Although superconducting qubits are one of the most promising systems for quantum information applications, a separate interface is required to allow for information distribution through optical links. Here, the authors investigate the suitability of ${}^{167}$Er${}^{3+}$:Y${}_{2}$SiO${}_{5}$ as a microwave-to-optical memory interface. This material holds considerable promise as it has an optical transition in the telecommunication band. The authors identify hyperfine transitions with long coherence times without an external magnetic field, which are suitable for interfacing with superconducting qubit systems.
Although superconducting qubits are one of the most promising systems for quantum information applications, a separate interface is required to allow for information distribution through optical links. Here, the authors investigate the suitability of 167Er3+:Y2SiO5 as a microwave-to-optical memory interface. This material holds considerable promise as it has an optical transition in the telecommunication band. The authors identify hyperfine transitions with long coherence times without an external magnetic field, which are suitable for interfacing with superconducting qubit systems.
Spin echoes in the ground and an optically excited state of 167Er3+:Y2SiO5 at near-zero magnetic fields using Raman heterodyne spectroscopy
Erbium-167-doped yttrium orthosilicate is an ideal candidate for a microwave-addressed quantum memory due to its telecom wavelength optical transition and hyperfine structure with and without an applied magnetic field. However, to date there has been little investigation in coherence times for transitions around zero magnetic field, or for hyperfine structure other than from the ground state. Through the use of Raman heterodyne spectroscopy, we have identified transitions at zero magnetic field with a small dependence on field that are suitable for detecting spin echoes for both the ground and excited state. We measured coherence times of transitions at 879.4 MHz and 896.7 MHz as 370 μs and 1.4 ms respectively at 3.2 K. This is a 100-fold increase in coherence time compared to previous measurements at the same dopant concentration and 200 times greater than the even isotopes of erbium-doped yttrium orthosilicate previously used to demonstrate a microwave memory.
Microwave-to-optical quantum transducers are essential for entangling remote superconducting qubits. Among the available transduction platforms, ensembles of Er3+ and Yb3+ ions doped into solids have emerged as leading candidates. While external magnetic fields are needed to split the Zeeman levels of erbium ions and enable a microwave--qubit interface, superconducting qubits suffer decoherence in such fields. In contrast, ytterbium ions exhibit zero-first-order Zeeman transitions and large hyperfine splittings at zero magnetic field (when doped into inorganic crystals). Owing to its long optical and spin coherence times, Yb:YSO has been widely used as a quantum memory, yet its potential for quantum transduction remains largely unexplored. Investigating this material could enable the integration of quantum memory and transduction in a single platform. Here, we demonstrate microwave-to-optical transduction in the continuous-wave regime using a 5\,ppm doped Yb:YSO crystal. The internal transduction efficiency is 2×10−8 with a bandwidth of 200\,kHz, achieved using a 3D loop-gap microwave resonator (LGR) and a single-pass optical configuration. We explore all the ground states that form a V-type three-level system with the first and second optical excited states and assert the use of the ground state, which provides the highest efficiency and isolated optical transition. We further establish strong spin-microwave coupling from avoided crossing measurements. With a strong microwave drive to saturate the spin transition, we estimate the spin population pumped into the excited state, close to the simulated value. Finally, we calculate target parameter values for maximum efficiency with our system and suggest using 50\,ppm doped Yb:YSO crystal. With the calculated target parameters, the internal transduction efficiency is predicted to reach up to 10−4 in the current LGR.
Erbium-167-doped yttrium orthosilicate (167Er3+:Y2SiO5) is a rare-earth-ion-doped crystal which possesses unique properties that would make it an ideal microwave-addressed quantum memory. It has an optical transition at 1.5 µm, which lies in the telecom C-band where much of the optical telecommunications infrastructure is already operating. It also possesses both nuclear and electron spin states, and hyperfine structure with transitions at microwave frequencies. The hyperfine structure exhibits microwave frequency transitions with or without an applied magnetic field, which would allow for a memory compatible with superconducting systems. However, the complicated hyperfine structure has prevented the transitions of 167Er3+:Y2SiO5 from being fully utilised.\nWith the recent publication of new spin Hamiltonian parameters for the ground state of 167Er3+:Y2SiO5, we can predict which transitions should have the longest coherence time at zero field. Based on calculations using these spin Hamiltonian parameters, we used Raman heterodyne spectroscopy to investigate the hyperfine structure of 167Er3+:Y2SiO5 for small magnetic fields and for energy level differences from 600 to 1200 MHz. We observed many transitions from the 4I15/2 ground state, as well as the 4I13/2 excited state that until now has had little investigation regarding its hyperfine structure.\nBy comparing our spectra to the existing ground state spin Hamiltonian parameters, and unpublished excited state parameters, we identified the origin of many of the transitions. We observed differences between the predicted transition frequencies from both sets of parameters and the experimental data. The data obtained using Raman heterodyne was used to improve both ground and excited state parameters to give a better description of the zero-field hyperfine splittings.\nIn addition, we identified transitions from both the 4I15/2 ground and 4I13/2 excited state that have a small dependence on magnetic field. These transitions, with zero field frequencies of 879.4 MHz and 896.7 MHz respectively, yielded coherence times of 67 µs and 300 µs at 3.2 K, when measured with a two-pulse spin echo sequence. By using a dynamic decoupling sequence, we extending the coherence times of the transitions at 879.4 MHz to 380 µs and for the transitions at 896.7 MHz, to 1.4 ms.\nThese coherence time measurements demonstrate an improvement of a previous zero field coherence measurement in 167Er3+:Y2SiO5. By operating at lower temperatures, reducing the 167Er3+ ion concentration or using a different transition, it should be possible to extend the coherence time of 167Er3+:Y2SiO5 even further.
