Abstract Quantum information processing based on magnetic ions has potential for applications as the ions can be modified in their electronic properties and assembled by a variety of chemical methods. For these systems to achieve individual spin addressability and high energy efficiency, we exploited the electric field as a tool to manipulate the quantum behaviours of the rare-earth ion which has strong spin-orbit coupling. A Ce:YAG single crystal was employed with considerations to the dynamics and the symmetry requirements. The Stark effect of the Ce3+ ion was observed and measured. When demonstrated as a quantum phase gate, the electric field manipulation exhibited high efficiency which allowed up to 57 π/2 operations before decoherence with optimized field direction. It was also utilized to carry out quantum bang-bang control, as a method of dynamic decoupling, and the refined Deutsch-Jozsa algorithm. Our experiments highlighted rare-earth ions as potentially applicable qubits because they offer enhanced spin-electric coupling which enables high-efficiency quantum manipulation.
Abstract Quantum information processing based on magnetic ions has potential for applications as the ions can be modified in their electronic properties and assembled by a variety of chemical methods. For these systems to achieve individual spin addressability and high energy efficiency, we exploited the electric field as a tool to manipulate the quantum behaviours of the rare-earth ion which has strong spin-orbit coupling. A Ce:YAG single crystal was employed with considerations to the dynamics and the symmetry requirements. The Stark effect of the Ce3+ ion was observed and measured. When demonstrated as a quantum phase gate, the electric field manipulation exhibited high efficiency which allowed up to 57 π/2 operations before decoherence with optimized field direction. It was also utilized to carry out quantum bang-bang control, as a method of dynamic decoupling, and the refined Deutsch-Jozsa algorithm. Our experiments highlighted rare-earth ions as potentially applicable qubits because they offer enhanced spin-electric coupling which enables high-efficiency quantum manipulation.
Quantum information processing based on magnetic ions are considered potential candidates for applications because they can be modified and scaled up by a variety of chemical methods. For these systems to achieve individual spin addressability and high energy efficiency, we exploited the electric field as a tool to manipulate their quantum behaviours, functioning via spin-orbit coupling. A Ce:YAG single crystal was employed due to that rare-earth ions have strong spin-orbit coupling and with considerations regarding the dynamics and the symmetry requirements. The Stark effect of the Ce3+ ion was observed and measured. When demonstrated as a quantum phase gate, the electric field manipulation exhibited high efficiency which allowed up to 57 {\pi}/2 operations before decoherence with optimized field directions. It was also utilized to carry out quantum bang-bang control, as a method of dynamic decoupling, and the refined Deutsch-Jozsa algorithm. Our experiments highlighted rare-earth ions as potentially applicable qubits since they offer enhanced spin-electric coupling which enables high-efficiency quantum manipulation.
Without using any trapping lasers, rare-earth (RE) ions can be doped into some nanofabricated materials in form of nanocrystals in a solid state matrix, thus rendering a natural trap for potential application as a quantum computing device. In particular, passive nuclear spin states of RE ions can be utilized as (i) optical quantum memory (with huge density as yielded from nanocrystals), (ii) qubits by encoding in ground hyperfine states and operated as (iii) two-qubit gate when transferring them to active magnetized electronic states. A feasible implementation of qubits is realised by using those doped RE ions whose open-shell (for inner highly shielded 4f shell electrons) energy levels and statevectors are well described by the crystal field (CF) interaction and hyperfine coupling in which the Hamiltonian is composed of various freeion interactions, the CF potential, electronic and nuclear Zeeman effects as well as the hyperfine interaction. For those qubit encoded in the two ground hyperfine states of RE ions, they can have fairly long lifetimes of days and coherence times (from 1.3s for Er3+ to 6 hours for Eu3+) due to the unique spectroscopic properties of RE ions. Because of the recent progress in optical single-ion detection for addressing individual qubits with a specific frequency channel, RE ions could be packed in a solid state 3D matrix at nanometer spacing, hence rendering very high qubit densities for quantum memories. Meanwhile, this configure also leads to strong dipole-dipole interactions (or high connectivity) between qubits which are not nearest neighbors. In this study, Kramers ions like 167Er and 171Yb doped in yttrium orthosilicate Y2SiO5 (YSO) nanocrystals will be investigated as a promising system for quantum computing because of their weak spin bath and possibility for being directly milled in single nanocrystals as nano-resonators. By using the famous Wien2k package to carry out the first-principles calculations, we can obtain the CF parameters and hyperfine constants as well as various electronic properties like energy gap and band structure for those Kramers RE ions doped in YSO. We shall present some essential findings from first-principles calculations to obtain various properties of the ground and excited CF and hyperfine states for those RE ions with an aim to optimize RE ions doping in YSO nanocrystals for quantum memories and qubits, contributing to scalable quantum computing architectures.
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.
