Tesis sobre el tema "Molecular qubits"

Information processors that harness quantum mechanics may be able to outperform their classical counterparts at certain tasks. Quantum information processing (QIP) can utilize the quantum mechanical phenomenon of entanglement to implement quantum algorithms. Endohedral fullerenes, where atoms, ions or clusters are trapped in a carbon cage, are a class of nanomaterials that show great promise as the basis for a solid-state QIP architecture. Some endohedral fullerenes are spin–active, and offer the potential to encode information in their spin-states. This thesis addresses the challenges of how to engineer the components of a scalable QIP architecture based on endohedral fullerenes. It focuses on the synthesis and characterization of molecules which may, in the future, permit the demonstration of entanglement; the optical read-out of quantum states; and the creation of quasi-one-dimensional molecular arrays. Due to its long spin decoherence time, N@C₆₀ is the selected as the basic molecular unit for ‘coupled’ fullerene pairs, molecular systems for which it may be possible to demonstrate entanglement. To this end, isolated fullerene pairs, in the form of spin-bearing fullerene dimers, are created. This begins with the processing of N@C₆₀ at the macroscale and leads towards the synthesis of ¹⁵N@C₆₀-¹⁵N@C₆₀ dimers at the microscale. High throughput processing is introduced as the most efficient technique to obtain high purity N@C₆₀ on a reasonable timescale. A scheme to produce symmetric and asymmetric fullerene dimers is also demonstrated. EPR spectroscopy of the dimers in the solid-state confirms derivatization, whilst permitting the modelling of spin–spin interactions for 'coupled' fullerene pairs. This suggests that the optimum inter–spin separation for which to observe spin–spin coupling in powders is circa 3 nm. Motivated by the properties of the trivalent erbium ion for the optical detection of quantum states, optically–active erbium–doped fullerenes are also investigated. These erbium metallofullerenes are synthesized and isolated as individual isomers. They are characterized by low temperature photoluminescence spectroscopy, emitting in the infra- red at a wavelength of 1.5 μm. The luminescence is markedly different where a C₂ cluster is trapped alongside the erbium ions in the fullerene cage. Er₂C₂@C₈₂ (isomer I) exhibits emission linewidths that are comparable to those observed for Er³⁺ in crystals. Finally, the discovery of a novel praseodymium-doped fullerene is reported. The balance of evidence favours the structure being assigned as Pr₂@C₇₂. This novel endohedral fullerene forms quasi-one-dimensional arrays in carbon nanotubes, which is a useful proof-of-principle of how a scaled fullerene-based architecture may be achieved.

