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 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.
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 m3 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.
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.
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.
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.
Rare-earth ions doped into a transparent crystal can have optically excited states with coherence times of milliseconds and hyperfine levels with coherence times of hours when cooled down to liquid helium temperatures. This makes them attractive for developing quantum computing hardware. A quantum transistor can be implemented in a rare-earth-ion-doped crystal by utilizing a dipole blockade effect, where one excited ion prevents nearby ions from being excited. By using single rare-earth ions as qubits, the quantum processor is believed to be scalable to several qubits. In this thesis a readout mechanism for qubits represented by single ions (Eu or Pr) in a Y2SiO5 crystal is explored. A single cerium ion, in the same crystal as the qubits, could potentially be used as an indicator ion for non-demolition quantum state detection of the qubits. Cerium has a strong transition with high fluorescence yield which makes it possible to detect single ions. A cerium ion can be controlled by a qubit via the dipole blockade effect, and fluoresce if the qubit is in state |1> but stay dark if the qubit is in state |0>. Relevant spectroscopic properties of Ce:Y2SiO5 are studied, as well as interactions between cerium ions and qubit ions. The inhomogeneous and homogeneous linewidth of the Ce:Y2SiO5 4f-5d transition is measured and fluorescence spectra for ions in site 1 and site 2 are characterized. The change in electric dipole moment as a cerium ion is brought to the excited state is measured. The static dipole interaction between a single cerium ion and a qubit ion is shown to be strong enough for efficient qubit readout. Energy transfer from cerium to qubit ions is investigated. A lower bound on the cerium-qubit distance is found in order to avoid energy transfer. Satellite lines belonging to cerium-qubit pairs are mapped out. A microscope set-up is built to detect single ions in a crystal. Single ion detection is believed to be within reach.
Quantum computing with single instances of rare earth-ions doped into inorganic crystals shows great promise as a scalable design in the field of quantum information. A detectable and controllable single readout ion is necessary for the scheme proposed in Lund to work. Due to its short excited state lifetime and its cyclable 4f-5d transition, cerium has been deemed suitable for just this purpose. The approach taken in Lund for this single cerium detection is to use a homemade confocal microscopy setup. In previous work using this setup on bulk crystals, it has been assumed that the undetectability of single cerium is due to out of focus ions contributing to a noise floor that is higher than the fluorescence signal from a single one. Hence single ion detection is being attempted in microcrystals. This thesis outlines the process behind converting the confocal microscope into a microcrystal detection setup. Subsequently, Ce3+:Y2SiO5 microcrystal spectroscopy experiments were performed. The energy level structure of cerium is reported to be identical to bulk, with a slight shift in wavelength, and the inhomogenous linewidth has proven to be inconclusive, although it hints towards being much wider than in bulk. Quantifying the homogenous linewidth of the cerium ions using Zeeman hole burning techniques was impervious to our attempts.