This master's thesis explores the possibility to use a plasmonic antenna to scale a quantum computer based on rare-earth-ion-doped crystals to a large number of qubits.To obtain a fully scalable rare-earth-ion quantum computer it is necessary to create entanglement between spatially remote qubits.This can be done using a photon pair with entangled polarization states.One single photon must act as a pi-pulse for an ion in a crystal.To enhance the interaction between the photon and the ion a toroidal microresonator in combination with an optical antenna is proposed.The microresonator can enhance the interaction time between the photon and the ion and the optical antenna can focus the evanescent eld down to a sub-wavelength spot.This report gives basic theory of quantum computing and plasmonics.The idea of how to entangle remote ions using a plasmonic antenna is presented.An optical bowtie antenna is designed and simulated using COMSOL Multiphysics R .The method is evaluated by comparison to a theoretical model for a simple case.Simulations show that the designed antenna can enhance an evanescent eld more than 1000 times at the surface of a crystal.The enhancement is enough to make a single photon act as a pi-pulse for an ion sitting at the surface.Diculties with this approach to a scalable rare-earth-ion quantum computer are discussed and further investigations are suggested. SammanfattningDetta examensarbete utforskar möjligheten att använda en plasmonisk antenn för att skala upp en kvantdator baserad på kristaller dopade med joner av sällsynta jordartsmetaller till ett stort antal kvantbitar.För att skapa en fullt skalbar kvantdator baserad på jordartsjoner är det nödvändigt att sammanäta kvanttillstånden hos rumsligt separerade kvantbitar.Detta är möjligt genom att använda ett fotonpar med sammanätade polarisationstillstånd.En enda foton måste motsvara en pi-puls for en jon som sitter i en kristall.Enligt förslaget som presenteras i rapporten kan en toroid-formad mikroresonator i kombination med en optisk antenn användas för att förstärka interaktionen mellan en foton och en jon.Mikroresonatorn kan förlänga interaktionstiden mellan fotonen och jonen och den optiska antennen kan fokusera det evanescenta fältet till en punkt mindre än ljusets våglängd.I rapporten ges grundläggande teori för kvantdatorer och plasmonik.Idén för att sammanäta separerade joner presenteras.En optisk antenn utformas och simuleras i COMSOL Multiphysics R .Metoden utvärderas genom en jämförelse med en teoretisk beräkning för ett enkelt fall.Simuleringarna visar att den utformade antennen kan förstärka ett evanescent fält mer än 1000 gånger på ytan av en kristall.Förstärkningen är tillräcklig för att skapa en pi-puls från en enda foton för en jon som sitter på ytan av kristallen.Svårigheter med det beskrivna angreppssättet för att skala en kvantdator baserad på jordartsjoner diskuteras och ytterligare undersökningar föreslås.
This master's thesis explores the possibility to use a plasmonic antenna to scale a quantum computer based on rare-earth-ion-doped crystals to a large number of qubits.To obtain a fully scalable rare-earth-ion quantum computer it is necessary to create entanglement between spatially remote qubits.This can be done using a photon pair with entangled polarization states.One single photon must act as a pi-pulse for an ion in a crystal.To enhance the interaction between the photon and the ion a toroidal microresonator in combination with an optical antenna is proposed.The microresonator can enhance the interaction time between the photon and the ion and the optical antenna can focus the evanescent eld down to a sub-wavelength spot.This report gives basic theory of quantum computing and plasmonics.The idea of how to entangle remote ions using a plasmonic antenna is presented.An optical bowtie antenna is designed and simulated using COMSOL Multiphysics R .The method is evaluated by comparison to a theoretical model for a simple case.Simulations show that the designed antenna can enhance an evanescent eld more than 1000 times at the surface of a crystal.The enhancement is enough to make a single photon act as a pi-pulse for an ion sitting at the surface.Diculties with this approach to a scalable rare-earth-ion quantum computer are discussed and further investigations are suggested. SammanfattningDetta examensarbete utforskar möjligheten att använda en plasmonisk antenn för att skala upp en kvantdator baserad på kristaller dopade med joner av sällsynta jordartsmetaller till ett stort antal kvantbitar.För att skapa en fullt skalbar kvantdator baserad på jordartsjoner är det nödvändigt att sammanäta kvanttillstånden hos rumsligt separerade kvantbitar.Detta är möjligt genom att använda ett fotonpar med sammanätade polarisationstillstånd.En enda foton måste motsvara en pi-puls for en jon som sitter i en kristall.Enligt förslaget som presenteras i rapporten kan en toroid-formad mikroresonator i kombination med en optisk antenn användas för att förstärka interaktionen mellan en foton och en jon.Mikroresonatorn kan förlänga interaktionstiden mellan fotonen och jonen och den optiska antennen kan fokusera det evanescenta fältet till en punkt mindre än ljusets våglängd.I rapporten ges grundläggande teori för kvantdatorer och plasmonik.Idén för att sammanäta separerade joner presenteras.En optisk antenn utformas och simuleras i COMSOL Multiphysics R .Metoden utvärderas genom en jämförelse med en teoretisk beräkning för ett enkelt fall.Simuleringarna visar att den utformade antennen kan förstärka ett evanescent fält mer än 1000 gånger på ytan av en kristall.Förstärkningen är tillräcklig för att skapa en pi-puls från en enda foton för en jon som sitter på ytan av kristallen.Svårigheter med det beskrivna angreppssättet för att skala en kvantdator baserad på jordartsjoner diskuteras och ytterligare undersökningar föreslås.