Grâce à leur propriétés uniques, les nanofils d'InAs et de Bi1-xSbx sont important pour les domaines de la nanoélectronique et de l'informatique quantique. Alors que la mobilité électronique de l'InAs est intéressante pour les nanoélectroniques; l'aspect isolant topologique du Bi1-xSbx peut être utilisé pour la réalisation de Qubits basés sur les fermions de Majorana. Dans les deux cas, l'amélioration de la qualité du matériau est obligatoire et ceci est l'objectif principal cette thèse ou` nous étudions l'intégration des nanofils InAs sur silicium (compatibles CMOS) et où nous développons un nouvel isolant topologique nanométrique: le Bi1-xSbx. Pour une compatibilité CMOS complète, la croissance d'InAs sur Silicium nécessite d'être auto- catalysée, entièrement verticale et uniforme sans dépasser la limite thermique de 450 ° C. Ces normes CMOS, combineés à la différence de paramètre de maille entre l'InAs et le silicium, ont empêché l'intégration de nanofils InAs pour les dispositifs nanoélectroniques. Dans cette thèse, deux nouvelles préparations de surface du Si ont été étudiées impliquant des traitements Hydrogène in situ et conduisant à la croissance verticale et auto-catalysée de nanofils InAs compatible avec les limitations CMOS. Les différents mécanismes de croissance résultant de ces préparations de surface sont discutés en détail et un passage du mécanisme Vapor-Solid (VS) au mécanisme Vapor- Liquid-Solid (VLS) est rapporté. Les rapports d'aspect très élevé des nanofils d'InAs sont obtenus en condition VLS: jusqu'à 50 nm de diamètre et 3 microns de longueur. D'autre part, le Bi1-xSbx est le premier isolant topologique 3D confirmé expérimentalement. Dans ces nouveaux matériaux, la présence d'états surfacique conducteurs, entourant le coeur isolant, peut héberger les fermions de Majorana utilisés comme Qubits. Cependant, la composition du Bi1-xSbx doit être comprise entre 0,08 et 0,24 pour que le matériau se comporte comme un isolant topologique. Nous rapportons pour la première fois la croissance de nanofils Bi1-xSbx sans défaut et à composition contrôlée sur Si. Différentes morphologies sont obtenues, y compris des nanofils, des nanorubans et des nanoflakes. Leur diamètre peut être de 20 nm pour plus de 10 microns de long, ce qui en fait des candidats idéaux pour des dispositifs quantiques. Le rôle clé du flux Bi, du flux de Sb et de la température de croissance sur la densité, la composition et la géométrie des structures à l'échelle nanométrique est étudié et discuté en détail
InAs and Bi1-xSbx nanowires with their distinct material properites hold promises for nanoelec- tronics and quantum computing. While the high electron mobility of InAs is interesting for na- noelectronics applications, the 3D topological insulator behaviour of Bi1-xSbx can be used for the realization of Majorana Fermions based qubit devices. In both the cases improving the quality of the nanoscale material is mandatory and is the primary goal of the thesis, where we study CMOS compatible InAs nanowire integration on Silicon and where we develop a new nanoscale topological insulator. For a full CMOS compatiblity, the growth of InAs on Silicon requires to be self-catalyzed, fully vertical and uniform without crossing the thermal budge of 450 °C. These CMOS standards, combined with the high lattice mismatch of InAs with Silicon, prevented the integration of InAs nanowires for nanoelectronics devices. In this thesis, two new surface preparations of the Silicon were studied involving in-situ Hydrogen gas and in-situ Hydrogen plasma treatments and leading to the growth of fully vertical and self-catalyzed InAs nanowires compatible with the CMOS limitations. The different growth mechanisms resulting from these surface preparations are discussed in detail and a switch from Vapor-Solid (VS) to Vapor- Liquid-Solid (VLS) mechanism is reported. Very high aspect ratio InAs nanowires are obtained in VLS condition: upto 50 nm in diameter and 3 microns in length. On the other hand, Bi1-xSbx is the first experimentally confirmed 3D topololgical insulator. In this new material, the presence of robust 2D conducting states, surrounding the 3D insulating bulk can be engineered to host Majorana fermions used as Qubits. However, the compostion of Bi1-xSbx should be in the range of 0.08 to 0.24 for the material to behave as a topological insula- tor. We report growth of defect free and composition controlled Bi1-xSbx nanowires on Si for the first time. Different nanoscale morphologies are obtained including nanowires, nanoribbons and nanoflakes. Their diameter can be 20 nm thick for more than 10 microns in length, making them ideal candidates for quantum devices. The key role of the Bi flux, the Sb flux and the growth tem- perature on the density, the composition and the geometry of nanoscale structures is investigated and discussed in detail

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.

