analytically that, under a weak-coupling approximation, the decoherence rate of the qubit is proportional to the local density of states of the environment. In studying environments featuring finite subsystems with discrete states, the local density of states mapped by the qubit probe can extract state amplitude profiles, resulting in a full spatial characterization of states. We explicitly study a tripartite system consisting of a qubit coupled to a finite SSH chain with conducting leads attached to each end and demonstrate the probe’s ability to infer the presence of, and characterize, edge states. The parameter space of the probe is studied. Notably, we show the lead coupling strength effectively shifts the SSH chain boundaries resulting in emergent edge-type states, dubbed ghost states, with support on sites which are forbidden in an isolated SSH chain for a given topological phase.

<p>In recent years, correlated magnetic phenomena have emerged as a unique resource for enabling alternative computing, memory, and sensing applications. This has led to the exploration of novel magnetic hybrid platforms with the promise of improved figures of merit over the state-of-the-art. In this dissertation, we delve into several example platforms where magnets interact with various other degrees of freedom, resulting in enhanced figures of merit and/or the emergence of novel functionalities.</p><p>First, we investigate the possibility of utilizing the collective resonant mode of nanomagnets to enhance the electric field sensitivity of quantum spin defects. While quantum systems have garnered significant attention in recent years for their extraordinary potential in information processing, their potential in the field of quantum sensing remains yet to be fully explored. Quantum systems, with their inherent fragility to external signals, can be harnessed as powerful tools to develop highly efficient sensors. In this dissertation, we explore the potential of a specific type of quantum sensor, namely the quantum spin defects as an electric field sensor, when integrated with a nanomagnet/piezoelectric composite multiferroic. This integration yields at least an order of magnitude enhancement in sensitivity, presenting a promising avenue for quantum sensing applications.</p><p>Next, we shift our focus towards harnessing magnetic correlation in the emerging class of atomically thin magnets known as van der Waals magnets. These magnets provide distinctive opportunities for controlling and exploiting magnetic correlations. Specifically, these platforms allow for tunable magnetic interactions by twisting two vertically adjacent layers of the magnet, features that are unique to van der Waals materials. By capitalizing on such twist degrees of freedom, we demonstrate the creation of twist-tunable nanoscale magnetic ground states. This capability opens up avenues for applications such as high-density memories and magnon crystals.</p><p>Interestingly, the same material platform also allows for exploiting magnetic correlation by controlling the local electrical environment. We uncover the symmetry-allowed spin-charge coupling mechanisms in the heterostructures of such magnets, a prediction that has received experimental support. Utilizing such an understanding, we propose a setup for the electrical generation of magnons. Magnons—the elementary excitation of spin waves—have garnered a lot of attention these days due to their potential to couple various diverse physical systems and in the field of low dissipation computing. Our findings offer a potential pathway towards the realization of magnon-based spintronic devices.</p>

Qubits (quantum bits) are what runs quantum computers, like a bit in classical computers. Quantum gates are used to operate on qubits in order to change their states. As such they are what ”programmes” a quantum computer. An unfortunate side effect of quantum physics is that coupling a quantum system (like our qubits) to an outside environment will lead to a certain loss of information. Reducing this decoherence effect is thus vital for the function of a quantum computer. Geometric quantum computation is a method for creating error robust quantum gates by using so called geometric phases which are solely reliant on the geometry of the evolution of the system. The purpose of this project has been to develop physical schemes of geometric entangling two-qubit gates along the Schmidt sphere, a geometric construct appearing in two-qubit systems. Essentially the overall aim has been to develop new schemes for implementing robust entangling quantum gates solely by means of interactions intrinsic to the computational systems. In order to create this gate four mutually orthogonal states were defined which together spanned the two-qubit state space. Two of the states were given time dependent variables containing a total of two angles,which were used to parameterize the Schmidt sphere. By designing an evolution for these angles that traced out a cyclical evolution along geodesic lines a quantum gate with exclusively geometric phases could be created. This gate was dubbed the ”Schmidt gate” and could be shown to be entangling by analyzing a change in the concurrence of a two qubit system. Two Hamiltonians were also defined which when acted upon the predefined system of states would give rise to the aforementioned evolution on the Schmidt sphere. The project was successful in creating an entangling quantum gate which could be shown by looking at difference in the concurrence of the input and output state of a two-qubit system passing through the gate.

