Centuries after ancient Greek philosophers pondered over the conceptual idea of atom to explain the universe, the concept of atom revived in France to establish stoichiometry.Nowadays, atoms and molecules are no longer conceptual ideas but their existence is a solid fact.Real atoms and molecules drive scientists to observe and to control behavior of individual atoms and molecules.Observation of photo-activity of a single quantum system in condensed media, so-called single-molecule spectroscopy, has initiated in 1989.Today, the single-molecule spectroscopy has enormous significance in the context of quantum information technologies, where the observation and the control of a quantum system are inseparable from each other. This thesis describes the single-ion spectroscopy of Rare-Earth (RE) ion doped in crystal.When cooled down to a few kelvins, the nuclear spin transition of RE ions doped in a crystal is known to be detected using its optical transition.RE ions have forbidden optical transitions between two 4 f electronic configurations with a long radiation lifetime reaching to 100 µs.The hyperfine splitting about 10 MHz due to the nuclear spin appears on the spectral line of the ions, whose linewidth narrows down to 10 kHz of its lifetime-limited width at a few K.Aiming at the optical detection and manipulation of a single RE nuclear spin quantum state, the author has consulted on the low-temperature spectroscopy of single praseodymium ions doped in a lanthanum trifluoride crystal (Pr 3+ :LaF 3 ).Spectroscopy of a single Pr 3+ requires the sensitivity enough to detect the weak luminescence due to the long radiation lifetime and the frequency resolution close to the narrow spectral linewidth of the ion.Thus, the author needed to build the cryogenic confocal microscope dedicated to carry out the single-ion spectroscopy of Pr 3+ :LaF 3 .A high performance objective for the cryogenic microscopy was newly developed with the numerical aperture of 0.97 and the detection efficiency of the confocal setup was as large as 0.48%.The excitation lightsource consists of a commercial continuous-wave diode laser and an optical Fabry-Perot cavity as the stable laser frequency reference.The laser linewidth was made narrower than Preface 0.4 MHz and the long-time stability of the output frequency was ±0.018 MHz/day.Photo-luminescence excitation measurement of individual Pr 3+ ions was demonstrated with a bulk crystal of 0.05% Pr 3+ -doped LaF 3 cooled down at 1.5 K. Spectral lines of the 3 H 4 → 3 P 0 transition of individual Pr 3+ ions were resolved as luminescence peaks with intensities of 20 -30 cps and the full-width at half-maximum of approximately 3 MHz at an excitation intensity of 80 W cm -2 .The population transfer of a single Pr nuclear spin was demonstrated via the optical pumping process of the ion.This study is the first success of the single-RE spectroscopy with a bulk crystal sample which contains multiple RE ions in the microscopic volume.It benefits future implementation of multi-qubit operations based on the ion-ion interaction to address the individual ions close in the sub-micrometer distance by the inhomogeneous distribution of their transition frequency.In application to nuclear spin qubit, qubit manipulation is conducted under the magnetic field to use Zeeman sub-levels.Because the Zeeman effect is anisotropic, the orientation of the magnetic field must be accurately controlled with respect to the host crystal.The experiment using the bulk crystal sample paves the way for the optical access to a single ion under the Zeeman field.The author believes this study established the first step to utilizing the RE-doped crystal as the solid-state quantum-information processor.This thesis is organized into five chapters.Chapter 1 introduces the significance and also the difficulty of the spectroscopy of single RE ions doped in a crystal.Chapter 2 covers physical and chemical properties of the sample material Pr 3+ :LaF 3 and the spectroscopic method to resolve individual Pr 3+ ions abundantly contained in the bulk crystal sample.Chapter 3 describes the development of the home-build cryogenic confocal setup to carry out the single-ion spectroscopy.Chapter 4 includes the results of the photo-luminescence excitation spectroscopy of Pr 3+ :LaF 3 at 1.5 K and the discussion about the success of the single-Pr 3+ detection and origins of observed spectral widths of individual ions.Chapter 5 summarizes the entire study and declares the outlook of quantum information processing using a RE-doped bulk crystal.