Esta tesis presenta una serie de estudios computacionales basados en métodos de estructura electrónica en los que se analizan la anisotropía magnética y las propiedades derivadas de esta en complejos magnéticos candidatos a imán molecular y bit cuántico con la particularidad de tener un espín total S = ½. En los primeros tres capítulos de esta tesis se estudian complejos de metales de transición. Por otro lado, el cuarto y último capítulo se centra en analizar complejos de lantánidos, concretamente de YbIII. En el primer capítulo se incluye un trabajo a través del cual se relaciona la configuración electrónica y la geometría de coordinación de un compuesto con su anisotropía magnética, en la forma del tensor g. Se puede establecer dicha conexión gracias a la dependencia del tensor g con la energía de los orbitales d. Esta energía se obtiene mediante cálculos ab initio analizados con el modelo de AILFT. Estos se realizan a partir de la función de onda obtenida en cálculos NEVPT2 realizados en modelos sencillos [MIILn], siendo MII el correspondiente metal divalente de la primera serie de transición con S = ½, L ligandos NH3 Cl- y n un número de coordinación entre 2 y 8. La observación de una anisotropía magnética de eje fácil fuerte indicar la presencia de un posible imán unimolecular mientras que una anisotropía débil es adecuada para presentar comportamiento de bit cuántico. El segundo capítulo realizado en colaboración con el grupo de “Molecular Magnetism and Quantum Computing” dirigido por el Dr. Alejandro Gaita Ariño del Institut de Ciència Molecular de Valencia (ICMol), se centra en el estudio del acoplamiento espín-fonón en tres bits cuánticos de VIV: [VOPc], [VO(dmit)2]2- y [V(dmit)3]2- donde Pc es el ligando ftalocianina y dmit es el ligando 2-tioxo-1,3-ditiol-4,5-ditiolato. A través de la variación que se produce en la anisotropía magnética al deformarmse las distintas moléculas debido al movimiento de cada modo vibracional, se calculó la fuerza del acoplamiento espín-fonón correspondiente a los distintos estados vibracionales, mediante cálculos a nivel NEVPT2/AILFT. Esta magnitud se utilizó para entender las diferencias en los tiempos de coherencia para los distintos sistemas estudiados. El tercer capítulo, finalizando el bloque dedicado a metales de transición, recopila una serie de colaboraciones con distintos grupos experimentales. Se realizó un análisis computacional similar al delos capítulos anteriores para cada compuesto en concreto: estudio de la estructura electrónica mediante cálculos NEVPT2/AILFT, anisotropía magnética en base a los orbitales d de cada compuesto, y comparación de las distintas propiedades magnéticas calculadas con las medidas experimentales. Además, se realizó el ajuste de los tiempos de relajación del espín, examinando los distintos mecanismos de relajación posibles en cada caso. En el último capítulo se analizó el caso del YbIII, un lantánido con S = ½, haciendo uso de cálculos CASPT2+RASSI con el programa MOLCAS. Dichos cálculos de estructura electrónica se realizaron en una serie de modelos [Yb(H2O)n]3+ y [Yb(OH)3(H2O)n-3], utilizando geometrías ideales para números de coordinación entre 2 y 10. Estos cálculos muestran el efecto de la geometría de coordinación y la distribución de carga de los ligandos sobre propiedades fundamentales como la energía de los distintos estados electrónicos, la anisotropía magnética del estado fundamental, o las probabilidades para los distintos mecanismos de relajación. A partir de estos resultados se explican las propiedades como imanes unimoleculares de los sistemas de YbIII encontrados en la bibliografía y se propusieron una serie de geometrías adecuadas para el fenómeno de imán unimolecular en estos sistemas.
This thesis presents a series of theoretical studies based on electronic structure methods to analyze the magnetic anisotropy and other related properties of magnetic complexes with total spin S = ½. The first three chapters are devoted to transition metal complexes while the fourth one addresses lanthanides systems, specifically YbIII. The first chapter determines a relationship between the d orbitals occupation and the coordination geometry of S = ½ transition metal complexes with their magnetic anisotropy, through its g-tensor. This connection is possible due to the relationship between the g-tensor and the splitting of the d manyfold. These energies were obtained using NEVPT2/AILFT calculation on [MIILn] models, screening for different MII metals, coordination numbers (n) and geometries, and ligand nature (L = NH3 or Cl-). The second chapter is a study carried out in collaboration with Dr. Gaita Ariño’s group from the molecular Science Institute of Valencia (ICMol) analyzing the spin-phonon coupling in three VIV qubits: [VOPc], [VO(dmit)2]2- y [V(dmit)3]2-, being Pc = Phthalocyanine and dmit = 1,3-dithiole-2-thione-4,5-dithiolate. In order to analyze the spin-phonon coupling we examined the variation of the magnetic anisotropy using NEVPT2/AILFT calculations for each vibrational mode. The spin-phonon coupling constants obtained for the vibrational modes in the three complexes were used to rationalize their different decoherence times. The third chapter, the last one dedicated to transition metal complexes, compiles a series of collaborations with experimental groups. In these studies, using the same methods as in the previous chapters, we analyzed the electronic structure and magnetic properties of the compounds, explaining experimental results through theoretical calculations. Also, we fitted the spin relaxation times considering the all possible spin relaxation mechanisms. Finally, the fourth chapter explores the magnetic anisotropy and electronic structure of YbIII compounds on the basis of theoretical calculations in a series of [Yb(H2O)n]3+ y [Yb(OH)3(H2O)n-3] model using ideal geometries corresponding to coordination numbers between 2 and 10. These calculations explain the properties of the YbIII single-molecule

