Rare-earth-doped crystals can be attractive materials for quantum information processing, because of the long coherence times that can be expected, in particular, from non-Kramers ions. In this paper, Ho3+-doped yttrium and lutetium vanadate single crystals have been investigated using linear and coherent optical spectroscopy. For Ho3+:YVO4, the crystal-field levels of the I-5(8), F-5, F-5(4) and S-5(2) multiplets have been determined and compared with crystal-field level calculations. This allowed us to unambiguously assign most of the observed transitions, although some results suggest that the site symmetry of the Ho3+ ion could deviate from D-2d. Similar conclusions were reached for Ho3+:LuVO4. Hole burning measurements indicate that the coherence time of the I-5(8)-F-5(5) optical transitions is rather short in both compounds (around 40 ns). Assuming that the coherence is limited by spin interactions, this is accounted for by the high nuclear moment of the nearby vanadium ions, since the large crystal-field level splittings of the I-5(8) and F-5(5) multiplets do not favour a large enhanced nuclear Zeeman effect.
Rare-earth-doped crystals can be attractive materials for quantum information processing, because of the long coherence times that can be expected, in particular, from non-Kramers ions. In this paper, Ho3+-doped yttrium and lutetium vanadate single crystals have been investigated using linear and coherent optical spectroscopy. For Ho3+:YVO4, the crystal-field levels of the I-5(8), F-5, F-5(4) and S-5(2) multiplets have been determined and compared with crystal-field level calculations. This allowed us to unambiguously assign most of the observed transitions, although some results suggest that the site symmetry of the Ho3+ ion could deviate from D-2d. Similar conclusions were reached for Ho3+:LuVO4. Hole burning measurements indicate that the coherence time of the I-5(8)-F-5(5) optical transitions is rather short in both compounds (around 40 ns). Assuming that the coherence is limited by spin interactions, this is accounted for by the high nuclear moment of the nearby vanadium ions, since the large crystal-field level splittings of the I-5(8) and F-5(5) multiplets do not favour a large enhanced nuclear Zeeman effect.
Rare-earth doped insulators have been widely recognized as excellent candidate materials for optical quantum computing and information processing. This is principally due to a combination of optical coherence times of up to milliseconds and ground-state hyperfine coherence times of seconds exhibited by rare-earth 4𝑓 𝑁 states. A key contender among rare-earth doped materials is Er3+:Y2SiO5, for which homogeneous linewidths as narrow as 50 Hz have been reported, and for which transitions between the ground and first excited states fall within the 1.5 𝜇m telecommunications wavelength band. However, attempts to utilize this material for spin-wave storage have been hampered by the complexity of the excited-state hyperfine structure, which inhibits the necessary theoretical work required to predict the location of zero first-order zeeman transitions. To address this, a novel crystal-field fitting method was developed to allow an accurate analysis of the 𝐶1 point-group symmetry sites of Y2SiO5. This work was complemented with spectral hole-burning spectroscopy, which revealed ground-state hyperfine level storage with a lifetime of 1.6 ± 0.4 seconds for the 4I15/2𝑍1 → 4F9/2𝐷1 transition. This type of storage time is uncharacteristic for erbium without an external magnetic field, since spin-flips of the unpaired electron in nearby Er3+ ions are typically understood to lead to fast hole filling. The development process of the theoretical and experimental tools required to perform the above work enabled several additional investigations. In particular, the novel crystal-field fitting methods were applied to the 𝑆4 site of Ce3+:LiYF4 and to the 𝐶2𝑣 site of Sm3+:Na+/Li+:CaF2/SrF2. These studies consisted of excellent tests for the developed methods yet also amounted to interesting investigations in their own respect. Similarly, the experimental work afforded an opportunity to directly determine the hyperfine splittings of the 5I8𝑍1 → 5F5𝐷1 transition in Ho3+:KY3F10. This was achieved using high-resolution excitation spectroscopy. Furthermore, the experimentally determined hyperfine structure could be accurately reproduced using a crystal field model. Finally, a lifetime measurement of the 6H7/2 state of Sm3+:LiYF4 was conducted. By utilizing an infrared free-electron laser, pico-second pump-probe spectroscopy allowed for a direct measurements of one of the shortest lifetimes of an RE3+ doped insulator reported in the literature to date. This confirmed the previously suggested two-gradient modification required for the energy-gap law at very short time scales.
Quantum information uses special properties of quantum systems to manipulate or transmit data. This results in new processes, which are impossible to obtain with classical devices. For example, quantum computing and quantum storage, which are two important fields in quantum information research, aim respectively at performing very fast calculations and at storing quantum states of photons. These two applications could be obtained in solid-state systems using rare earth doped crystals. In this context, the most important property of these materials is the long coherence lifetimes of rare earth ion optical and hyperfine transitions. This allows one to create long-lived superposition states, which is a fundamental requirement for efficient quantum computing and storage. Promising results have already been demonstrated in rare earth doped crystals but it will be difficult to improve them with current materials. In this paper, we discuss the general and specific requirements for rare earth ions and crystals in order to perform quantum computing with a large number of quantum bits as well as all solid-state quantum storage. We also present the properties of a few recently studied crystals: Ho3+:YVO4, Ho3+:LuVO4 (quantum computing) and Tm3+:Y3Al5O12 (quantum storage).
