A systematic analysis of decoherence rates due to electron–phonon interactions for optical transitions of rare-earth dopant ions in crystals is presented in the frame of the point charge model. For this model, the large value of any one of the matrix elements of the unit tensor operator U ( k ) of rank k for transitions within the 4f-electronic configuration, viz. U2, U4 or U6, is enough to ensure the strong optical transition between different levels, while the Stark–Stark transitions within the multiplet can be characterized by the matrix element U2 alone, the influence of elements U4, U6 being of much smaller order of magnitude and neglected. The circumstance that exactly such Stark–Stark transitions within the multiplet define the efficiency of electron–phonon interaction and, consequently, the decoherence rate (except for the case of lowest, less than approximately 2–4 K, temperatures), enables selection of optical transitions which are strong enough and at the same time are characterized by relatively small decoherence rates. Correspondingly, these optical transitions, provided that they lie in an appropriate spectral range and the gap to the nearest neighboring energy level is large enough (>500 cm−1) to prevent eventual fast phonon-assisted relaxation, should be considered as prospective for subsequent use in quantum informatics processing and communication. The list of such pre-selected transitions is given; the applicability area and limitations of our approach are discussed.
A systematic analysis of decoherence rates due to electron–phonon interactions for optical transitions of rare-earth dopant ions in crystals is presented in the frame of the point charge model. For this model, the large value of any one of the matrix elements of the unit tensor operator U ( k ) of rank k for transitions within the 4f-electronic configuration, viz. U2, U4 or U6, is enough to ensure the strong optical transition between different levels, while the Stark–Stark transitions within the multiplet can be characterized by the matrix element U2 alone, the influence of elements U4, U6 being of much smaller order of magnitude and neglected. The circumstance that exactly such Stark–Stark transitions within the multiplet define the efficiency of electron–phonon interaction and, consequently, the decoherence rate (except for the case of lowest, less than approximately 2–4 K, temperatures), enables selection of optical transitions which are strong enough and at the same time are characterized by relatively small decoherence rates. Correspondingly, these optical transitions, provided that they lie in an appropriate spectral range and the gap to the nearest neighboring energy level is large enough (>500 cm−1) to prevent eventual fast phonon-assisted relaxation, should be considered as prospective for subsequent use in quantum informatics processing and communication. The list of such pre-selected transitions is given; the applicability area and limitations of our approach are discussed.
Effects of the electron-phonon interaction for rare earth ions (RE) in crystals are multi-phonon relaxation, vibronic bands, band broadening depending on temperature or non-resonant energy transfer assisted by phonons. Since the Stark splitting for RE ions are of the order of lattice phonon energy, it could arise and other related effects, especially in the approximation of quasi-resonant processes. If the distance between two Stark levels is close to the region of resonance phonon spectrum, then electron-phonon interaction creates mixed vibronic states, which causes changes in the optical spectral lines (widening, asymmetry, splitting or displacement). The modeling of interaction of the electron-phonon resonance for RE ion Yb3+ in three different laser crystals is the purpose of this paper. Keywords: electron-phonon interaction, rare earth ions, adaptive application.
The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals. Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when the crystals are cooled down to ~ 4 K. There are several reasons for these extraordinary coherence times, which are approximately 8 orders of magnitude greater than those typical for electronic transitions in solids. The most important one is the cage-like shield which the outer 5s and 5p shells provide for the 4f electrons. Furthermore, since these ions are naturally trapped inside the crystal lattice there is no Doppler broadening of the line-width. The coherence properties of these optical transitions is one of the features that makes these materials attractive for use as a solid-state platform for quantum computing, using these ions as qubits. Another appealing characteristic is the fact that different ions have different optical resonance frequencies, which means that ions belonging to different qubits, which only have nm separation, can still be addressed separately by using different laser frequencies. Since the inter-ion spacing is so small, it is possible to make two ions interact strongly, although they are well shielded, through a permanent dipole-dipole interaction. This interaction can be turned on and off by switching between two different ways of encoding the qubit, a most useful feature. When the qubit is represented as a superposition between two ground state hyperfine levels, the interaction is turned off. The interaction is turned on selectively by transferring this superposition to the optical transition with a pi-pulse, for the specific ions that are to interact. This thesis describes how peaks of ions, absorbing on a single transition, residing in spectral pits with no other ions, have been isolated. It is shown how these ions can be coherently transferred between hyperfine levels via the optically excited state, how the interaction between such peaks of ions representing qubits can be turned on and off, and how subgroups of ions with strong interaction can be distilled out. All the work described here has been performed using the ensemble approach. The ensemble approach will, however, be difficult to scale up to large numbers of qubits. A method employing a single ion in each qubit, using a specialised ion for readout, has therefore also been proposed. The rare-earth-metal-ion-based quantum computing experiments require a laser with coherence properties which at least match those of the material. To this end a frequency stabilisation system was developed for a dye laser. This system uses a transient spectral hole in a rare-earth-metal-ion-doped crystal, of the same kind that is used in the experiments, as frequency reference, and is to the authors knowledge the first demonstration of locking a dye laser to a spectral hole. This system provides a line-width of 1 kHz on a 10 microseconds timescale and a frequency drift below 1 kHz/s.
Calculations made of the rates for several processes involving interactions between rare earth ions in crystals, such as resonance energy transfer, cooperative excitation transfer and cooperative optical transitions. These processes are assumed to originate from the electric multipole interactions between the ions concerned. A tensor operator method is employed in order to take account of the individual characters of the energy levels involved in the transition. Evaluation of the typical transition probability is also made on the lowest-order parity-allowed processes in nearest neighbour ions. The rates for the resonance transfer and cooperative transfer processes thus estimated are much smaller than those obtained by Miyakawa and Dexter.