This Master's thesis explores some of the limitations of the rare-earth quantum computing (REQC) scheme by investigating how the design of the computing scheme and experimental errors will affect gate fidelity.The quantum bits that constitute a quantum logic gate were modeled and their interaction with the laser pulses that control the gate operation was simulated in MATLAB.Emphasis was put on exploring and finding pulse shapes and developing the gate implementation scheme to assure robust quantum operations.Expected sources of errors were introduced and modeled and their impact on the fidelity of the operation was studied.The results showed that it was possible to find pulse shapes that yielded high fidelity gate operations also in the presence of experimental complications.Detta examensarbete utforskar nagra av begransningarna i en kvantdatormodell baserad pa sallsynta jordartsjoner genom att undersoka hur designen av beriikningsschemat och experimentella fel paverkar tillfOrlitligheten hos de logiska grindarna.Kvantbitarna, som kvantgrindarna utfcir operationer pa, modellerades och deras viixelverkan med laserpulserna som anviinds for att kontrollera de logiska operationerna simulerades i MATLAB.Arbetet fokuserades darefter pa att utforska och designa pulsformer samt pa att utveckla metoderna fcir implementation av kvantgrindar med avsikt att siikerstalla robusta kvantoperationer.Formodade felkiillor introducerades och modellerades och deras inverkan pa operationens fidelitet studerades.De erhallna resultaten visar att designen av laserpulserna har mycket stor inverkan pa fideliteten hos kvantgrindsoperationerna men att det anda gar att hitta pulsformer som ger mycket god fidelitet.
This thesis describes investigations of the use of cryogenically cooled rare-earth-ion-doped crystals for quantum information processing and quantum optics. Several aspects of the coherent interaction between light and rare-earth ions in solids are addressed. Quantum information science has given physicists new views of quantum mechanics. The transmission of quantum states has already found practical use and full scale quantum computers may one day perform computations and simulations that would be impossible on a conventional computer. The work presented in this thesis can be seen as a part of a broad effort to learn how to control and manipulate quantum mechanical systems, which will become necessary as science and technology continue to push ever deeper into the nanoscopic world. Coherent radiation, such as laser light, provides us with an ideal tool for these investigations and, along the way, we may also learn more about the quantum nature of light. Rare-earth ions in inorganic crystals have several unusual properties that are interesting for applications within quantum information science, including long coherence times and long-lived ground state sublevels that can be used for storage of quantum and classical information. As part of the work presented in this thesis, new materials have been investigated with respect to these properties, and ways to enhance the useful properties of the materials were explored. In one investigation, the lifetime of information stored in the ground state population distribution of Tm3 ions in YAG was shown to increase by several orders of magnitude with the application of a magnetic field. It is demonstrated how the optical inhomogeneous absorption profile can be prepared, so that the light only interacts with a selected group of ions, absorbing on a specific transition. Narrow absorbing structures, with widths approaching the optical homogeneous linewidth, have been prepared with no absorption in the surrounding spectral interval. This thesis addresses the use of such structures as hardware for quantum bits. Tailored pulses, capable of inducing controlled changes in the quantum states of the ions (qubits), even in the presence of unknown variations of coupling strengths and frequencies, have been realised experimentally and used for multiple transfer of ions between energy levels. Ion-ion interactions, which can be used for performing quantum logic operations, have been investigated in some detail. Techniques for selecting strongly interacting ions, by transferring weakly interacting ions to auxiliary states, have been demonstrated. A scheme for storing the quantum state of light in a solid, using photon-echo-like techniques, is proposed and analysed. In the proposed scheme, an optical wave packet is absorbed and subsequently re-emitted by an inhomogeneous absorption profile, which is tailored and externally controlled by the application of an electric field Additionally, an accumulated photon echo experiment has been performed using faint optical pulses. The experiment can be viewed as a demonstration of delayed self-interference of a single photon and as a demonstration of how a single photon can act as two of the fields in a photon echo process.
