Coherent Interactions in Rare-Earth-Ion-Doped Crystals for Applications in Quantum Information Science

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

Time domain measurement of the nonlinear refractive index in optical fibers and semiconductor film

A new technique to measure the nonlinear refractive index n2 in optical fibers and semiconductor films has been developed. It is based on the time delay two-beam coupling of very intense picosecond laser pulses that have been self-phase modulated in the nonlinear optical medium. The two beams are coupled in a slow responding medium that is sensitive to time dependent phase distortions. We determine that the amount of phase distortion experienced by the pulse is proportional to the nonlinear refractive index of the medium, This time domain approach can also be applied to optical fiber amplifiers in the presence of gain and to semiconductor films. Because the technique is base on pure refraction the measurement of n2 is insensitive to nonlinear absorption, thermal effects, and surface roughness. With this technique we have measured n2 in 20-m. length of Silica-glass, Ytterbium-doped, and Erbium-doped optical fibers at 1.064-µm. Also we have measured the change of n2 at 1.064-µm in the presence of a 980-nm pump laser in Yb3+ -doped and Er3+ -doped fibers. Finally we have extended the technique to measure n_2 in 2-mm thick samples of GaAs, CdTe and ZnTe semiconductors. In the language of ultrafast spectroscopist, if the best tool to characterize an ultrashort optical pulse is the pulse itself, then the best tool to characterize an optical nonlinear medium is a pulse that has been modified by the medium

Towards single Ce ion detection in a bulk crystal for the development of a single-ion qubit readout scheme

The work presented in this thesis was concerned with investigating the relevant spectroscopic properties of Ce ions randomly doped in an Y2SiO5 crystal at low temperatures (around 4 K), in order to develop a technique and an experimental set-up to detect the fluorescence photons emitted by a single Ce ion. The aim of the work was to determine whether a single Ce ion (referred to as the readout ion) can be used as a local probe to sense the quantum state of a neighbouring single-ion qubit via a state-selective interaction between the readout and qubit ion. More precisely, if the qubit ion is in state |1> or |0> state, the single Ce ion will, or will not, emit fluorescence photons. This single ion readout concept is a key step towards single-rare-earth-ion quantum computing, which is believed to be a promising approach for a scalable quantum computer. Rare-earth ion based quantum computing is an attractive scheme for several reasons. Firstly, the qubit coherence time can be on the timescale of a minute while the optical coherence time can be on the millisecond timescale, despite the fact that the ions are in a solid (crystal), which means that more than 10000 optical pulses could be implemented before the system decoheres. Secondly, any sub-ensemble of ions in a frequency interval equal to or larger than the homogeneous linewidth within the inhomogeneously broadened absorption line can be used as a frequency-selectively addressed qubit. The proof of principle of the qubit-qubit interaction has been previously demonstrated. Thirdly, no special material engineering is required, and the crystal is commercially available. Ways of initializing a sub-ensemble of Pr ions as a qubit in the random system, manipulating the quantum state of the ions in a controlled way, and characterizing the quantum state created are presented. In order to achieve better scalability, the idea of letting a single rare-earth ion represent a qubit was investigated. The fidelity of the single-ion readout scheme was briefly studied. The influence of the energy transfer process between two neighbouring ions on quantum computing is discussed. A readout ion should possess a number of specific spectroscopic properties. Therefore, the position and the linewidths of the zero-phonon line of Ce ions were measured using an external cavity diode laser (at 371 nm) as the excitation source. The difference in the permanent dipole moment of the ground and excited states of Ce ions was measured in a photon echo experiment on Pr ions in a Ce-Pr co-doped Y2SiO5 crystal. The last and most important task was to realize single Ce ion detection. Fluorescence of Ce ions has been detected from a crystal, where there is on average 1 ion within 4.6 \micro m$^3$ interacting with the excitation laser at a time. Estimates were made of the number of ions contributing to an observed signal. A trial experiment to investigate whether the signal was emitted by a single Ce ion was carried out, but was unsuccessful. Potential reasons why the experiment failed are presented

Solar-pumped laser Final report

Solar pumped modulated laser to generate coherent radiation at optical wavelengths for long range, real time television data transmissio