Microwave and optical transitions of rare-earth ions enable microwave-to-optical frequency transduction. This transduction is a coherent process; therefore, the narrow linewidths and long coherence times of rare-earth ions are crucial for achieving efficient frequency conversion. Particularly long coherence times can be achieved with small-spin materials, as unpaired electronic and nuclear spins introduce magnetic noise, serving as a decoherent source of the transitions. However, complete spin-free rare-earth materials cannot exist without charge compensation. Consequently, residual spins in existing rare-earth materials act as a bottleneck, limiting both their spin and optical coherence times. Rather than focusing on nearly spin-free materials, this thesis investigates the microwave and optical transitions of rare-earth ions in materials that are fully concentrated with electronic spins. Recent studies on rare-earth magnetic materials have demonstrated narrow optical linewidths resulting from magnetic ordering and a particularly strong coupling between microwave cavity modes and the collective excitations of rare-earth ions. Although these recent studies are noteworthy, the energy-level transitions, especially optical transitions, of rare-earth ions in magnetic materials remain largely unexamined. In this thesis, various spectroscopic studies are employed to characterise their transition properties and to develop a model of energy levels. The model presented is expected to be applicable to other rare-earth magnetic materials, thereby opening avenues for further investigation in this class of systems. Two types of rare-earth magnetic materials are investigated: neodymium gallate with a stoichiometric concentration of neodymium ions, and gadolinium vanadate doped with a low (ppm) concentration of erbium ions. Microwave and optical transmission spectroscopy are employed under externally applied magnetic fields to characterise the energy-state transitions of the rare-earth ions in both materials. The magnetic phases and corresponding spin configurations influence the observed spectra, making conventional approaches to spectral simulation inadequate. To address this challenge, mean field and magnon-coupled crystal-field models are developed in this thesis to predict magnon and optical transition spectra. These simulations exhibit good agreement with experimental results, allowing for the characterisation of transition properties. Following the characterisation of the material, a new transduction approach is introduced, developed, and implemented using doped rare-earth ions in a magnetic material. In this scheme, coherent conversion between microwave and optical modes is achieved by exciting an optical transition of the doped ions.
Recently, we showed the first high-resolution spectroscopy and manipulation of single Pr3+ ions in the solid state using rare-earth doped crystals. The special feature of these systems is access to the hyperfine splitting caused by the interaction of the 4f electrons and the nucleus, leading to sets of sublevels with exceptionally long coherence times at cryogenic temperatures, on the order of minutes and hours. This ground state splitting can serve as a lambda level scheme, a key ingredient for many prospective applications in quantum optics, in particular for qubit storage and manipulation. In this presentation, we discuss our latest results and future challenges in reducing spectral diffusion and line broadening down to the expected natural linewidth, prospects for the use of microcavities or plasmonic nano-antennas to enhance the photon yield, and schemes for on-chip integration.
The main aim of the present thesis is to demonstrate the efficient quantum memories for light employing coherent processes in rare-earth-ion-doped crystals. Rare-earth (RE) ions between lanthanum, with atomic number 57, and lutetium, with atomic number 71, have a partly filled 4f shell, which is spatially inside the full shells 5s, 5p, and 6s. Therefore, 4f-4f transitions are shielded from environmental noise. Less noise means longer lifetime and coherence times and, when the crystals are cooled down to about 4 K, these can be about 8 orders of magnitude longer than what is typical for electronic transitions in solids. In quantum information processing, we are looking for physical systems which are isolated from the environment and consequently have good coherence properties. The long coherence time of both optical and spin transitions, is the main attraction of rare-earth ions for quantum information processing. In the present thesis, we map a quantum state of light employing a 4f-4f transition of praseodymium doped in yttrium silicate. We mainly employed the ensemble approach and the atomic frequency comb (AFC) protocol for quantum memory demonstrations. Among several parameters that define quantum memory performance, we mostly focused on quantum memory efficiency. The overall memory efficiency is simply defined as the energy of the pulse recalled from the memory divided by the energy of the pulse sent in for storage in the memory. To maximize quantum memory efficiency, most protocols require high optical depth. This is a limitation for materials with rather good coherence properties but low optical depth. In the research described in the present thesis, we combined the use of a low finesse cavity and the ensemble approach and designed an impedance-match cavity to obtain the advantages of both approaches and thereby to implement an efficient quantum interface in a weakly absorbing solid-state medium. Based on the cavity configuration, we obtained 56% storage and retrieval efficiency, which is the highest storage and retrieval efficiency based on the AFC protocol reported in the research so far. In the present thesis, we demonstrated a narrow-band (about 2 MHz) spectral filter with a >30 dB intensity absorption/transmission ratio, which is based on the large (6 orders of magnitude) ratio between the inhomogeneous and homogeneous broadening of Pr3+ : Y2SiO5. Slow-light effects due to the strong dispersion created by the spectral filter improved the suppression of the filter by also utilizing the time domain. As an application, we detected weak diffuse light shifted by ultrasound from the carrier about 2 MHz, after a 9 cm thick biological tissue. The coupling between light and matter is directly related to the relative direction of the light polarization and transition dipole moment of atoms. I developed a simulation program that was able to investigate the polarization direction and ellipticity of polarization of optical radiation propagating through the crystal. This might open up new opportunities for the investigation of interesting physics regarding propagation effects and for the improvement of spectral engineering of RE ions in the future. In order to deal with the sharp homogeneous transitions of the RE ions, the frequency of our dye laser was stabilized against a highly stabilized Fabry-Perot cavity using the Pound-Drever-Hall locking scheme.