Contrary to the well-known spin qubits, rare-earth-metal qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground state which nutates (for several $\ensuremath{\mu}\mathrm{s}$) and the Rabi frequency ${\ensuremath{\Omega}}_{R}$ is anisotropic. Here, we present a study of the variations of ${\ensuremath{\Omega}}_{R}({\stackrel{\ensuremath{\rightarrow}}{H}}_{0})$ with the magnitude and direction of the static magnetic field ${\stackrel{\ensuremath{\rightarrow}}{H}}_{0}$ for the odd 167Er isotope in a single crystal CaWO4:Er3+. The hyperfine interactions split the ${\ensuremath{\Omega}}_{R}({\stackrel{\ensuremath{\rightarrow}}{H}}_{0})$ curve into eight different curves which are fitted numerically and described analytically. These ``spin-orbit qubits'' should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields.
Light-matter interaction at single quantum object level is a long-lived challenge and dream of physicists. From the 1970s, the development of single ion spectroscopy and the observation of single photon states pave a way to a new era of detecting, and coherently manipulating quantum objects with electromagnetic field at single-ion levels. Later on, the invention of single molecular spectroscopy offers a new approach to investigate single quantum objects in condensed matter, where the sophisticated trapping systems like in ions and cold atoms are not needed, resulting in the discovery of various of single photon emitters embedded in solids. Among all, single quantum dots and single negatively charged nitrogen-vacancy centers in diamond attract most attentions, since their single spins can be coherently manipulated and entangled by the light field giving rise to numerous applications from nanoscale sensing to quantum computing. They are intensively studied as the most promising candidates for the realization of solid-state quantum bits. However, these systems coupled to a complex environment which can result in rapid loss of spin coherence or optical instability. Finding an alternative solid-state single system with remarkable optical and spin properties is the motivation of this dissertation. Rare earth ions doped in inorganic crystal hosts provide promises not only by the high quality factor 4f-4f optical transitions but also by the well preserved and long-lived spin states, with the applications from solid-state laser spectroscopy to quantum information processing. However, for almost three decades, not being able to identify single rare earth elements in solids is the obstacle to achieve their full potential functionality. We demonstrated the first direct optical detection of single rare earth ions (praseodymium) in solids in 2012. This research was covered in my Master Degree Thesis. This dissertation presents experimental progress in optically detecting other single rare earth species in crystals, understanding their fundamental spectroscopy properties and coherently controlling them, which is mainly focused on single trivalent cerium ions in different host materials. Following the optical detection of single cerium ions in yttrium aluminum garnet (YAG), the optical and spin properties of single Ce ions are investigated. Single Ce ions show good photostability under the pulsed laser excitation. Still, like in other solid emitters, photo-induced dynamics of single Ce ions is observed, however, in a counterintuitive way under the continuous laser irradiation. To understand this behavior, we proposed a charge dynamics model, and developed a novel method to suppress this undesired charge dynamics. With this approach, we obtain the photoluminescence excitation spectrum of single Ce ions in YAG under a CW laser excitation. Narrow (~80 MHz) and spectrally stable optical transitions between the lowest Kramers doublets of the ground and the excited states are observed. In comparison with the large inhomogeneous broadening (500 GHz), narrow resonant transitions provide the good selectivity in the spectral domain. Moreover, the single Ce ground spin state presents a spin 1/2 system with anisotropy g factor. It results in the optical selection rules dependent on the directions of the external magnetic field. Under parallel external magnetic field with respect to the quantization axis, only the spin-flip transitions are allowed with high transition contrast. It gives the opportunity to optically initialize the ground spin state of single Ce ions with 97.5% fidelity. The coherent spin properties of single Ce ions can be investigated, after the successful optical initialization. By scanning the microwave frequency, we obtain the electron spin resonance of single Ce spin transitions. We show the spin state has a coherence time of 290 ns, which is dominated by the surrounding aluminum nuclear spin bath and impurities induced electron spin bath. The coherence time can be extended to 2 ms through dynamical decoupling method, which approaches closely to the upper limit 4.5 ms due to spin-lattice relaxation. This result indicates single Ce electron spin can be a good solid-state qubit. With the combination of optical and spin manipulations of single Ce ions, a quantum interface between a single spin and a single photon is observed by monitoring the temporal behavior of circularly polarized emission photons from the ion. We obtain the Larmor precession of the excited spin state, indicating the direct mapping of the excited spin states of single Ce ions onto the polarization states of the fluorescence photons. Furthermore, with both optical and spin access, we all-optically demonstrate coherent population trapping of a single Ce spin qubit. To scale up the system for further applications, we present the nano-scale engineering of rare earth species in YAG crystal, with the acquirement of the production yield of Ce and Pr implantation (53 and 91% respectively). The optical and spin properties of single implanted Ce ions show fairly good performance, which paves the way towards coherent coupling of single rare earth qubits in a small volume. Besides the study of single Ce ions, the spectroscopy properties of single praseodymium ions in YAG crystal are investigated. We obtain the photoluminescence excitation spectrum and the hyperfine splitting of a single praseodymium ion. All-optical control of a single praseodymium ion is achieved. In this dissertation, we solve the key problem of optically detecting, spectrally studying and coherently manipulating single rare earth ions in solids. The developed methods including optical detection, initialization, readout, coherent control and nanoscale production of single rare earth elements in crystals offer novel and powerful tools for understanding and exploring the fundamental spectroscopy properties of single rare earth elements in solids. It paves a way towards constructing scalable quantum network based on single rare earth solid-state qubits.
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.