Detection of a single erbium ion in a nanoparticle

Encoding information into quantum mechanical properties of a system can lead to applications many fields, including computing and communication. Devices that will enable these applications could be part of a quantum network in the future. Quantum networks can be implemented using nodes that have the ability to generate and store entanglement efficiently for long durations as well as to process quantum information. The nodes also need to be interfaced with photons, which can faithfully carry information over long distances. Single rare-earth ions doped in crystals offer all these capabilities. The main goal of this thesis was to detect a single erbium ion, which operates in the telecommunication wavelength, and to investigate its feasibility as a spin-photon interface. Detecting a single erbium is challenging due to its low emission rate, but it can be aided by Purcell-enhancing its emission via coupling to an optical cavity. In this thesis, we utilize erbium ions doped into nanoparticles, which facilitates their integration into cavities with small mode-volumes. In addition, nanoparticles provide the confinement required to individually manipulate spatially close-by single ion qubits, which is required for dipolar quantum gates. We hence first study the optical coherence properties of Er:Y2O3 nanoparticles at cryogenic temperatures. We identify the limiting mechanisms and identify avenues for improvement in the future. We also study the optical and spin coherence properties of Pr:Y2O3, which is a promising alternative to erbium. Fiber-based microcavities can achieve high Purcell factors as they can simultaneously realize high finesse and small mode-volume. They are also ideally suited to be coupled to nanoparticles due to their tuning capabilities. However, stabilizing such a cavity inside a cryogenic environment is challenging. We hence first describe the construction of a custom setup, which enables us to stabilize the cavity while being coupled to a suitable nanoparticle. Utilizing the first iteration of this setup, we then report on the coupling of Er:Y2O3 nanoparticles to a fiber-based high finesse microcavity. We achieve an average Purcell factor of 14 for a small ensemble of ions, while a small subset of ions show Purcell factor up to 70. We explain the obtained multi-exponential decay behaviour using a detailed model. Furthermore, we demonstrate dynamic control of the Purcell-enhanced emission by tuning the cavity resonance on a time-scale faster than the spontaneous emission rate of the ions. This allows us to extract the natural lifetime of the ions as well as to shape the waveform of the emitted photons. However, we conclude that the achieved signal-to-noise ratio is not high enough to resolve single erbium ions. For the final experiment, we operate the second iteration of the setup, which improves our sensitivity to single erbium ions by more than a factor 50. This enables us to demonstrate the first detection of a single erbium ion in a nanoparticle. The ion exhibits a Purcell factor of 60, leading to a cavity enhanced lifetime of 225 us, and a homogeneous linewidth of 380 MHz. The counts received from the ion show a clear saturation and we measure the second-order auto-correlation of the emitted photons to be 0.59, which reduces to 0.29 after background-subtraction. This is strong evidence that the photons are emitted by a single erbium ion. Our work opens the path for exploring single rare-earth-ions doped into nanoparticles as spin-photon interfaces for quantum information processing.La codificación de la información en las propiedades mecánico-cuánticas de un sistema puede dar lugar a aplicaciones en muchos campos, como la informática y la comunicación. Podemos imaginar que los dispositivos que permitan estas aplicaciones formen parte de una red cuántica en el futuro. Las redes cuánticas pueden implementarse utilizando nodos que tengan la capacidad de generar y almacenar el entrelazamiento de forma eficiente durante largos periodos de tiempo, así como de procesar la información cuántica. Los nodos también necesitan una interfaz con fotones, ya que estos pueden transportar fielmente la información a largas distancias. Los iones individuales de tierras raras dopados en cristales ofrecen todas estas capacidades. El objetivo principal de esta tesis fue detectar un ion individual de erbio, que opera en la longitud de onda de las telecomunicaciones, e investigar su viabilidad como interfaz espín-fotón. La detección de un ion individual de erbio es un reto debido a su baja tasa de emisión, pero esta puede mejorarse mediante el acoplamiento a una cavidad óptica, debido al efecto Purcell. En esta tesis, utilizamos iones de erbio dopados en nanopartículas, lo que facilita su integración a cavidades con volúmenes de modo pequeños. Además, las nanopartículas proporcionan el confinamiento necesario para manipular bits cuánticos de iones individuales cercanos espacialmente, lo cual es necesario para construir puertas cuánticas dipolares. Por ello, estudiamos primero las propiedades de coherencia óptica de las nanopartículas de Er:Y2O3 a temperaturas criogénicas. Identificamos los mecanismos limitantes e identificamos las vías de mejora en el futuro. También estudiamos las propiedades de coherencia óptica y de espín de Pr:Y2O3, que es una alternativa prometedora al erbio. Las microcavidades basadas en fibra pueden alcanzar elevados factores de Purcell, ya que pueden lograr simultáneamente una gran finura y un pequeño volumen de modo. También son idóneas para ser acopladas a nanopartículas debido a su capacidad para ajustar la frecuencia de resonancia. Sin embargo, estabilizar una cavidad de este tipo en un entorno criogénico es un reto. Primero, describimos la construcción de un sistema personalizado que nos permitió estabilizar la cavidad mientras se acoplaba a una nanopartícula adecuada. Utilizando la primera iteración de esta configuración, informamos sobre el acoplamiento de nanopartículas de Er:Y2O3 a una microcavidad de alta precisión basada en fibra. Conseguimos un factor Purcell medio de 14 para un pequeño conjunto de iones, mientras que un pequeño subconjunto de iones mostró un factor Purcell de hasta 70. Explicamos el comportamiento de decaimiento multiexponencial obtenido utilizando un modelo detallado. Además, demostramos el control dinámico de la emisión potenciada por el efecto Purcell ajustando la resonancia de la cavidad en una escala de tiempo más rápida que la tasa de emisión espontánea de los iones. Esto nos permitió extraer el tiempo de vida natural de los iones, así como moldear la forma de onda de los fotones emitidos. Para el experimento final, operamos la segunda iteración de la configuración, que mejoró nuestra sensibilidad a los iones individuales de erbio en más de un factor 50. Esto nos permitió demostrar la primera detección de un ion de erbio en una nanopartícula. El ión presentó un factor Purcell de 60, lo que da un tiempo de vida realzado por la cavidad de 225 us, y un ancho de línea homogéneo de 380 MHz. Los recuentos recibidos del ion mostraron una clara saturación y la medida de autocorrelación de segundo orden de los fotones emitidos resultó en 0,59, que se reduce a 0,29 tras la sustracción de fondo. Esto es una fuerte evidencia de que los fotones son emitidos por un ion individual de erbio. Nuestro trabajo abre el camino para explorar los iones individuales de tierras raras dopados en nanopartículas como interfaces de espín-fotón para el procesamiento de información cuánticaPostprint (published version

