In this thesis we investigate the potential of erbium ions coupled to crystalline whispering-gallery mode resonators as hardware for quantum information processing. Achieving strong coupling between the erbium ions and the cavity would be a significant breakthrough for multiple quantum computing applications. To this end, we fabricate millimetre-sized resonators made from 0.001% erbium-doped yttrium orthosilicate (Er 3+ :Y 2 SiO 5 ). We show that the mechanical fabrication procedure used in making the resonators does not significantly impact the coherence properties of the erbium dopants. We find that strong coupling should be achievable using currently available technologies, so long as significant absorption in the Y 2 SiO 5 crystals is not present at the wavelength of the erbium transition.
In this thesis we investigate the potential of erbium ions coupled to crystalline whispering-gallery mode resonators as hardware for quantum information processing. Achieving strong coupling between the erbium ions and the cavity would be a significant breakthrough for multiple quantum computing applications. To this end, we fabricate millimetre-sized resonators made from 0.001% erbium-doped yttrium orthosilicate (Er 3+ :Y 2 SiO 5 ). We show that the mechanical fabrication procedure used in making the resonators does not significantly impact the coherence properties of the erbium dopants. We find that strong coupling should be achievable using currently available technologies, so long as significant absorption in the Y 2 SiO 5 crystals is not present at the wavelength of the erbium transition.
Rare-earth-ion doped crystals are an interesting system for quantum computing investigations due to their long optical and hyperfine coherence times. In particular, the ground-state coherence times can be longer than one second, which makes them perfect for long-term storage of quantum states. They also have the advantage of being a solid-state system. At present, many of the fundamental requirements for quantum computing have been demonstrated using rare-earth-ions; however, quantum state readout has yet to be achieved. The strong-coupling regime is of great importance in cavity quantum electrodynamics, as in this regime interactions between single atoms and single photons can be realized. Strong coupling thereby provides a method of enabling qubit-qubit interactions. It is desirable to achieve this regime with rare-earth-ion doped resonators, as it would enable on-demand readout of quantum states, a necessity for quantum computing, and provide the scalability required for implementation of quantum networks. This thesis describes the work that has gone into investigating the suitability of rare-earth-ion doped whispering-gallery mode resonators for quantum computing applications. A theoretical analysis of the strong-coupling regime is performed, followed by experiments investigating the properties of ions in resonators, and of new rare-earth-ion materials. A final set of experiments studies a new quantum memory protocol for use with rare-earth-ions. A theoretical investigation is undertaken to determine whether the strong-coupling regime will be attainable with rare-earth-ion doped whispering-gallery mode resonators. Emphasis is given to determining which rare-earth-ion materials will have the best properties when used as resonators. Specific applications of the strong-coupling regime are examined for this system; in particular, whether it will be possible to demonstrate the reversible transfer of quantum states, and detection of single dopants. Experiments are performed, measuring the properties of millimetre-sized Pr3+:Y2SiO5 resonators. Direct measurements of cavity quantum electrodynamics parameters are made using photon echoes, giving good agreement with theoretical predictions. Interactions between the atom and cavity are observed and a theoretical model is presented to describe these effects. Thus, a more realistic picture is obtained of the experimental requirements for achieving the strong-coupling regime. The properties of different rare-earth-ion doped materials are measured and analysed to determine their suitability for quantum computing applications. The spin Hamiltonian parameters of Pr3+:YAG are measured using Raman heterodyne spectroscopy, and then used to find the optical transitions with zero first-order Zeeman shift, as this should allow the coherence time to be extended to a point where this system is useful for resonator applications. Hyperfine transitions with zero first-order Zeeman shift are also calculated for Er3+:Y2SiO5, with the aim of enabling long-term storage in a telecommunication-wavelength memory. The thesis concludes with an experimental investigation into a new quantum memory technique that does not require spectral hole burning. The hybrid photon echo rephasing protocol uses strong optical pulses to perform rephasing, thus utilizing the advantageous properties of the two-pulse photon echo. Furthermore, the use of external broadening fields removes the usual problem of noise from amplified spontaneous emission. The properties of this memory are examined using a Pr3+:Y2SiO5 crystal.
