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Spins in silicon that are accessible via a telecom-compatible optical transition are a versatile platform for quantum information processing that can leverage the well-established silicon nanofabrication industry. Key to these applications are long coherence times on the optical and spin transitions to provide a robust system for interfacing photonic and spin qubits. Here, we report telecom-compatible Er3+ sites with long optical and electron spin coherence times, measured within a nuclear spin-free silicon crystal (<0.01% 29Si) using optical detection. We investigate two sites and find 0.1 GHz optical inhomogeneous linewidths and homogeneous linewidths below 70 kHz for both sites. We measure the electron spin coherence time of both sites using optically detected magnetic resonance and observe Hahn echo decay constants of 0.8 ms and 1.2 ms at around 11 mT. These optical and spin properties of Er3+:Si are an important milestone towards using optically accessible spins in silicon for a broad range of quantum information processing applications., Comment: 14 pages, 6 figures

The 1538 nm ${}^4$I$_{15/2}$ - ${}^4$I$_{13/2}$ transition of Er$^{3+}$ has an unusual hybrid electric-magnetic dipole character, and signatures of the hybrid moment can be expected in coherent transient measurements. Here, we investigate the effect of the hybrid moment in both sites of Er$^{3+}$:Y$_2$SiO$_5$ on Stark-modulated photon echo measurements, showing that it results in a reduction of visibility of the modulated signal as well as phase and polarization shifts. We interpret these effects using a simple optical Bloch equation model, showing that site 1 has a strongly mixed moment and site 2 is predominantly magnetic dipole. We discuss the implications of the hybrid moment for quantum information applications of quantum memories. We also use the echo measurements to extract the Stark shift of the optical transition along three orthogonal directions, finding values between 10.50 and 11.93 kHz/(V/cm) for site 1 and 1.61 and 15.35 kHz/(V/cm) for site 2. We observe a modification of the Zeeman shift by the electric field in both sites and discuss how this may be used to electrically control Er$^{3+}$ spin qubits., Comment: 10 pages, 6 figures, supplemental information included

We studied the recall efficiency as a function of optical depth of rephased amplified spontaneous emission (RASE), a protocol for generating entangled light. The experiments were performed on the $^{3}\! H_{4}$ $\rightarrow$ $^{1}\! D_{2}$ transition in the rare-earth doped crystal Pr$^{3+}$:Y$_{2}$SiO$_{5}$, using a four-level echo sequence between four hyperfine levels to rephase the emission. Rephased emission was observed for optical depths in the range of $\alpha L$ = 0.8 to 2.0 with a maximum rephasing efficiency of 14 % observed while incorporating spin storage. This efficiency is a significant improvement over the previously reported non-classical result but is well short of the predicted efficiency. We discuss the possible mechanisms limiting the protocol's performance, and suggest ways to overcome these limits., Comment: 5 pages, 5 figures

We investigate the prospect of achieving negative permittivity and permeability at optical frequencies in a dielectric crystal containing stoichiometric rare-earth ions. We derive the necessary transition linewidth, ion density and electric and magnetic oscillator strengths using a simplified model of non-interacting dipoles. We identify Erbium crystals in a magnetically ordered phase as the most promising material to meet these conditions, and describe initial optical measurements of two potential candidates, \ercl{} and ${}^7$\lierf{}, which display linewidths of 3~GHz and 250~MHz, respectively. The properties of ${}^7$\lierf{} satisfied our criterion for negative permeability.

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 the first 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$\pm$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 (ZEFOZ) fields are identified for this site and could be used to reduce decoherence of hyperfine spin states in future experiments.

Computational crystal-field models have provided consistent models of both electronic and Zeeman-hyperfine structure for several rare earth ions. These techniques have not yet been applied to the Zeeman-hyperfine structure of Eu$^{3+}$ because modeling the structure of the $J=0$ singlet levels in Eu$^{3+}$ requires inclusion of the commonly omitted lattice electric quadrupole and nuclear Zeeman interactions. Here, we include these terms in a computational model to fit the crystal field levels and the Zeeman-hyperfine structure of the $^7F_0$ and $^5D_0$ states in three Eu$^{3+}$ sites: the C$_{4v}$ and C$_{3v}$ sites in CaF$_2$ and the C$_2$ site in EuCl$_3$.6H$_2$O. Close fits are obtained for all three sites which are used to resolve ambiguities in previously published parameters, including quantifying the anomalously large crystal-field-induced state mixing in the C$_{3v}$ site and determining the signs of Zeeman-hyperfine parameters in all three sites. We show that this model allows accurate prediction of properties for Eu$^{3+}$ important for quantum information applications of these ions, such as relative transition strengths. The model could be used to improve crystal field calculations for other non-Kramers singlet states. We also present a spin Hamiltonian formalism without the normal assumption of no $J$ mixing, suitable for other rare earth ion energy levels where this effect is important.