Hybrid quantum system based on rare earth doped crystals = Hybrides Quantensystem basierend auf Kristallen mit Seltenerddotierung

Hybrid quantum circuits interfacing rare earth spin ensembles with microwave resonators are a promising approach for application as coherent quantum memory and frequency converter. In this thesis, hybrid circuits based on Er and Nd ions doped into Y2SiO5 and YAlO3 crystals are investigated by optical and on-chip microwave spectroscopy. Coherent strong coupling between the microwave resonator and spin ensemble as well as a multimode memory for weak coherent microwave pulses are demonstrated

Rare-earth ion doped planar waveguides for integrated quantum photonics

This thesis presents a spectroscopic study of Pr3+ ions in a novel passive waveguide architecture. To make this structure, the high refractive glass TeO2 was selected as the thin film and it was deposited on a Pr3+:Y2SiO5 crystal. In this waveguide, the 3H4 to 1D2 transition of Pr3+ ions were probed by the optical evanescent field extending into the substrate. The main concern in assessing the suitability of this material for quantum information applications was ensuring that the coherence properties of rare-earth ions, making them suitable for quantum information purposes, are preserved in this architecture. After which, to make low loss devices with these waveguides, efficient coupling techniques had to be developed. To prove that the coherence properties of the rare-earth ion doped crystal were preserved, the critical parameters of inhomogeneous linewidth, the absorption of the ions, the coherence time and spin lifetimes of the Pr3+ ions were studied. The inhomogeneous linewidth of evanescent coupled ions was about 10.0 GHz, which was consistent with the linewidth of bulk samples with the same Pr3+ doping concentration (Hedges, 2011). The absorption due to the evanescent coupling was 9.38 dB, approximately 90% of what was expected with respect to the bulk crystal with the same doping concentration. Therefore, despite using the evanescent field, the absorption is high enough for quantum memory applications. An optical coherence time of about 121 microseconds was measured, which corresponded to a homogeneous linewidth of about 2.6 kHz. This is very close to bulk sample measurements of 111 microseconds, with the same temperature and doping concentration (R. W. Equall, 1995). The spin state lifetime observed was about 9.8 s, which is also very close to the bulk sample measurement of 8.67 s (Mieth, 2016). Initial Stark shifting experiments were performed to determine whether the active ions in the substrate of the passive waveguides could be electrically controlled by applying a small voltage to electrodes on the thin film. In these experiments with a voltage change of 100 mV, the measured holewidth broadening was increasing about 0.55 MHz, which was similar to the calculated values of 0.45 MHz. The Stark coefficient for site 1 was 51.6 kHzcm/V along the D2 axis of the crystal (site 1 will be explained in Section 4.3). (F.R. Graf, 1997). Prism coupling and grating coupling were used to couple light to the ions in the substrate. Prism coupling is an easy and quick method to couple light into a waveguide and observe the properties of the system. However, grating coupling is much more practical when moving towards building a device using this method. The measurements described above indicated that the properties of ions interacting with the evanescent tail of the waveguide mode were consistent with those of bulk ions. This investigation also showed that depositing a glass thin film on a rare-earth ion doped crystal was not affecting the good coherence properties of the substrate. These results establish the foundation for large, integrated, controllable and high performance rare earth ion quantum waveguide systems