This thesis work contributes to the effort of detecting single rare earth ions doped into crystals, an operation crucial for the development of rare earth quantum computer hardware. Doping crystals with rare earth elements, their trivalent ions substitute some of the crystal’s original bonds. These ions have a partially filled 4f shell, protected by the full 5s and 5p shell from the environment which makes them good candidates for qubits. Because not every ion experiences the same electric field from the imperfect crystal, their total linewidth is inhomogeneously broadened. If the doping is sufficiently low and the crystal sufficiently small, each ion undergoes a different optical shift and can thus be addressed separately. Communication between ions happens due to their permanent dipole moments which change according to their energy level. So far no single ions could be detected in Lund because highly doped bulk crystals were used. It was nevertheless tried to construct quantum logic gates using qubits that consisted of an ensemble of ions. Constructing logic gates with these means that every single ion of one qubit needs to be able to communicate with every single ion of another qubit, a method that becomes increasingly difficult when more and more qubits are to be entangled. Connecting as many qubits as possible is a crucial step in building a quantum computer that could outperform classical computers and this could be facilitated if every qubit consisted of only one ion which is the reason for the recent explorations towards nano crystals. This development also makes it possible to address another problem of rare earth ions, their low probability of spontaneous emission. Placing nano crystals into an optical cavity promises the enhancement of spontaneous emission by the Purcell effect. Ideal cavities are Fiber Fabry-Pérot resonators of which one side consists of a mirror coated fiber tip and the other of a plane mirror functioning as the substrate for the nano crystals. It was the aim of this thesis to build a cryostat holder that would bring these two mirrors together with high stability and would allow for vertical and horizontal scanning.
In the last decade, the solid-state rare-earth-ion system has demonstrated increasing appeal for quantum computation. Despite this progress, two hardware limitations prevent a scalable implementation. These current limitations are the inability to miniaturise and the inability to perform single-ion qubit readout. This thesis addresses both these limitations and demonstrates that neither poses a fundamental restriction on increasing the scale of rare-earth-ion quantum computers. The challenge in miniaturising rare-earth-ion quantum hardware arises from the increases in homogeneous and inhomogeneous broadening that accompany micron-scale architectures. The success of miniaturised architectures, such as waveguides, depends on the properties of bulk ions being preserved within microns of the crystal surface. In addition, bulk ion properties must also be preserved in regions of high residual stress resultant from waveguide fabrication. The inhomogeneous and homogeneous properties of near-surface ions and ions in highly stressed environments in Pr3+:Y2SiO5 were studied via white light interferometry combined with micron resolution fluorescence microscopy. It was found that the bulk ion properties could be preserved both near the surface and in highly stressed regions close to micron-scale surface damage. The observation of excess inhomogeneous and homogeneous broadening was found to be consistent with the damage present at the crystal surface. The main outcome of the study was a set of waveguide fabrication guidelines to ensure that the appealing properties of bulk crystals can be maintained in a miniaturised architecture. The current inability to perform single-ion qubit readout is a consequence of the difficulty in isolating a single ion and lack of cyclicity in rare-earth-ion materials. Two techniques are proposed to form a solution: Stark activation and Zeeman enhanced cyclicity. When combined, these techniques offer direct readout for single-ion frequency-based quantum computing. Stark activation is designed to isolate a single rare-earth ion in a macroscopic crystal. The proposal is based on defining the condition for resonant excitation through a spatially varying electric field. A proof-of-principle experiment successfully created a 10 um absorption region within a millimetre thick crystal. In addition, the signal-to-noise ratio of the technique was characterised in experiments probing Pr3+:Y2SiO5 at the single-ion level. Future improvements to the apparatus should allow the nanometre spatial resolution and the noise level to be reduced to allow single-ion optical detection. High cyclicity is essential for high-fidelity optical readout of a single-ion qubit. Zeeman enhanced cyclicity achieves this by manipulating the hyperfine structure of the resonant crystal field levels to induce strong hyperfine selection rules. The technique is shown to be applicable to even the lowest symmetry sites. The simulated level of cyclicity in Pr3+:Y2SiO5 was greater than 99.99% by applying a 10 T field. The investigation of scalability in the rare-earth-ion system marks a movement away from the traditional ensemble-based methods in macroscopic crystals. This study required an understanding of these materials at a single-ion level and the development of high spatial resolution spectroscopic techniques. These advances extend the ability to engineer rare-earth-ion systems for applications including, but not limited to, quantum computing.
