Er-doped Si is a promising candidate for quantum information applications due to its telecom wavelength optical transition and its compatibility with Si nanofabrication technologies. Recent spectroscopic studies based on photoluminescence excitation have shown multiple well-defined lattice sites that Er occupies in Si. Here we report a measurement of the Zeeman and hyperfine tensors of a single
167Er3+ ion in Si. All the obtained tensors are highly anisotropic with the largest value principal axes aligning in nearly the same direction, and the trace of the lowest crystal field level
g-tensor is $17.78\ifmmode\pm\else\textpm\fi{}0.40$. The results indicate that this specific Er site is likely to be a distorted cubic site that exhibits monoclinic (
C1) symmetry. Finally, zero first-order-Zeeman fields are identified for this site and could be used to reduce decoherence of hyperfine spin states in future experiments.
We present the complete Zeeman
g tensors for the lowest-energy
4I15∕2 and
4I13∕2 states of
Er3+ doped into
Y2SiO5 for both crystallographic sites deduced from orientation-dependent optical Zeeman spectroscopy over three orthogonal crystal planes. From these data, principal axes of the
g tensors were determined for each crystallographic site. Along axes with maximum values, the effective
g factors are 14.65 (site 1) and 15.46 (site 2) for the ground state, and 12.97 (site 1) and 13.77 (site 2) for the excited state. To minimize optical decoherence and spectral diffusion in device applications and high resolution spectroscopy, special directions for applying an external magnetic field have been found for each site, for which the ground- and excited-state
g factors are equal. Among those directions, choices are presented that also maximize the ground-state splittings for all four magnetically inequivalent sites, thus optimizing the prospects for freezing out electron spin fluctuations and reducing decoherence and spectral diffusion significantly.
Abstract Individual optical emitters coupled via coherent interactions are attractive qubits for quantum communications applications. Here, we present the first study of single pairs of interacting rare earth ions and determine the interactions between ions in the pair with high resolution. We identify two examples of Er 3+ pair sites in Er implanted Si and characterise the interactions using optical Zeeman spectroscopy. We identify one pair as two Er 3+ ions in sites of at least C 2 symmetry coupled via a large, 200 GHz, Ising-like spin interaction in both optical ground and excited states. The high measurement resolution allows non-Ising contributions to the interaction of < 1 % to be observed, attributed to site distortion. By bringing two optical transitions into resonance with a magnetic field, we observe a 0.8 GHz optical interaction of unusual magnetic-dipole/electric-dipole character with strong polarization selection rules. We discuss the use of this type of strongly coupled, field-tunable rare earth pair system for quantum processing.
Photoluminescence (PL) spectra of Er3+ in an Er-doped silicon film were recorded at 2 and 77 K over the wavelength range from 1.52 to 1.68 μm, which includes optical transitions between the Er3+ I13/24 and I15/24 manifolds. These spectra were then analyzed to determine the nature of the electrostatic field at the site of the Er ion that governs the ion’s optical behavior. The PL spectra were analyzed three different ways: by considering the Er3+ ions to be occupying sites of Td, C3, or D2d point group symmetry. Transition energies and magnetic dipole transition probabilities were calculated for each case by diagonalizing a Hamiltonian representing the free-ion and crystal-field interactions in a Russell–Saunders basis of states spanning the lowest 15 J multiplets of the 4f11 electronic configuration of Er3+. Crystal-field parameters were varied in each case to find the best agreement with the experiment. Our results showed that the site symmetry of the Er3+ ions most consistent with the data is D2d. For this case, the rms deviation between the experimental and calculated energy levels is 3.3 cm−1 with the calculated magnetic dipole transition probabilities in qualitative agreement with the experiment.
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.