An overview of current status and prospects of the development of quantum computer hardware based on inorganic crystals doped with rare-earth ions are presented. Major parts of the experimental work in this area have been done in two places, Canberra, Australia and Lund, Sweden, and the present description follows more closely the Lund work. Techniques will be described that include optimal filtering of the initially inhomogeneously broadened profile down to well separated and narrow ensembles, as well as the use of advanced pulse-shaping in order to achieve robust arbitrary single-qubit operations with fidelities above 90%, as characterized by quantum state tomography. It is expected that full scalability of these systems will require the ability to determine the state of single rare-earth ions. It has been proposed that this can be done using special readout ions doped into the crystal and an update is given on the work to find and characterize such ions. Finally, a few aspects on possibilities for remote entanglement of ions in separate rare-earth-ion-doped crystals are considered.
An overview of current status and prospects of the development of quantum computer hardware based on inorganic crystals doped with rare-earth ions are presented. Major parts of the experimental work in this area have been done in two places, Canberra, Australia and Lund, Sweden, and the present description follows more closely the Lund work. Techniques will be described that include optimal filtering of the initially inhomogeneously broadened profile down to well separated and narrow ensembles, as well as the use of advanced pulse-shaping in order to achieve robust arbitrary single-qubit operations with fidelities above 90%, as characterized by quantum state tomography. It is expected that full scalability of these systems will require the ability to determine the state of single rare-earth ions. It has been proposed that this can be done using special readout ions doped into the crystal and an update is given on the work to find and characterize such ions. Finally, a few aspects on possibilities for remote entanglement of ions in separate rare-earth-ion-doped crystals are considered.
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.
We present a scheme for quantum computing in rare-earth-ion doped inorganic crystals. We use two of the ground state hyperfine levels as the qubit states, with different qubits absorbing light at different frequencies within an inhomogeneously broadened optical transition. Interaction between different qubits is accomplished using the change in permanent dipole moment that is induced at the optical excitation of the ions. The two most important aspects of the scheme have been accomplished experimentally: The isolation of a single qubit in a pure state and interaction between ions absorbing at different frequencies.
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.
Solid state quantum computer hardware may be based on rare-earth-ion-doped crystals. The qubits can be encoded as nuclear spin states of an ensemble of, e.g., Pr3+ ions, randomly doped into a Y2SiO5 crystal. Two such qubits can control each other through the dipole blockade effect, and transfers between the two qubit states can be done at a high fidelity, despite the strongly inhomogeneous nature of the ensemble approach. In this paper full control over the qubit Bloch sphere is demonstrated, by performing arbitrary qubit rotations and characterizing the outcomes using quantum state tomography.
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.