Rare-earth doped crystals are promising systems for quantum information processing. In particular, paramagnetic rare earths could be used to build coherent interfaces with optical and microwave photons. In addition, isotopes with nonzero nuclear spins could provide long-lived states for quantum state storage and processing. Yb3+ is particularly interesting in this respect since it is the only paramagnetic rare earth with a spin-21 isotope, which corresponds to the simplest possible level structure. In this paper, we report on the optical and magnetic properties of Yb3+ in the two sites of Y2SiO5, a commonly used crystal for quantum applications. We measured optical inhomogeneous linewidths, peak absorption coefficients, oscillator strengths, and excited-state lifetimes. The Zeeman tensors were also determined in the ground and excited states, as well as the ground-state hyperfine tensor for the 171Yb3+ (I=21) isotope. These results suggest that Yb3+:Y2SiO5 is a promising material for applications like solid-state optical and microwave quantum memories.
In the context of quantum information technologies superconducting qubits (SQs) are very attractive devices for the manipulation of quantum states, and present themselves as one of our best candidates to build a quantum processor. They couple naturally to microwave photons, for which suitable quantum memories or a long distance propagation channel don’t exist. A way around these limitations is to turn these microwave photons into optical ones by building a quantum frequency converter: a device by which the frequency of a photon can be changed while preserving its non-classical correlations. Then, optical fibres could be used to link distant SQ-based devices together, facilitating the creation of a network of quantum computers. Moreover, SQs could then be coupled to quantum memories compatible with photons at optical frequencies, which are the most well developed kind of quantum memories at the present time. This thesis explores the possibility to convert single microwave photons into optical photons using erbium doped in a yttrium orthosilicate crystal (Er3+:Y2SiO5). Er3+:Y2SiO5 is a good candidate because it has a naturally occurring optical transition near 1536 nm close to the point where silica optical fibres show their minimum loss. A microwave transition can be found in two different ways: one way is to use the 167 isotope of erbium, which is the only stable isotope that shows hyperfine splitting as it has non-zero nuclear spin. The hyperfine structure of the ground state of 167Er3+:Y2SiO5 spans over about 5 GHz. The other possibility is to use the other stable isotopes of erbium and Zeeman split their ground state using an external magnetic field. A microwave transition near 5 GHz can be achieved with moderate magnetic fields due to the high 𝑔-factors of Er3+:Y2SiO5. The physical process of interest is a three wave mixing process involving two fields at optical frequencies and one field at microwave frequencies. In order to boost the efficiency of the frequency conversion process the Er3+:Y2SiO5 crystal is placed inside a microwave and an optical resonator. The problem is first explored from the theoretical point of view, where a nonlinear coefficient Λ(2) is derived (analogous to the 𝜒(2) often used in nonlinear optics), and the interaction between cavity modes and the nonlinear medium is studied. It is predicted that with a sample cooled down to millikelvin temperatures total frequency conversion between microwave and optical fields can be achieved. A preliminary hole burning spectroscopy experiment is performed with the objective of reconstructing the hyperfine structure of the excited state of 167Er3+:Y2SiO5, but the complexity of the problem makes it too difficult to achieve this goal. Then a series of experiments are shown, aimed at determining whether or not frequency conversion at the single photon level is achievable using the even isotopes of erbium in a magnetic field. These experiments are based in the Raman heterodyne spectroscopy technique, which is used in combination with electron paramagnetic resonance and optical absorption spectroscopy. In all experiments the sample is cooled down to cryogenic temperatures near 4 K. A first experiment shows that the frequency conversion process exists in Er3+:Y2SiO5, in a setup where only a microwave resonator is used, but not an optical one. A second experiment is performed in a similar setup, this time presenting a quantitative study of the properties of the frequency conversion process, and its comparison with the theoretical model previously derived. A third experiment is performed, which incorporates an optical cavity to the system. The interaction between the erbium ions and the optical cavity introduces a whole new range of experimental complications, which are studied and discussed. Then, the frequency conversion signal is studied anew, showing an unexpected highly non-linear scaling behaviour with the input powers. A hypothesis explaining this unexpected behaviour is given, referring to stray optical absorption in the inhomogeneous line of Er3+:Y2SiO5 (and in particular 167Er3+:Y2SiO5), which can be bleached out under certain circumstances due to spectral hole burning effects. The overall maximum frequency conversion efficiency observed is of 3 × 10^−4 per Watt of pump laser power. While this value is still far from the target several ways of improvement are proposed, including cooling down the system to millikelvin temperatures, increasing the dopant concentration and modifying the geometry of the resonators.
Efficient and reversible optical to microwave transducers are required for entanglement transfer between superconducting qubits and light in quantum networks. Rare-earth-doped crystals with narrow optical and spin transitions are a promising system for enabling these devices. Current resonant transduction approaches use ground-state electron spin transitions that have coherence lifetimes often limited by spin flip-flop processes and spectral diffusion, even at very low temperatures. We investigate spin coherence in an optically excited state of an Er^{3+}: Y_{2}SiO_{5} crystal at temperatures from 1.6 to 3.5 K for a low 8.7 mT magnetic field compatible with superconducting resonators. Spin coherence and population lifetimes of up to 1.6 μs and 1.2 ms, respectively, are measured by optically detected spin echo experiments. Analysis of decoherence processes suggest that ms coherence can be reached at lower temperatures for the excited-state spins, whereas ground-state spin coherence would be limited to a few μs due to resonant interactions with other Er^{3+} spins in the lattice and greater instantaneous spectral diffusion from the radio-frequency control pulses. We propose a quantum transducer scheme with potential for close to unity efficiency that exploits the advantages offered by spin states of the optically excited electronic energy levels.