In this thesis, aspects of the use of cryogenically cooled rare-earth-ion-doped crystals in the fields of quantum optics and quantum information processing are addressed. The experiments and theoretical considerations referred to in this thesis are based on the coherent transient interaction between light and the ions in the crystals. A photon echo experiment has been performed where faint optical pulses were accumulated in the crystal. In this experiment, the possibility of single photons acting as two of the optical fields in the photon echo process was investigated. Different aspects on the experiment, which can be viewed as delayed self-interference of a single photon, are discussed in this thesis. A scheme for the possible implementation of quantum information processing in rare-earth-ion-doped crystals is presented. A key feature in this scheme is that small groups of ions, which can be optically manipulated and which interact in a controlled way, can be extracted from a collection of randomly positioned ions in the crystal host. Initial experimental investigations of the scheme, indicating the possibility of implementing quantum gates, are also presented in this thesis. In another experiment, the application of magnetic fields of up to 5 T was seen to increase the lifetime of information stored as frequency-dependent modulation of the population of thulium ions doped into a YAG crystal by several orders of magnitude. This mechanism might be useful in data storage and information processing applications. An experiment in which the same type of crystal was used as the active medium in a photon-echo-based pulse compression experiment, where microsecond long pulses were compressed to nanosecond duration using frequency-chirped light pulses, is also reported in this thesis.
In this thesis, aspects of the use of cryogenically cooled rare-earth-ion-doped crystals in the fields of quantum optics and quantum information processing are addressed. The experiments and theoretical considerations referred to in this thesis are based on the coherent transient interaction between light and the ions in the crystals. A photon echo experiment has been performed where faint optical pulses were accumulated in the crystal. In this experiment, the possibility of single photons acting as two of the optical fields in the photon echo process was investigated. Different aspects on the experiment, which can be viewed as delayed self-interference of a single photon, are discussed in this thesis. A scheme for the possible implementation of quantum information processing in rare-earth-ion-doped crystals is presented. A key feature in this scheme is that small groups of ions, which can be optically manipulated and which interact in a controlled way, can be extracted from a collection of randomly positioned ions in the crystal host. Initial experimental investigations of the scheme, indicating the possibility of implementing quantum gates, are also presented in this thesis. In another experiment, the application of magnetic fields of up to 5 T was seen to increase the lifetime of information stored as frequency-dependent modulation of the population of thulium ions doped into a YAG crystal by several orders of magnitude. This mechanism might be useful in data storage and information processing applications. An experiment in which the same type of crystal was used as the active medium in a photon-echo-based pulse compression experiment, where microsecond long pulses were compressed to nanosecond duration using frequency-chirped light pulses, is also reported in this thesis.
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.
This thesis describes a number of coherent processes, such as quantum information processing, superradiance and electromagnetically induced transparency, which have been experimentally implemented using rare-earth-ion-doped crystals. The rare-earths are a class of elements that have in common, an atomic structure that allows for very long lifetimes as well as coherence times, both on optical transitions and on spin transitions. These ions can be naturally trapped inside host crystals, and with the phonon vibrations removed by cooling down to cryogenic temperatures (< 4 K), they can be used for a number of different quantum information processes. Most experiments were carried out using PrYSO, but also other crystal types were investigated, such as Nd:YVO4, and La2(WO4)3. The characterization of the ions were done with a variety of methods, including among others, photon echo techniques and electromagnetically induced transparency. Quantum computing is a rapidly growing field and there are still many potential candidates for its implementation. In our work we have utilized the spin states of the Pr rare-earth ion as a qubit, and demonstrated arbitrary single qubit gates, which are important pieces towards a quantum computing realization in these systems. Most of the experimental work done for the thesis was carried out using an ensemble approach, that has the advantage of giving a strong readout signal, but for future scaling to multiple qubits, single instances are more promising, which is discussed. Quantum memories are crucial components in applications such as quantum networks and long distance quantum communication. In this thesis, work has been done to investigate how quantum memories can be implemented in rare-earth crystals. In particular, there are two protocols, CRIB and AFC, which were suggested with rare-earth crystals directly in mind, and both of these require high optical depth, for maximum recall efficiency. In this thesis, implications of being in the high optical depth regime, with phenomena such as superradiance, a collective effect that could cause the stored light to be immediately reemitted, and slow light effects that come from performing the storage inside spectrally structured materials, were investigated. In order to carry out the phase-sensitive experiments, a laser system with a very narrow linewidth of ~1 kHz at 606 nm was constructed, by locking the laser to a semi-persistent spectral hole. In addition, many experiments required advanced pulse shapes, such as complex sechyp pulses or pulses obtained from optimal control theory. In order to be able to accurately create such shapes, an elaborate system using an arbitrary waveform generator and two well calibrated AOMs, controlled from a computer, was also built.
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.