Solids containing rare earth (RE) ions have attracted spectroscopists' attention since the beginning of this century.In the last 30 years, their extremely narrow spectral features in combination with the use of non linear spectroscopy have served to sensitively measure ion-solid interactions and to progressively observe narrower homogeneous linewidths.The potential for using RE ion doped crystals as optical storage materials and processors has lately been a driving force in their investigations, Here, the ratio of inhomogeneous to homogeneous linewidth is regarded as an adequate measure of storage density and can become as big as 10 7 at cryogenic temperatures.Therefore, the analysis of line broadening is of fundamental as well as applied interest.This work is concerned with the investigation of interactions of RE ions with their environment.By means of a laser with a kilohertz resolution and non-linear spectroscopy, spectral dynamics as a function of intrinsic, external electric field, or light-pulse induced perturbations are analyzed on different time scales.In the first part, the theoretical background for the spectroscopy of RE ion doped crystals is outlined.The energy levels are presented and it is shown that due to their electronic properties RE ions have spectrally narrow electronic transitions, sometimes in the sub-kHz regime.The investigations of these narrow spectral features on the seconds to minutes time scale require very stable tunable laser sources.At present, such devices are not commercially available.In the second part, the performance of ahorne built laser system is characterized using persistent spectral holes, The results show that frequency selective materials can be used as powerful tools for the high resolution Vlll Abstract spectral analysis of laser sources.Complementary to that, they give a measure for the long term evolution of the spectral holes for the particular hole burning substance.In the third part, the effect of an external electric field on RE ion doped crystals is investigated.It is shown that for these systems the electric field induced frequency shifts are fully reversible.A general theory of Stark splittings of RE doped crystals is introduced and two methods are presented which allow for the determination of the magnitude and orientation of the electric dipole moment differences with sub-degree accuracy.Finally in the last part, spectral line broadening mechanisms of RE ion doped crystals are discussed and investigated by means of two-pulse photon echoes.Through variation of the experimental parameters, a discrimination between the different contributions is partly achieved and characteristic properties for different dephasing mechanisms are presented.In combination with the measurements from the third part, quantitative predictions of the electric dipole-dipole induced broadening are carried out, which are compared to the experimental results,
Spin dynamics are investigated in several rare-earth-ion-doped crystals, both for so-called Kramers ions and non-Kramers ions. I have studied two illustrative examples of such systems, Neodymium (Kramers) and Europium (non-Kramers). The main motivation behind these studies is the search for long relaxation and coherence times in solid state atomic ensembles. To this end I employ spectroscopic techniques to probe different kinds of interactions and relaxation mechanisms taking place in the samples. I perform spectroscopy of Neodymium (Kramers) in two different crystal lattices, yttrium orthosilicate and yttrium orthovanadate. I propose new methods to improve the relaxation lifetimes, and make precise characterizations of the interactions taking place within the atomic ensemble. In particular we achieve the most precise measurement of a kind of interaction which has received considerable attention recently in other areas of physics, the Dzyaloshinskii-Moriya interaction. These spectroscopic studies are of course of fundamental interest, but they can also be applied to quantum communication and computation. In this context, we were able to increase the efficiency of a quantum memory based on a Kramers ion (Nd) to be on par with the best non-Kramers (Eu,Pr) memories. Using Neodymium ions, I have certified that multi-dimensional entanglement can be stored in a quantum memory. The second part of this thesis concerns the study of Europium (non-Kramers), starting with a characterization of the Zeeman and quadrupole interactions. I believe these studies will pave the way for long duration (100 ms or more) quantum storage in a rare-earth-ion-doped crystal.
We report Zeeman infra-red spectroscopy of electronic-nuclear levels of 5I8 →5I7 transitions of Ho3+ in the C4v(F−) centre in CaF2 with the magnetic field along the ⟨111⟩ direction of the crystal. Transitions to the lowest 5I7 state, an isolated electronic doublet, and the next group of states, a pseudo-quadruplet consisting of a doublet and two nearby singlets, exhibit strongly non-linear Zeeman splittings and intensity variations. Simulated spectra based upon a crystal-field analysis give an excellent approximation to the data, illustrating the strong predictive ability of the parametrised crystal-field approach. Anti-crossings in the hyperfine splittings, the basis of quantum information storage in rare-earth doped insulating dielectrics, are also predicted.
High-resolution spectroscopy (as fine as $0.01\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) was applied to a 1mol holmium-doped single crystal of yttrium aluminum tetraborate with the purpose of studying the hyperfine splitting of Ho3+ energy levels of interest for possible quantum manipulation media. The hyperfine structure was clearly revealed for a high number of lines in a wide wave number range (up to $\ensuremath{\simeq}21\phantom{\rule{0.2em}{0ex}}300\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) and for a large number of multiplets. Several different hyperfine patterns were monitored, differing in the number of lines, in their separation, and in their relative statistical weight. These features were all understood by a crystal-field model, whose results are in very good agreement with experiments and account for the involved level symmetry, the type of transitions (electric and magnetic dipole allowed), the possibility of a second-order (pseudoquadrupolar) hyperfine coupling between close levels, and a slight distortion of the local D3 symmetry in Ho-occupied sites.