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.
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.
We show that crystal-field calculations for C_{1} point-group symmetry are possible, and that such calculations can be performed with sufficient accuracy to have substantial utility for rare-earth based quantum information applications. In particular, we perform crystal-field fitting for a C_{1}-symmetry site in ^{167}Er^{3+}:Y_{2}SiO_{5}. The calculation simultaneously includes site-selective spectroscopic data up to 20 000 cm^{-1}, rotational Zeeman data, and ground- and excited-state hyperfine structure determined from high-resolution Raman-heterodyne spectroscopy on the 1.5 μm telecom transition. We achieve an agreement of better than 50 MHz for assigned hyperfine transitions. The success of this analysis opens the possibility of systematically evaluating the coherence properties, as well as transition energies and intensities, of any rare-earth ion doped into Y_{2}SiO_{5}.
This thesis investigates the potential of Er:YSO and Er:Si for quantum communication and computation applications. Erbium uniquely possess optical transitions in the 1.5 um region, making it suitable for both fibre telecommunication and silicon photonics. The properties of the I15/2↔I13/2 optical transition in Er:YSO have already been extensively studied. Over two decades ago, improvements in Er3+ dephasing time at 1.5 um were achieved by applying a 5T field along the D1 axis. More recently, a record 4.4 ms coherence time on the same optical transition was achieved using a 7T field. These investigations, among others, illustrate that large Er electron spins become thermally polarised with sufficient magnetic field. However, no long lived and coherent spin transitions associated with the Er ions had previously been identified, and such transitions are necessary for on-demand quantum state storage. To address this requirement, the optical and hyperfine transition properties of 167-Er:YSO were investigated in large magnetic fields. In a field of 7T, spectral hole lifetimes of 1 minute and hyperfine population lifetimes of 12 minutes were observed. These measurements illustrate the effect of spin-lattice relaxation in this system, and how it can be mitigated. Efficient spin-polarisation of the entire 167-Er hyperfine ensemble is also demonstrated. This is the first such demonstration in rare earth systems, and a key requirement for broadband optical storage. Moreover, a 1.3 second coherence time was recorded for an 167-Er:YSO hyperfine transition at 7T and 1.4 K. This is an improvement of several orders-of-magnitude over previous coherence measurements on spin-transitions in Er doped solids. This is also sufficient for maximal entanglement rates in quantum repeater networks that span distances of 1000 km or greater. With an optical transition at 1.5 um, Er is also an ideal candidate to connect silicon based quantum computers to the future quantum Internet. In particular, single Er:Si ions could be used to develop an optical-spin bus between P:Si qubits and fibre based quantum networks. Presented here is the first spectroscopic investigation of single Er:Si ions. This required a novel opto-electronic approach to single ion detection, where the Er ions are implanted into a nanometre scale fin-shaped Field Effect Transistor. With this approach it was possible to develop high resolution optical spectra, where both the electronic and hyperfine levels of individual Er ions were resolved. Long optical and spin coherence times are also important requirements for an optical-spin bus. To address the first requirement, an investigation of the optical lineshape was undertaken. Here it was determined that sources of Stark noise external to the transistor channel contribute a significant amount to optical homogeneous linewidth. However, the dominant noise contribution was determined to be short-range (from within the 30 nm wide channel) and the total homogeneous linewidth was measured to be 50 MHz. The site structure of an individual Er:Si ion was then analysed, using magnetic field rotation patterns and optical transitions between multiple crystal field levels. This site was determined to have approximately axial (C3) symmetry. The purpose of this study was to determine a magnetic field regime in which the Er electrons spin can be polarised, which is necessary for realising of long hyperfine lifetimes and coherence times.
Most of the experiments related to quantum information applications, involving rare-earth doped inorganic crystals, are performed on yttrium orthosilicate single crystals. The work presented here is motivated by the search of new compounds which can be used in the field of quantum computing and/or quantum storage. Relaxation times and hyperfine structure of the $^{3}H_{4}(0)\ensuremath{\rightarrow}^{1}D_{2}(0)$ transition in 1.4% Pr3+:La2(WO4)3 at 4K have been measured by photon-echo and spectral-hole-burning techniques. The hyperfine splittings of the ground 3H4(0) and the excited 1D2(0) states are $14.9\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $24.6\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $5.0\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $7.3\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, respectively. An inhomogeneous linewidth of $18.8\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ was measured. A homogeneous linewidth of $25.3\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ was obtained with or without an external magnetic field of about 14mT. The fluorescence dynamics of the 1D2 level obtained by a direct excitation in the $^{3}H_{4}\ensuremath{\rightarrow}^{1}D_{2}$ transition gives a nonexponential decay which indicates energy-transfer processes. This decay can be accurately fitted by the Inokuti-Hirayama model [J. Chem. Phys. 43, 1978 (1965)] with a radiative lifetime of $61\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ giving a minimal homogeneous linewidth of 2.6kHz. The spectral-hole lifetime due to population redistribution within the ground hyperfine levels is $16\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The results obtained for the La2(WO4)3 compound make this crystal an interesting host for quantum applications.
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,
Rare-Earth (RE) atoms possess a unique atomic energy level structure, leading to excellent electronic and spin coherence properties [1]. Consequently, RE-ion-doped materials are promising candidates for implementing light-matter interfaces for photonic quantum technologies, such as quantum memories. To exploit these properties in quantum technologies, the REs must be hosted in a solid-state material [1]. RE organic molecular crystals offer advantages over the well-known RE-doped inorganic crystals. In organic molecular crystals, RE ions are integral parts of the molecular structure, unlike in inorganic crystals, in which the RE ions are distributed randomly into the crystal lattice structure. This can potentially lead to narrower inhomogeneous broadening. These crystals provide unmatched flexibility in combining with photonic structures and in material composition, allowing the choice of different ligands and point group symmetries around the RE ion [2], [10], [4]. Our research focuses on crystals formed from a molecular complex hosting erbium ions⌈Er(C5H7O2)3(C12H8N2)⌉. As these crystals have not yet been studied for quantum information purposes, we conducted a series of optical spectroscopy measurements to characterize the platform. We performed absorption measurements and obtained the absorption profiles at room and cryogenic temperatures. The results show a narrow inhomogeneous broadening in samples with different relative concentrations, even at 100%, for which all molecules contain an erbium ion. We measured the lifetime of the second lowest crystal field level of the ground state manifold(30cm−1above ground state) to be 1.759 seconds. Additionally, we measured the inhomogeneous broadening of the lowest crystal field level versus temperature to investigate the effects of phonon processes. Finally, under an external magnetic field, we observed Zeeman splitting and determined the g-factor to be 3.23 for erbium ions in this molecular complex.
Rare-earth doped crystals are promising systems for quantum information processing. In particular, paramagnetic rare earths could be used to build coherent interfaces with optical and microwave photons. In addition, isotopes with nonzero nuclear spins could provide long-lived states for quantum state storage and processing. Yb3+ is particularly interesting in this respect since it is the only paramagnetic rare earth with a spin-21 isotope, which corresponds to the simplest possible level structure. In this paper, we report on the optical and magnetic properties of Yb3+ in the two sites of Y2SiO5, a commonly used crystal for quantum applications. We measured optical inhomogeneous linewidths, peak absorption coefficients, oscillator strengths, and excited-state lifetimes. The Zeeman tensors were also determined in the ground and excited states, as well as the ground-state hyperfine tensor for the 171Yb3+ (I=21) isotope. These results suggest that Yb3+:Y2SiO5 is a promising material for applications like solid-state optical and microwave quantum memories.