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.
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.
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.
The thesis is primarily concerned with rare earth ions doped into yttrium ortho silicate crystals, RE:YSO. It is considered to be an ambitious platform for the development of quantum computing schemes. One such scheme requires the detection of single cerium ions. The project was aimed at measuring the saturation intensity of cerium 5d-4f transition which is needed for the single ion detection. This work contains theoretical simulations as well as measurements of fluorescence from rare earth ions sitting inside of a crystal as a function of excitation power. For practical reasons the measurement could not be carried out on cerium, but praseodymium was used instead. By measuring the saturation intensity one can derive the homogeneous linewidth that contributes to the detection procedure. The major complication in this type of measurement is the power broadening. Therefore, the measurement was aided by a theoretical simulation. The data was then fit with simulated theoretical results. The measurement was inconclusive for several reasons that are discussed at the end. However, this work is a priceless reference for the future cerium saturation intensity measurement or another experiment that needs to consider power broadening effects.
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.
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.
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 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.