Spin-frustrated molecular triangles have four low-lying energy states, so called chiral states, which can be employed as the unit of information, qubit, in a quantum computer. The fact that the chiral states are characterized by two quantum numbers chirality and spin allows the control of the magnetization of the molecule by an electric field due to the spin-electric interaction. Unlike a magnetic field, electric fields can be applied spatially and temporally on the scale of single molecules, as an electric impulse by using a scanning tunneling microscope (STM) tip. In this thesis, I report on, i. Theoretical description of spin-frustrated molecular triangles based on sym-metry group theory, ii. Modeling of the system by using an extended Hubbard Hamiltonian includ-ing spin-orbit coupling and an external magnetic field. iii. Modeling of the spin-electric interaction for a spin-frustrated molecular tri-angle. iv. Studying the chiral states by performing numerical calculations based on exact diagonalization of the Hubbard Hamiltonian. v. Investigating the electrical control of the chiral qubits through numerical calculation.

Abstract Elementary experiments of atomic physics and quantum optics can be reproduced on a circuit board using elements built of superconducting materials. Such systems can show discrete energy levels similar to those of atoms. With respect to their natural cousins, the enhanced controllability of these ‘artificial atoms’ allows the testing of the laws of physics in a novel range of parameters. Also, the study of such systems is important for their proposed use as the quantum bits (qubits) of the foreseen quantum computer. In this thesis, we have studied an artificial atom coupled with a harmonic oscillator formed by an LC-resonator. At the quantum limit, the interaction between the two can be shown to mimic that of ordinary matter and light. The properties of the system were studied by measuring the reflected signal in a capacitively coupled transmission line. In atomic physics, this has an analogy with the absorption spectrum of electromagnetic radiation. To simulate such measurements, we have derived the corresponding equations of motion using the quantum network theory and the semi-classical approximation. The calculated absorption spectrum shows a good agreement with the experimental data. By extracting the power consumption in different parts of the circuit, we have calculated the energy flow between the atom and the oscillator. It shows that, in a certain parameter range, the absorption spectrum obeys the Franck-Condon principle, and can be interpreted in terms of vibronic transitions of a diatomic molecule. A coupling with a radiation field shifts the spectral lines of an atom. In our system, the interaction between the atom and the field is nonlinear, and we have shown that a strong monochromatic driving results in energy shifts unforeseen in natural or, even, other artificial atoms. We have used the Floquet method to calculate the quasienergies of the coupled system of atom and field. The oscillator was treated as a small perturbation probing the quasienergies, and the resulting absorption spectrum agrees with the reflection measurement.

Many quantum information tasks require measurements to distinguish between different quantum-mechanically entangled states (Bell states) of a particle pair. In practice, measurements are often limited to linear evolution and local measurement (LELM) of the particles. We investigate LELM distinguishability of the Bell states of two qubits (two-state particles) and qutrits (three-state particles), via standard projective measurement and via generalized measurement, which allows detection channels beyond the number of orthogonal single-particle states. Projective LELM can only distinguish 3 of 4 qubit Bell states; we show that generalized measurement does no better. We show that projective LELM can distinguish only 3 of 9 qutrit Bell states that generalized LELM allows at most 5 of 9. We have also made progress on distinguishing qubit $\times$ qutrit hyperentangled Bell states, which are made up of tensor products of the qubit Bell states and the qutrit Bell states, showing that the maximum number distinguishable with projective LELM measurements is between 9 and 11.

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.

