One-photon rare earth optical transitions: recent theoretical developments

M. C. Downer

Michael Stavola

The absorption of a single photon by the simultaneous excitation of two rare-earth ions was first reported by Varsanyi and Dieke in 1961.1 D. L. Dexter explained this unusual observation by including the electron-electron interactions (that also give rise to energy transfer) between the rare earth ions with perturbation theory.2 In the 70's Dexter became interested in electronic-vibrational coupling. A theory of two-center optical transitions was developed for a rare-earth ion weakly coupled to a high energy, internal vibrational mode of a near-lying ion.3 Using theoretical techniques that had been developed for rare-earth ion pairs, intensities and selection rules could be determined.

N. Bloembergen

Tian Zhong

Coherent quantum devices play a central role in quantum science and engineering. Rare-earth ions such as erbium in solids feature numerous 4f- intra-shell transitions that are effectively shielded from their crystalline surroundings by closed outer shells, allowing for long spin coherence times and narrow optical transitions. Recent ensemble experiments have established the rare-earth doped crystals as the leading materials for optical quantum memories. However, the development of large-scale quantum devices based on rare-earth doped materials has remained a challenge. Here we describe a scalable quantum photonic platform based on epitaxially grown oxide thin films doped with trivalent ions on silicon substrates. The platform builds upon the recent developments of high quality epitaxial rare-earth doped oxides on silicon, and highlights the integration of quantum coherent materials with existing silicon technologies for ultimate device scalability. The proposed device platform builds upon our capability to epitaxially grow high quality, near-lattice-matched Y2O3 thin films on silicon. The epitaxial thin film is of high structural quality and offers several distinct advantages: (1) significantly less optical loss and better quantum emitter coherence; (2) atomic precision placement of rare-earth emitters (via delta doping) with respect to the photonic mode for controllable ion-photon coupling; (3) scalable top-down device fabrication using standard lithography and etching techniques; (4) heterogeneous integration with silicon takes full advantage of existing silicon photonics technologies for routing, tuning, and modulation of the quantum emission from rare-earth ions.

Jarosław Sztucki, W. Stręk

Masaya Hiraishi

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.