A multimode solid-state quantum memory for single photons

Quantum memories (QMs) for light represent a fundamental ingredient for the development of a quantum internet. Among other applications, they are a building block for the distribution of entanglement on large scale, i.e. for the realization of a quantum repeater architecture. Rare earth doped crystals (REDCs) are a promising candidate towards this goal. In my thesis I use a Pr3+:Y2SiO5 crystal. The longest storage time and the highest retrieval efficiency for a solid-state memory measured so far, were demonstrated with this system (in the classical regime). However, the main advantages of solid-state platforms are their suitability for miniaturization and integration as well as their inhomogeneous broadening, which enables broadband storage and spectral multiplexing. In this thesis we demonstrate an on-demand solid-state QM for real single photons. Moreover we study new platforms for integrated QM based on the same material. We employ the atomic frequency comb (AFC) technique, which is the most promising storage protocol in terms of temporal multiplexing up to now. Until the start of my PhD there was still no demonstration of storage of a real quantum state of light with an on-demand readout in REDCs. We achieved this in the course of this thesis, measuring also for the first time (and only, at the time of writing) non-classical correlation between a single spin wave in a solid-state QM and a telecom photon. After proving the suitability of Pr3+:Y2SiO5 crystals for on-demand QMs, we demonstrated novel types of integrated optical memories based on the same system. We studied the spectroscopic and coherence properties of the ions in laser-written waveguides fabricated by fs-laser micromachining. These projects were developed in collaboration with Dr. R. Osellame and Dr. G. Corrielli at Politecnico di Milano, who fabricated the waveguides and analysed their guiding properties. In a first kind of waveguide, called type II, we performed the first storage with on-demand retrieval ever done in solid-state integrated optical memories (with classical light). We continued analysing a so-called type I waveguide, in which the mode-size is comparable with the mode guided in a single-mode fiber at the same wavelength. Here we showed storage of heralded single-photons for a pre-programmed time. The demonstrated storage time, 5.5 µs, is the longest quantum storage demonstrated in any integrated waveguide up to now. Finally, we performed in the same waveguide storage of the whole spectrum of a frequency-multiplexed heralded photon, spanning a range of frequencies of ˜ 4 GHz. The photon is naturally multiplexed due to the generation method used, namely cavity-enhanced SPDC. The possibility of storing such a broad spectrum comes from the intrinsic inhomogeneous broadening present in REDCs. Together with the 15 frequency modes constituting the multiplexed photon, 9 temporal modes were stored thanks to the intrinsic temporal multimodality of the AFC protocol. The method used to fabricate our waveguides, fs-laser micromachining, is the only one to our knowledge that allows for direct 3D fabrication in the substrate. In the future, this will yield matrices of fiber-pigtailed waveguide-based QMs, thus enabling a high degree of spatial multiplexing, which nowadays is mostly exploited in atomic clouds, where temporal and spectral multiplexing are more difficult to achieve. The crystal, the protocol and the waveguide fabrication technique employed in this thesis, represent all together a very promising system, opening the way for a future quantum repeater architecture based on scalable highly multiplexed QMs.Les memòries quàntiques (MQs) per a la llum constitueixen un ingredient fonamental