We make the first study the optical energy level structure and interactions of pairs of single rare earth ions using a hybrid electro-optical detection method applied to Er-implanted silicon. Two examples of Er3+ pairs were identified in the optical spectrum by their characteristic energy level splitting patterns, and linear Zeeman spectra were used to characterise the sites. One pair is positively identified as two identical Er3+ ions in sites of at least C2 symmetry coupled via a large, 200 GHz Ising-like spin interaction and 1.5 GHz resonant optical interaction. Small non-Ising contributions to the spin interaction are attributed to distortion of the site measurable because of the high resolution of the single-ion measurement. The interactions are compared to previous measurements made using rare earth ensemble systems, and the application of this type of strongly coupled ion array to quantum computing is discussed., Comment: 11 pages, 5 figures

We studied the optical properties of a resonantly excited trivalent Er ensemble in Si accessed via in situ single photon detection. A novel approach which avoids nanofabrication on the sample is introduced, resulting in a highly efficient detection of 70 excitation frequencies, of which 63 resonances have not been observed in literature. The center frequencies and optical lifetimes of all resonances have been extracted, showing that 5% of the resonances are within 1 GHz of our electrically detected resonances and that the optical lifetimes range from 0.5 ms up to 1.5 ms. We observed inhomogeneous broadening of less than 400 MHz and an upper bound on the homogeneous linewidth of 1.4 MHz and 0.75 MHz for two separate resonances, which is a reduction of more than an order of magnitude observed to date. These narrow optical transition properties show that Er in Si is an excellent candidate for future quantum information and communication applications., Comment: 12 pages, 13 figures

Most investigations of rare earth ions in solids for quantum information have used rare earth ion doped crystals. Here we analyse the conversion of quantum information from microwave photons to optical frequencies using crystals where the rare earth ions, rather than being dopants, are part of the host crystal. The potential of large ion densities and small linewidths makes such systems very attractive in this application. We show that, as well as high efficiency, large bandwidth conversion is possible. In fact, the collective coupling between the rare earth ions and the optical and microwave cavities is large enough that the limitation on the bandwidth of the devices will instead be the spacing between magnon mode modes in the crystal., Comment: 9 pages, 3 figures

Quantum memories for light will be essential elements in future long-range quantum communication networks. These memories operate by reversibly mapping the quantum state of light onto the quantum transitions of a material system. For networks, the quantum coherence times of these transitions must be long compared to the network transmission times, approximately 100 ms for a global communication network. Due to a lack of a suitable storage material, a quantum memory that operates in the 1550 nm optical fiber communication band with a storage time greater than 1 us has not been demonstrated. Here we describe the spin dynamics of $^{167}$Er$^{3+}:$Y$_{2}$SiO$_{5}$ in a high magnetic field and demonstrate that this material has the characteristics for a practical quantum memory in the 1550 nm communication band. We observe a hyperfine coherence time of 1.3 seconds. Further, we demonstrate efficient optical pumping of the entire ensemble into a single hyperfine state, the first such demonstration in a rare-earth system and a requirement for broadband spin-wave storage. With an absorption of 70 dB/cm at 1538 nm and $\Lambda$-transitions enabling spin-wave storage, this material is the first candidate identified for an efficient, broadband quantum memory at telecommunication wavelengths., Comment: 7 pages, 5 figures

We describe an experimental technique for associating the satellite lines in a rare earth optical spectrum caused by a defect with the rare earth ions in crystal sites around that defect. This method involves measuring the hyperfine splitting caused by a magnetic dipole-dipole interaction between host ions and a magnetic defect. The method was applied to Ce3+:EuCl3.6H2O to assign 13 of the outermost 22 satellite lines to sites. The assignments show that the optical shift of a satellite line is loosely dependent on the distance to the dopant. The interaction between host and dopant ions is purely dipole-dipole at distances greater than 7 Angstroms, with an additional contribution, likely superexchange, at distances less than 7 Angstroms., Comment: 6 pages, 6 figures