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 Er3+167 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±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.
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}.
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.
Erbium-doped solids are a promising platform for quantum technology due to the
Er3+ 1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic
C2 site of
Er3+ in
Y2O3 for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the
Er3+4I15/2$\ensuremath{\leftrightarrow}$
4I13/2 transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state
g tensors. The
C2-site
g tensor components for the ground state are
gx=1.60,
gy=4.71, and
gz=11.93 with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are
gx=1.08,
gy=4.36, and
gz=10.07 with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all
C2 sites become nearly magnetically equivalent with large
g values so that spin flips of neighboring
Er3+ ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With
Er3+:
Y2O3 absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.