We manipulate two superconducting qubits using digital microwave electronics. Starting fromtheir characterization, we develop a real-time reset scheme and implement the iSwap gate. Thequbits’ parameters are obtained using standard single-qubit characterization techniques, such asRabi and Ramsey oscillations and frequency sweep of the resonators. We also characterized theexperimental setup, including finding the working point of a Josephson Parametric Amplifierand the coupler between the two qubits. We solve the linear differential equations that modelthe resonator, in order to design a high-fidelity, single-shot qubit-measurement pulse shape,which actively empties the cavity. Using this pulse, we achieve a readout assignment fidelity of99.9%. The readout is formed in real-time using template matching. In addition, we implementa conditional reset of the qubit’s state in 1.4 μs, which resets the excited state population from5.4% to 0.5%. We simulate the cavity using QuTip to further optimize the readout pulse.Furthermore, we characterize the third energy level of the qubit to implement a qutrit readoutand observe a second excited state population of 0.3%, in accordance with theory. Finally,we implement the iSwap gate that, together with single-qubit gates, constitute a set of universalquantum gates, where we swap the 95.4% of the quantum state between the qubits in 690 ns. Allexperiments, including the pulse events and synchronization of the readout and feedback, wereperformed using a digital microwave platform based on a radio-frequency-on-a-chip system,and implemented using a Python interface. / Vi manipulerar två supraledande kvantbitar med digital mikrovågselektronik. Vi utgår frånderas karakterisering och utvecklar en realtidsåterställningsschema och implementerar iSwap-grinden. Kvantbitarnas parametrar erhålls med standardtekniker för karakterisering av enskildakvantbitar, såsom Rabi- och Ramsey-svängningar och frekvenssvep av resonatorerna. Vikaraketeriserar även den experimentella uppställningen, där vi finner arbetspunkten för enJosephson-parametrisk förstärkare, samt kopplaren mellan de två kvantbitarna. Vi löser delinjära differentialekvationerna som modellerar resonatorn, i syfte att designa en pulsformför en enkelmätning av en kvantbit med hög tillförlitlighet som aktivt tömmer kaviteten.Med denna puls uppnår vi en avläsningstillförlitlighet på 99,9 %. Avläsningspulsen bildas irealtid med hjälp av mallmatchning. Därtill implementerar vi en villkorlig återställning avkvantbitens tillstånd på 1,4 μs, vilket återställer den exciterade tillståndspopulationen från 5,4 %till 0,5 %. Vi simulerar kaviteten med QuTip för att ytterligare optimera avläsningspulsen.Dessutom karakteriserar vi den tredje energinivån på kvantbiten för att implementera enså-kallad qutrit-avläsning och observerar en andraexciterad tillståndspopulation på 0,3 %,i enlighet med teorin. Slutligen implementerar vi iSwap-grinden som, tillsammans medgrindarna för enskilda kvantbitar, utgör en uppsättning universella kvantgrindar, är vi byter95,4 % av kvanttillståndet mellan våra kvantbitarna på 0,6 μs. Alla experiment, såsompulshändelserna och synkroniseringen av avläsningspulsen och återkopplingspulsen, utfördesmed hjälp av en digital mikrovågsplattform, baserad på ett radiofrekvens-på-ett-chip-system,och implementerades med ett Python-gränssnitt.