The growing interest in optical quantum systems has led to the exploration of multiple platforms. Though pioneering experiments were performed in trapped atom and trapped ion systems, solid state systems show promise of being scalable and robust. Rare earth dopants in crystalline hosts are an appealing option because they possess a rich spectrum of energy levels that result from a partially filled electron orbital. While level structure varies across the period, all elements possess crystal field splittings corresponding to near infra-red or optical frequencies, as well as Zeeman and often hyperfine levels separated by radio frequency and microwave frequencies. These levels demonstrate long excited-state lifetimes and coherence times and have been used in diverse applications, including demonstrating storage of a photonic state, converting of optical to microwave photons, and manipulating a single ion as a single qubit. The ions' weak interaction with their environment results in low coupling to optical fields, which had previously required measurements with macroscopically large ensembles of ions. Coupling the ions to an optical cavity enables the use of a smaller ensemble, which is required for the development of the aforementioned technologies in an on-chip scalable architecture. This thesis contains recent progress towards fabricating optical micro and nanocavities coupled to ensembles of erbium ions, mainly erbium in yttrium orthosilicate. In one design, focused ion beam milling was used to create a triangular nanobeam photonic crystal cavity in a bulk erbium-doped substrate. A second design leveraged the fabrication capabilities of silicon photonics, defining amorphous silicon ring resonators using electron beam lithography and dry etching. These devices coupled evanescently to erbium ions below the ring, in the bulk substrate. Simulation, design, fabrication, and characterization of both resonators are discussed. Coupling between the ions and the resonator is demonstrated for each, and capabilities offered by these devices are described. Preliminary work implementing coherent control of erbium ions is presented. Lastly, alternative substrates are evaluated for possible future solid-state erbium systems.
Erbium dopants in crystals exhibit highly coherent optical transitions well suited for solid-state optical quantum memories operating in the telecom band. Here, we demonstrate coupling of erbium dopant ions in yttrium orthosilicate to a photonic crystal cavity fabricated directly in the host crystal using focused ion beam milling. The coupling leads to reduction of the photoluminescence lifetime and enhancement of the optical depth in microns-long devices, which will enable on-chip quantum memories.
Rare-earth ions in solid-state hosts are a compelling hardware platform for quantum networking due to their exceptional optical, and long-lived spin transitions. Erbium's transitions couple to photons in the Telecom-C band, making it compatible with fibre, and has demonstrated high coherence and low spectral diffusion in a range of materials. However, it has a low optical dipole moment, leading to low light-matter coupling. This limits the rate at which operations performed within a network. Despite decades of research, Er transitions remain poorly understood. Hosts are chosen based on convention, convenience, and (well-informed) heuristics, since calculations of the properties of lanthanide 4f shell are prohibitively difficult. This thesis addresses the challenge of this weak dipole through two complementary approaches; both of which constitute engineering the erbium-crystal system. Firstly, we engineer the emitter itself, from the bottom up. We seek an optimal crystal site for ions, which maintains coherence but increases transition strength. To this end, we have characterised four Er sites in CaF2 to understand how the crystal field affects ion properties. We identify sites with dipole moments as high as 1.63x10^-32 Cm despite lifetimes in excess of 10 ms, and coherence of up to 43.9 µs. This informs our next steps, in selecting an optimal site for single ion addressing, and our long-term goal of designing sites for high dipole moments. In the second approach, we engineer the crystal from the top down, fabricating whispering gallery mode resonators in calcium fluoride. I have fabricated five high Q resonators in doped and undoped CaF2, and commenced their characterisation. We have prototyped a coupler for use of these devices in a cryostat with no free-space optical access. This engineered crystal system - a high dipole erbium site coupled to a high Q resonator - provides a path toward competitive optical cooperativity for single erbium ions in the solid state.
We perform an investigation into the properties of Pr3+:Y2SiO5 whispering gallery mode resonators as a first step towards achieving the strong coupling regime of cavity QED with rare-earth-ion doped crystals. Direct measurement of cavity QED parameters are made using photon echoes, giving good agreement with theoretical predictions. By comparing the ions at the surface of the resonator to those in the center it is determined that the physical process of making the resonator does not negatively affect the properties of the ions. Coupling between the ions and resonator is analyzed through the observation of optical bistability and normal-mode splitting.
Rare-earth crystals are promising platforms for quantum information, with potentially long coherence times and telecom-compatible optical transitions. In this work, we investigate the optical properties of erbium atoms doped into a whispering gallery mode resonator produced by polishing a yttrium orthosilicate crystal. The multimode resonator demonstrates a bare quality factor of 2.56×10 5 . We demonstrate mode interaction between atoms and the resonator, where an effective quality factor of 8.7×10 7 is induced by spectral hole burning. The Fano interference between the atomic (spectral holes) and optical modes, and the small free-spectral range achieved here, can enable the study of tuning-free linear and nonlinear collective interactions.