In this thesis, crystals of yttrium orthosilicate (Y2SiO5) that are randomly doped with another rare-earth element, such as praseodymium (Pr), europium (Eu), or cerium (Ce), are investigated with lasers locked to ultra-stable cavities using the Pound-Drever-Hall locking technique. Many of these rare-earth elements have long-lived 4f-4f transitions, hundreds of microseconds to a few milliseconds, with even longer ground hyperfine lifetimes of up to several days. The coherence properties are, to the best of the author's knowledge, the longest achieved for any material, currently with a record of six hours for the nuclear spin states of Eu3+:Y2SiO5 measured at cryogenic temperatures. Furthermore, due to natural trapping and differences in the local environments, each dopant ion experiences a slightly different crystal field, and thus an inhomogeneity in the 4f-4f transition exists between all ions in a crystal. Since the homogeneous linewidth is in the order of kHz or below, whereas the inhomogeneous profile can be several GHz wide, these materials have dense storing capabilities.This thesis explores how light interacts with such rare-earth-ion-doped crystals; how the absorption and light polarization varies during propagation; how spectral features in the inhomogeneous absorption profile can be tailored to create narrowband spectral filters; how the speed of light is slowed down significantly in such narrow transmission windows; and how that can be used to either frequency shift incoming light, control its group velocity, or temporally compress pulses. It also uses rare-earth-ions to research quantum computing, the field of using quantum mechanical effects such as superpositions and entanglements to outperform classical computers on certain specific problems. This is done by examining how two-color pulses can be used to rapidly induce coherence from an initially mixed state; how qubit-qubit interactions can be performed experimentally using ensemble qubits, which opens the door to two-qubit experiments such as the CNOT-gate and entanglements; how a scalable quantum computer might be constructed using a single ion qubit approach with a dedicated readout ion and buffer ion(s) to improve readout fidelity; and how cerium is investigated as a candidate for such a dedicated readout ion.
Quantum photonics provides a powerful toolbox with vast applications ranging from quantum simulation, photonic information processing, all optical universal quantum computation, secure quantum internet as well as quantum enhanced sensing. Many of these applications require the integration of several complex optical elements and material systems which pose a challenge to scalability. It is essential to integrate linear and non-linear photonics on a chip to tackle this issue leading to more compact, high bandwidth devices. In this thesis we demonstrate a pathway to achieving several components in the quantum photonic toolbox on the same integrated photonic platform. We focus particularly on two of the more nontrivial components, a single photon source and an integrated quantum light-matter interface. We address the problem of a scalable, chip integrated, fast single photon source, by using atomically thin layers of 2D materials interfaced with plasmonic waveguides. We further embark on the challenge of creating a new material system by integrating rare earth ions with the emerging commercial platform of thin film lithium niobate on insulator. Rare earth ions have found widespread use in classical and quantum information processing. However, these are traditionally doped in bulk crystals which hinder their scalability. We demonstrate an integrated photonic interface for rare earth ions in thin film lithium niobate that preserves the optical and coherence properties of the ions. This combination of rare earth ions with the chip-scale active interface of thin film lithium niobate opens a plethora of opportunities for compact optoelectronic devices. As an immediate application we demonstrate an integrated optical quantum memory with a rare earth atomic ensemble in the thin film. The new light matter interface in thin film lithium niobate acts as a key enabler in an already rich optical platform representing a significant advancement in the field of integrated quantum photonics.