Centuries after ancient Greek philosophers pondered over the conceptual idea of atom to explain the universe, the concept of atom revived in France to establish stoichiometry.Nowadays, atoms and molecules are no longer conceptual ideas but their existence is a solid fact.Real atoms and molecules drive scientists to observe and to control behavior of individual atoms and molecules.Observation of photo-activity of a single quantum system in condensed media, so-called single-molecule spectroscopy, has initiated in 1989.Today, the single-molecule spectroscopy has enormous significance in the context of quantum information technologies, where the observation and the control of a quantum system are inseparable from each other. This thesis describes the single-ion spectroscopy of Rare-Earth (RE) ion doped in crystal.When cooled down to a few kelvins, the nuclear spin transition of RE ions doped in a crystal is known to be detected using its optical transition.RE ions have forbidden optical transitions between two 4 f electronic configurations with a long radiation lifetime reaching to 100 µs.The hyperfine splitting about 10 MHz due to the nuclear spin appears on the spectral line of the ions, whose linewidth narrows down to 10 kHz of its lifetime-limited width at a few K.Aiming at the optical detection and manipulation of a single RE nuclear spin quantum state, the author has consulted on the low-temperature spectroscopy of single praseodymium ions doped in a lanthanum trifluoride crystal (Pr 3+ :LaF 3 ).Spectroscopy of a single Pr 3+ requires the sensitivity enough to detect the weak luminescence due to the long radiation lifetime and the frequency resolution close to the narrow spectral linewidth of the ion.Thus, the author needed to build the cryogenic confocal microscope dedicated to carry out the single-ion spectroscopy of Pr 3+ :LaF 3 .A high performance objective for the cryogenic microscopy was newly developed with the numerical aperture of 0.97 and the detection efficiency of the confocal setup was as large as 0.48%.The excitation lightsource consists of a commercial continuous-wave diode laser and an optical Fabry-Perot cavity as the stable laser frequency reference.The laser linewidth was made narrower than Preface 0.4 MHz and the long-time stability of the output frequency was ±0.018 MHz/day.Photo-luminescence excitation measurement of individual Pr 3+ ions was demonstrated with a bulk crystal of 0.05% Pr 3+ -doped LaF 3 cooled down at 1.5 K. Spectral lines of the 3 H 4 → 3 P 0 transition of individual Pr 3+ ions were resolved as luminescence peaks with intensities of 20 -30 cps and the full-width at half-maximum of approximately 3 MHz at an excitation intensity of 80 W cm -2 .The population transfer of a single Pr nuclear spin was demonstrated via the optical pumping process of the ion.This study is the first success of the single-RE spectroscopy with a bulk crystal sample which contains multiple RE ions in the microscopic volume.It benefits future implementation of multi-qubit operations based on the ion-ion interaction to address the individual ions close in the sub-micrometer distance by the inhomogeneous distribution of their transition frequency.In application to nuclear spin qubit, qubit manipulation is conducted under the magnetic field to use Zeeman sub-levels.Because the Zeeman effect is anisotropic, the orientation of the magnetic field must be accurately controlled with respect to the host crystal.The experiment using the bulk crystal sample paves the way for the optical access to a single ion under the Zeeman field.The author believes this study established the first step to utilizing the RE-doped crystal as the solid-state quantum-information processor.This thesis is organized into five chapters.Chapter 1 introduces the significance and also the difficulty of the spectroscopy of single RE ions doped in a crystal.Chapter 2 covers physical and chemical properties of the sample material Pr 3+ :LaF 3 and the spectroscopic method to resolve individual Pr 3+ ions abundantly contained in the bulk crystal sample.Chapter 3 describes the development of the home-build cryogenic confocal setup to carry out the single-ion spectroscopy.Chapter 4 includes the results of the photo-luminescence excitation spectroscopy of Pr 3+ :LaF 3 at 1.5 K and the discussion about the success of the single-Pr 3+ detection and origins of observed spectral widths of individual ions.Chapter 5 summarizes the entire study and declares the outlook of quantum information processing using a RE-doped bulk crystal.
Optical read-out and manipulation of the nuclear spin state of single rare-earth ions doped in a crystal enable the large-scale storage and the transport of quantum information. Here, we report the photo-luminescence excitation spectroscopy results of single Pr(3+) ions in a bulk crystal of LaF3 at 1.5 K. In a bulk sample, the signal from a single ion at the focus is often hidden under the background signal originating from numerous out-of-focus ions in the entire sample. To combine with a homemade cryogenic confocal microscope, we developed a reflecting objective that works in superfluid helium with a numerical aperture of 0.99, which increases the signal by increasing the solid angle of collection to 1.16π and reduces the background by decreasing the focal volume. The photo-luminescence excitation spectrum of single Pr(3+) was measured at a wing of the spectral line of the (3)H4 → (3)P0 transition at 627.33 THz (477.89 nm). The spectrum of individual Pr(3+) ions appears on top of the background of 60 cps as isolated peaks with intensities of 20-30 cps and full-width at half-maximum widths of approximately 3 MHz at an excitation intensity of 80 W cm(-2).
Optical read-out and manipulation of the nuclear spin state of single rare-earth ions doped in a crystal enable the large-scale storage and the transport of quantum information. Here, we report the photo-luminescence excitation spectroscopy results of single Pr3+ ions in a bulk crystal of LaF3 at 1.5 K. In a bulk sample, the signal from a single ion at the focus is often hidden under the background signal originating from numerous out-of-focus ions in the entire sample. To combine with a homemade cryogenic confocal microscope, we developed a reflecting objective that works in superfluid helium with a numerical aperture of 0.99, which increases the signal by increasing the solid angle of collection to 1.16π and reduces the background by decreasing the focal volume. The photo-luminescence excitation spectrum of single Pr3+ was measured at a wing of the spectral line of the 3H4 right arrow 3P0 transition at 627.33 THz (477.89 nm). The spectrum of individual Pr3+ ions appears on top of the background of 60 cps as isolated peaks with intensities of 20–30 cps and full-width at half-maximum widths of approximately 3 MHz at an excitation intensity of 80 W cm−2.
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.
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.
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.
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.