The development of quantum mechanics led to the birth of the quantum computing, a new frontier of the computer science which exploits quantum phenomena such as the quantum states superposition and the entanglement to perform computation. The basic element of a quantum computer is the Qubit, a two-level quantum system that can be addressed whether in 0 or 1 , but also in a coherent superposition of these two states. Among the great variety of potential Qubit systems, molecular electron spins show interesting features as the great tunability of the electronic and magnetic properties as well as the possibility to interact with other Qubits by adopting an ad-hoc synthetic strategy. Despite these positive features, they suffer from relatively short coherence time, Tm, namely the time during which the quantum information stored inside the Qubit is maintained. The aim of this PhD work is the optimization of the molecular Qubits performances through the research of the key “elements” to enhance the spin-lattice relaxation time, T1, that sets the upper limit of Tm. The study has been focused on Vanadium(IV) coordination compounds whose magnetic properties are due to the single unpaired electron, resulting in a S= 1/2 spin value. This element shows a weak spin-orbit coupling and, consequently, a small spin-phonon coupling, that makes it particularly suitable for the purpose. Two classes of complexes have been taken into account: vanadyl-based molecules, which show the VO2+ metal centre in a square pyramidal coordination geometry, and V(IV)-based ones in which the metal centre is octahedrally coordinated. Several ligands have been used in order to test different structural effects on the spin relaxation. In this study we utilized different experimental techniques to investigate different aspects of the issue. We jointed standard magnetic techniques, as alternate-current (AC) susceptometry, continuous-wave (CW) and pulse electron paramagnetic resonance (EPR) spectroscopy, and TeraHertz time-domain spectroscopy (THz-TDS) for the characterization of the phonons of the complexes in the crystal phase. Moreover, a deeper investigation of the spin-lattice relaxation mechanisms required a more exotic technique, that is time-resolved THz-pump EPR-probe (TR-THz-EPR) measurements, which exploits the free electron laser radiation as THz source at the Novosibirsk Free Electron Laser (NovoFEL) facility. The whole work has been supported by theoretical calculations that has been fundamental in the rationalization of several experimental results. The manuscript is organized in several parts and each of them includes different chapters. Part I provides a general introduction about Qubits and, in particular, those based on molecular electronic spins. In part II, many theoretical concepts that I consider to be essential in the comprehension of this work are discussed, such as the theory of the spin relaxation and the spin-phonon interaction, with a short mention to the spin-orbit coupling. In part III, the techniques based on custom setups, as THz-TDS setups and the NovoFEL equipment, as well as the samples preparation, are examined. Part IV, which represents the main one, is devoted to the results obtained during the PhD. It is divided in two chapters, according to the two main topics: the former contains the outcomes obtained by the combination of magnetic techniques and THz-TD spectroscopy, arranged according to the publications; while the latter includes the investigation of THz-induced effects on the spin dynamics, performed at NovoFEL. In part V, that is the last one, a summary of this work helps in getting an overall view of it.

The investigation of the relaxation times of a series of vanadium(IV)-based molecular spin qubits in order to find a correlation to their structural properties. The magnetic system and the lattice structure have been studied by using a multitechnique investigation based on EPR, ac susceptometry, THz spectroscopy and 4D-Inelastic Neutron Scattering. New techniques have been proposed, such as Muon Spin Relaxation spectroscopy, and first preliminary results have been achieved by investigating Dy-based SMMs. A small part of the work is devoted to the characterization of a cobalt(II)-based SMM and 1D spin helices based on lanthanides by using Cantilever Torque Magnetometry.

This work highlights the different possibilities given by a rational chemical approach to obtain molecular-based quantum bits and quantum logic gates as an appealing and alternative platform for implementing quantum computation. This work resumes the three years of the author's work on this subject, mainly presenting and focusing on experimental results obtained for some new potential hydrogen-free molecular qubits, multi-qubit structures, and state-of-the-art EPR-based (Electron Paramagnetic Resonance) experiments on an archetypical vanadyl-based qubit.

碩士
國立高雄應用科技大學
電子與資訊工程研究所碩士班
96
This work presents the theory of exciton coupling to photons and LO phonons in quantum-dot molecules (QDMs). Resonant-round trips of the exciton between the ground (bright) and excited (dark or bright) states, mediated by the LO-phonon, alter the decay time and yield the Rabi oscillation. Novel schemes for a qubit reading/writing in an exciton-based quantum-dot-molecule (QDM) register are proposed. A bit of quantum information is coded into the superposition (molecule) states of the QDM, based on field-controllable combinations of these states. Population-dependent Rabi oscillation in QDMs provides a detectable signature for readout of quantum information that is stored in the register. Moreover, the field-convertibly optical transition rate of the molecule states promises the QDM system to be a field-controlled optical-gain switch or a field-controlled single-photon source.