per al desenvolupament d’un Internet quàntic. Entre altres aplicacions, són un element bàsic per a la distribució de l’entrellaçament a llargues distancies, és a dir, per a la realització d’un repetidor quàntic. Els cristalls dopats amb terres rares (REDC) són candidats prometedors cap a aquest objectiu. En la meva tesi uso el cristall Pr3+:Y2SiO5. Amb aquest sistema (en el règim clàssic) es va demostrar el temps d’emmagatzematge més llarg i la major eficiència d’una memòria d’estat sòlid. No obstant això, els principals avantatges de les plataformes en estat sòlid són la possibilitat de miniaturització i integració, així com la ampliació inhomogènia dels seus perfils d’absorció, que permet emmagatzemar fotons amb banda ampla o multiplexats en freqüència. En aquesta tesi demostrem una MQ d’estat sòlid amb lectura on-demand per a fotons únics reals. A més, estudiem noves plataformes per a MQs integrades basades en el mateix material. Utilitzem la tècnica de pinta de freqüència atòmica (AFC), que és el protocol d’emmagatzematge més prometedor per a multiplexació temporal fins ara. Al començament del meu doctorat no hi havia cap demostració d’emmagatzematge d’un real estat quàntic amb una lectura on-demand del fotó en REDC. Ho hem aconseguit en el curs d’aquesta tesi, mesurant també per primera vegada (i única, en el moment d’escriure), una correlació no-clàssica entre una única ona de spin en una MQ d’estat sòlid i un fotó de telecomunicacions. Després de demostrar la idoneïtat dels cristalls Pr3+:Y2SiO5 com MQs, vam demostrar nous tipus de memòries òptiques integrades basades en el mateix sistema. Vam estudiar les propietats espectroscòpiques i de coherència dels ions en guies d'ones escrites amb làser fabricades amb la tècnica del fs-làser micromachining. Aquests projectes van ser desenvolupats en col·laboració amb el Dr. R. Osellame i el Dr. G. Corrielli del Politècnic de Milà, que van fabricar les guies d'ones i van analitzar les seves propietats orientadores. En un primer tipus de guia d'ona, anomenada tipus II, vam realitzar el primer emmagatzematge amb lectura on-demand mai realitzada en memòries òptiques integrades en estat sòlid (amb llum clàssica). Després vam analitzar un altre tipus de guia d’ondes anomenada tipus I, en la qual la mida del mode és comparable amb el mode guiat en una fibra monomode a la mateixa longitud d’ona. Aquí vam mostrar l’emmagatzematge de fotons simples durant un temps preprogramat. El temps d’emmagatzematge demostrat, de 5.5 µs, és fins ara l'emmagatzematge quàntic més llarg demostrat en qualsevol guia d'ones integrada. Finalment, es va realitzar en la mateixa guia l’emmagatzematge de tot l'espectre d'un bi-fotó multiplexat en freqüència, abastant un rang de freqüències de ˜4 GHz. El fotó és multiplexat de forma natural gracies al mètode de generació utilitzat, és a dir, el SPDC millorat per cavitat. La possibilitat d’emmagatzemar un espectre tan ampli prové de l’ampliació intrínseca de l’absorció inhomogènia present en els REDC. Juntament amb els 15 modes de freqüència que constitueixen el fotó multiplexat, s'han emmagatzemat 9 modes temporals gràcies a la multimodalitat temporal intrínseca del protocol AFC. El mètode utilitzat per fabricar les nostres guies d'ona, fs-làser micromachining, és l'únic que coneixem que permet directament fabricar en 3D en el substrat. En el futur, això donarà matrius de MQs basades en guies d’onades integrades con fibres, que permetran un alt grau de multiplexació espacial, que avui en dia s’explota sobretot en núvols atòmics, on el multiplexatge temporal i espectral és més difícil d’aconseguir. El cristall, el protocol i la tècnica de fabricació de guies d'ona utilitzats en aquesta tesi, representen tots junts un sistemaPostprint (published version