When doped into solid state transparent crystals, rare-earth ions can have optically excited states with milliseconds coherence time and up to six hours coherence time for hyperfine levels after being cooled down to liquid helium temperature. This long coherence property makes them unique as solid state material and attractive for quantum information applications.The rare-earth ions have narrow homogeneous linewidths on the order of ~ kHz. When doped into a crystal, the lattice structure is slightly distorted due to the size mismatch between the dopant and the host ions, resulting in slight differences in the local crystal fields at the dopant sites. Therefore, the resonance frequencies of the rare-earth ions are shifted relatively, resulting in an inhomogeneously broadened absorption profile, typically on the order of a few GHz. This provides the possibility of addressing each group of ions individually and engineering the absorption profile for different purposes by optical pumping using a narrow linewidth laser, and makes rare-earth-ion-doped crystals suitable for ensemble based quantum memories.Quantum memories are vital components for developing longdistance quantum communication. Part of this thesis project focused on making quantum memories with high efficiency and long storage time, especially using materials with low optical depth. To achieve this goal, a low finesse, unsymmetrical cavity was employed and experiments were carried out at (or close to) the impedance matched condition. Atomic frequency comb (AFC) protocol proposed for such an inhomogeneously broadened system was used to store coherent light for a certain time. 56% overall efficiency was achieved, and the main limiting factor for reaching even higher efficiency was the inefficient coupling between incoming light and the cavity mode. Other possible loss mechanisms were analyzed as well.Long-time, on-demand, quantum memory experiments were conducted with the help of two efficient radio-frequency rephasing pulses. Storage time was extended from microseconds to milliseconds after compensating (most of) the residual earth magnetic field in the lab. The opportunities and challenges of combing the cavity assistant quantum memory and the long time, on demand quantum memory were analyzed and possible solutions were proposed. Another part of the thesis project involves slow light-based applications in rare-earth-ion-doped crystals. The strong slow light effect at the presence a spectral hole is due to the fact that the light interacts with the absorbing ions outside the spectral hole off-resonantly, and most of the light energy is stored inside the ions as a polarization. For example, with a group velocity of 300 km/s, 99.9% of the pulse energy is stored in the ions when the pulse propagates inside the crystal. The slower the light propagates, the more energy is stored inside the medium. Based on this, a frequency shifter that is capable of shifting the light frequency of ± 4 MHz was demonstrated, and frequency shift up to GHz was proposed. Group velocity control by a factor of 20 and pulse compression in time by a factor of 2 were also demonstrated. The frequency shift and group velocity of the light are solely controlled by the external electric field, which makes them ideal for weak light situation. The unique property of such a frequency shifter and group velocity controller is that they could be made to accept light from an arbitrary incoming angle and polarization, for example, scattered light.
This thesis describes experiments aimed at developing a key component in applications such as quantum networks and long-distance quantum communication systems: quantum memories. Quantum memories for light using photon-echo and coherent rephrasing techniques have been developed. The work is carried out on rare-earth-ion-doped inorganic crystals. Several properties are associated with these crystals such as long coherence times and long-lived ground state sublevels that are particularly interesting in connection applications in the area of quantum information science. It is demonstrated the preparation of optical inhomogeneous absorption profiles such that the light only interacts with a specific transition at a selected frequency. Narrow absorbing structures with widths of <100 kHz have been prepared with no absorption in the surrounding spectral interval. Most of the experiments were carried out using Pr3+:Y2SiO5. However, in our search for suitable a Λ-system in the material under consideration, we also performed spectral hole-burning spectroscopy in Nd:Y2SiVO4. As part of the search for host materials for Pr, Pr:La2(WO4)3 crystal was characterized using a variety of methods, such as, hole burning and photon-echoes. Electromagnetically induced transparency was also observed in this crystal. The most important criteria for evaluating quantum memory performance and the most important physical requirements are discussed. After investigating the standard photon echo techniques and controlled reversible inhomogeneous broadening (CRIB) for quantum state storage, we considered an efficient multimode quantum memory protocol; the atomic frequency comb (AFC) protocol. Combs with peaks of widths 100-300 kHz and an optical depth of~ 10 were created by optical pumping inside an emptied region of the inhomogeneous profile of Pr3+:Y2SiO5, allowing us to improve the efficiency of light storage. Light storage combining a photon-echo technique based on an AFC and spin-wave storage have been demonstrated, and an experimental AFC scheme for the storage of weak coherent light pulses in Pr3+:Y2SiO5 is presented. Finally, we have investigated superradiance and slow light effects. Both these effects occur in the high optical depth regime and can influence the memory performance. Under certain conditions superradiance results in the immediate re-emission of the stored light in a single burst of coherent radiation, and inside spectrally structured materials, slow light effects may result when storage is performed.
Rare-earth-doped crystals have been used for optical signal processing and storage applications. In this dissertation, their potential for quantum computing applications is explored. In one quantum computing scheme, information is stored in nuclear spin states and this information is then processed by using optical pulses through the coupling of these nuclear spin states to a common electronic level. To implement this scheme, nuclear spin states and coupling of these nuclear spin states to a common electronic level is required. Preliminary work in rare-earth materials like Pr3+ and Eu3+ has shown promising results regarding their suitability for quantum computing applications. One particular problem with these materials is that their transition wavelengths are only accessible with dye lasers. These lasers are inherently unstable, and currently few available systems exhibit the stability required for quantum computing applications. An alternative choice was to investigate other rare-earth ions like thulium. Thulium has a transition wavelength that can be accessed with diode lasers, which are commercially available, easy to stabilize, and compact. This dissertation is based on our investigations of Tm3+:YAG for quantum computing applications. Investigations involved a detailed characterization of the material. Nuclear spin states, in Tm3+:YAG, were obtained by applying an external magnetic field to the sample. First, interaction of an external magnetic field with the thulium ions at various sites in the crystal was analyzed. This analysis was used to measure the magnetic anisotropy in the material. These results show that it is possible, with the suitable choice of the magnetic orientation and the site in the crystal, to build a working 3-level quantum system. In the demonstration of single qubit operations in Tm3+:YAG, we first theoretically studied the effect of Gaussian spatial beam on the single qubit operations. Later on, we experimentally prepared a single isolated ensemble of ions in the inhomogeneously broadened absorption profile of the medium. This single isolated ensemble of ions was used as a test-bed to implement the single qubit operations. We also isolated two ensembles of ions in the inhomogeneous absorption profile of the medium. The interaction between these two isolated ensembles of ions was also studied.