<p>The recent groundbreaking demonstrations of quantum supremacy in noisy intermediate scale quantum (NISQ) computing era has triggered an intense activity in establishing finer boundaries between classical and quantum computing. In this dissertation, we use established techniques based on quantum Monte Carlo (QMC) to map quantum problems into probabilistic networks where the fundamental unit of computation, p-bit, is inherently probabilistic and can be tuned to fluctuate between ‘0’ and ‘1’ with desired probability. We can view this mapped network as a Boltzmann machine whose states each represent a Feynman path leading from an initial configuration of q-bits to a final configuration. Each such path, in general, has a complex amplitude, ψ which can be associated with a complex energy. The real part of this energy can be used to generate samples of Feynman paths in the usual way, while the imaginary part is accounted for by treating the samples as complex entities, unlike ordinary Boltzmann machines where samples are positive. This mapping of a quantum circuit onto a Boltzmann machine with complex energies should be particularly useful in view of the advent of special-purpose hardware accelerators known as Ising Machines which can obtain a very large number of samples per second through massively parallel operation. We also demonstrate this acceleration using a recently used quantum problem and speeding its QMC simulation by a factor of ∼ 1000× compared to a highly optimized CPU program. Although this speed-up has been demonstrated using a graph colored architecture in FPGA, we project another ∼ 100× improvement with an architecture that utilizes clockless analog circuits. We believe that this will contribute significantly to the growing efforts to push the boundaries of the simulability of quantum circuits with classical/probabilistic resources and comparing them with NISQ-era quantum computers. </p>

Conventional computing faces a huge technical challenge as traditional transistors will soon reach their size limitations. This will halt progress in reaching faster processing speeds and to overcome this problem, require an entirely new approach. Quantum computing (QC) is a natural solution offering a route to miniaturisation by, for example, storing information in electron or nuclear spin states, whilst harnessing the power of quantum physics to perform certain calculations exponentially faster than its classical counterpart. However, QCs face many difficulties, such as, protecting the quantum-bit (qubit) from the environment and its irreversible loss through the process of decoherence. Hybrid systems provide a route to harnessing the benefits of multiple degrees of freedom through the coherent transfer of quantum information between them. In this thesis I show coherent qubit transfer between electron and nuclear spin states in a ¹⁵N@C₆₀ molecular system (comprising a nitrogen atom encapsulated in a carbon cage) and a solid state system, using phosphorous donors in silicon (Si:P). The propagation uses a series of resonant mi- crowave and radiofrequency pulses and is shown with a two-way fidelity of around 90% for an arbitrary qubit state. The transfer allows quantum information to be held in the nuclear spin for up to 3 orders of magnitude longer than in the electron spin, producing a ¹⁵N@C₆₀ and Si:P ‘quantum memory’ of up to 130 ms and 1.75 s, respectively. I show electron and nuclear spin relaxation (T₁), in both systems, is dominated by a two-phonon process resonant with an excited state, with a constant electron/nuclear T₁ ratio. The thesis further investigates the decoherence and relaxation properties of metal atoms encapsulated in a carbon cage, termed metallofullerenes, discovering that exceptionally long electron spin decoherence times are possible, such that these can be considered a viable QC candidate.

In this thesis, large organic molecules (DM15N, DM18N, Cu(dbm)2) were deposited. These molecules are cannot be deposited by thermal sublimation due the fact that they decompose at lower temperature than they sublime. The employed molecules to single molecular magnets, which can be potentially used as quantum bites (qubit). The new method of deposition atomic layer injection made by Bihur Crystal company was introduced and tested. The method uses liquid solution with molecules which is driven by argon gas through pulse valve to the sample placed in ultra-high vacuum chamber. During the deposition, droplets of solution are formed on the sample surface. The solvent can be removed by light annealing or by keeping the sample in the vacuum for couple of days. The molecules were investigated by x-ray photoelectron spectroscopy and by scanning electron microscopy to determine fragmentation of the molecules, to study topography of the resultant surface and homogeneity of the deposited layer. We found conditions at which the intact molecules are deposited on the sample surfaces and form molecular nano- and micro- crystals.