We report microwave to optical upconversion in isotopically purified erbium-doped yttrium orthosilicate in a Fabry-Pérot resonator at millikelvin temperatures. This follows on from investigations made at higher temperatures and with natural isotopic ratios for the erbium dopants. In these previous investigations the highest efficiency was seen only for moderately strong microwave powers. The removal of the unwanted erbium-167 which has hyperfine structure and provides unwanted background optical absorption, and the lower temperatures has removed this problem. We now see efficiencies still increasing as the microwave power is decreased when we reach the smallest input powers for which we could measure an output. Efficiencies of $2\times10^{-6}$ were observed and we discuss potential improvements, including better optical cavity frequency stability and better thermalisation of the erbium spins.
We report microwave to optical upconversion in isotopically purified erbium-doped yttrium orthosilicate in a Fabry-Pérot resonator at millikelvin temperatures. This follows on from investigations made at higher temperatures and with natural isotopic ratios for the erbium dopants. In these previous investigations the highest efficiency was seen only for moderately strong microwave powers. The removal of the unwanted erbium-167 which has hyperfine structure and provides unwanted background optical absorption, and the lower temperatures has removed this problem. We now see efficiencies still increasing as the microwave power is decreased when we reach the smallest input powers for which we could measure an output. Efficiencies of 2×10−6 were observed and we discuss potential improvements, including better optical cavity frequency stability and better thermalisation of the erbium spins.
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.
The subject of this thesis is coherent conversion from microwave photons to optical photons. This has applications for quantum computing, and would allow interfacing between superconducting qubits and optical fibres. Specifically, we will focus on photon conversion via erbium ions in a doped crystal. \n\nWe model a device which has an erbium doped crystal inside overlapping microwave and optical cavities. Input microwave photons are combined with photons from an optical pump laser via interactions with the erbium ions. This will produce optical output photons carrying the same quantum information as the input microwave photons. We develop a description of the interaction between the atoms and the light fields, accounting for both loss effects in the single atoms, and inhomogeneous broadening of the ensemble. Our theory is compared with experimental data, and shows good agreement. \n \nWe explore various phenomena which arise in this system, including the effects of temperature and microwave power. \n\nIt is shown that the description of this device from earlier work is not valid in the regime where the conversion efficiency is greatest. Hence, this work is necessary to be able to predict the maximum conversion efficiency. \n\nWe develop a linearised model which is accurate in the regime where the microwave and optical fields are small, such as the regime used for quantum information. This model is used to maximise the photon number conversion efficiency of the device. We predict conversion efficiencies above 20%, far higher than has been achieved experimentally with using rare earth ions. Modifying our device should further increase the conversion efficiency to above 80%.
The ability to convert quantum states from microwave photons to optical photons is important for hybrid system approaches to quantum information processing. We report the up-conversion of a microwave signal into the optical telecommunications wavelength band using erbium dopants in a yttrium orthosilicate crystal via stimulated Raman scattering. The microwaves were applied to the sample using a three-dimensional copper loop-gap resonator and the coupling and signal optical fields were single passed. The conversion efficiency was low, in agreement with a theoretical analysis, but can be significantly enhanced with an optical resonator.
Rare-earth ions in solids are under active investigation for quantum microwave-optical signal converters. Here, light passed through an Er:YSO crystal sitting in a driven microwave resonator develops modulation due to three-wave mixing in the erbium dopants. Strong coupling between the microwave cavity and the spins causes modulation when the microwaves are resonant with the spin-cavity polaritons rather than the spins. This work extends the rare-earth microwave-optical conversion to both millikelvin temperatures and isotopically pure dopants.
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.
Yttrium orthosilicate ( \nY \n2 \nSi \nO \n5 \n, or YSO) has proved to be a convenient host for rare-earth ions used in demonstrations of microwave quantum memories and optical memories with microwave interfaces and shows promise for coherent microwave-optical conversion owing to its favorable optical and spin properties. The strong coupling required by such microwave applications could be achieved using superconducting resonators patterned directly on \nY \n2 \nSi \nO \n5 \n and hence we investigate here the use of \nY \n2 \nSi \nO \n5 \n as an alternative to sapphire or silicon substrates for superconducting-hybrid-device fabrication. A \nNb \nN \n resonator with frequency 6.008 GHz and low-power quality factor \nQ \n≈ \n400 \n000 \n is fabricated on a \nY \n2 \nSi \nO \n5 \n substrate doped with isotopically enriched \n145 \nNd \n. Measurements of dielectric loss yield a loss tangent \ntan \n \nδ \n= \n4 \n× \n10 \n− \n6 \n, comparable to that of sapphire. Electron spin resonance (ESR) measurements performed using the resonator show the characteristic angular dependence expected from the anisotropic \n145 \nNd \n spin and the coupling strength between the resonator and the electron spins is in the high-cooperativity regime ( \nC \n= \n30 \n). These results demonstrate that \nY \n2 \nSi \nO \n5 \n is an excellent substrate for low-loss, high- \nQ \n microwave resonators, especially in applications for coupling to optically accessible rare-earth spins.