Superconducting qubits are currently one of the leading qubit designs, showing great success in some of the world's most powerful quantum computers. Superconducting qubits, however, communicate at microwave frequencies, which is problematic when it comes to the task of long distance communication as unless the communication channel is cryogenically cooled the microwave photons are swamped by thermal noise. Optical photons, on the other hand, are ideal for long distance communication, particularly at frequencies that lie within the telecommunications band. One solution to the superconducting qubits communication problem is to create a device that can convert an input microwave photon into an optical photon with unit quantum efficiency. A device of such could then be used alongside existing optical fibre networks to connect distant superconducting processors. Furthermore, an upconversion device would allow superconducting qubit systems to take advantage of quantum technologies in the optical region, such as optical quantum memories.\n\nSeveral different approaches have been taken in attempts to experimentally implement such a device. Recently a theoretical proposal showed that the strong non-linearities that occur near the collective resonances in fully concentrated rare-earth crystals can be used to efficiently upconvert microwave photons. In this thesis we begin experimental investigations of two fully concentrated rare-earth crystals, GdVO4 and DyPO4, for their application to microwave upconversion.\n\nAbsorption spectra of the two crystals in the optical region are measured using a Fourier transform infrared spectrometer, in order to characterise and explore the possible optical states to be used in the upconversion process. Experiments are then carried out at microwave frequencies to explore the coupling between the collective spin resonances (magnons) that occur within the crystals and a microwave cavity. It is found that not only can the ultrastrong coupling regime be reached in these systems but that the linewidth of the magnon mode is narrow, measuring 35MHz at T = 25mK. This is the first experimental evidence of ultrastrong coupling between a microwave cavity and antiferromagnetic magnon modes in a rare-earth crystal. Furthermore, narrow transition linewidths are a crucial requirement in the proposed upconversion method, therefore the narrow linewidth experimentally measured here is an important validation of the proposals feasibility. \n\nThe results presented in this thesis show that microwave upconversion mediated by fully concentrated rare-earth crystals has an exciting future. Perhaps one day rare-earth crystals will be used to overcome the major communication problem superconducting qubits currently face.
Superconducting qubits are currently one of the leading qubit designs, showing great success in some of the world's most powerful quantum computers. Superconducting qubits, however, communicate at microwave frequencies, which is problematic when it comes to the task of long distance communication as unless the communication channel is cryogenically cooled the microwave photons are swamped by thermal noise. Optical photons, on the other hand, are ideal for long distance communication, particularly at frequencies that lie within the telecommunications band. One solution to the superconducting qubits communication problem is to create a device that can convert an input microwave photon into an optical photon with unit quantum efficiency. A device of such could then be used alongside existing optical fibre networks to connect distant superconducting processors. Furthermore, an upconversion device would allow superconducting qubit systems to take advantage of quantum technologies in the optical region, such as optical quantum memories.\n\nSeveral different approaches have been taken in attempts to experimentally implement such a device. Recently a theoretical proposal showed that the strong non-linearities that occur near the collective resonances in fully concentrated rare-earth crystals can be used to efficiently upconvert microwave photons. In this thesis we begin experimental investigations of two fully concentrated rare-earth crystals, GdVO4 and DyPO4, for their application to microwave upconversion.\n\nAbsorption spectra of the two crystals in the optical region are measured using a Fourier transform infrared spectrometer, in order to characterise and explore the possible optical states to be used in the upconversion process. Experiments are then carried out at microwave frequencies to explore the coupling between the collective spin resonances (magnons) that occur within the crystals and a microwave cavity. It is found that not only can the ultrastrong coupling regime be reached in these systems but that the linewidth of the magnon mode is narrow, measuring 35MHz at T = 25mK. This is the first experimental evidence of ultrastrong coupling between a microwave cavity and antiferromagnetic magnon modes in a rare-earth crystal. Furthermore, narrow transition linewidths are a crucial requirement in the proposed upconversion method, therefore the narrow linewidth experimentally measured here is an important validation of the proposals feasibility. \n\nThe results presented in this thesis show that microwave upconversion mediated by fully concentrated rare-earth crystals has an exciting future. Perhaps one day rare-earth crystals will be used to overcome the major communication problem superconducting qubits currently face.
Most investigations of rare-earth ions in solids for quantum information have used crystals where the rare-earth ion is a dopant. Here, we analyze 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. These concentrated crystals are attractive for frequency conversion because of their large ion densities and small linewidths. We show that conversion with both high efficiency and large bandwidth is possible in these crystals. 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 modes in the crystal.
The quantum bits (qubits) on which superconducting quantum computers are based have energy scales corresponding to photons with GHz frequencies. The energy of photons in the gigahertz domain is too low to allow transmission through the noisy room-temperature environment, where the signal would be lost in thermal noise. Optical photons, on the other hand, have much higher energies, and signals can be detected using highly efficient single-photon detectors. Transduction from microwave to optical frequencies is therefore a potential enabling technology for quantum devices. High conversion efficiency and high fidelity (the similarity of input microwave state to the output optical state.) are important characteristics of these devices. In such devices, the efficiency of the up-conversion process is typically improved by increasing the power in the pump. In addition to this, the optical pump is dissipated as thermal photons via absorption-induced heating into the system. Since the frequency of thermal photons and qubits are in the same range, this can affect the quality of the transferred quantum state which is characterized by fidelity. Thus, the optical pump can be a source of thermal noise and degrade the fidelity. Realizing an optimum pump power level while investigating its effect on fidelity via temperature are important tasks in the evolution of these upconversion devices. In this work, we explore two kinds of hybrid quantum devices that can be used as frequency upconverts; the first one is a resonant electro-optic modulator consisting of a microwave cavity and a WGM resonator (made of LiNbO3) and the next one is a magneto-optic modulator consisting of a microwave cavity and the rare earth crystal gadolinium vanadate (GdVO4) in the cuboid shape. We model the sub-Kelvin thermal behavior of an electro-optic transducer based on a lithium niobate whispering gallery mode resonator. We compute thermal photon numbers and find that there is an optimum power level for a continuous pump, whilst pulsed operation of the pump increases the fidelity of the conversion. In the magneto-optic modulator via photon-magnon coupling, we investigate the effect of GdVO4 temperature on the linewidth of magnons and the strength of photon-magnon coupling inside a dilution refrigerator. In the next step, we investigate the effect of absorption-induced heating of GdVO4 on the linewidth of magnons and the strength of photon-magnon coupling inside a dilution refrigerator, and the temperature of GdVO4 is estimated via comparison of two methods. The effect of heating of the GdVO4 via the mentioned methods on the transmission spectrum and the resonance frequency of the microwave cavity is studied. The transmission spectrum is used to comprehend the time evolution of the thermal equilibrium of the sample and estimate its temperature.
Microwave and optical transitions of rare-earth ions enable microwave-to-optical frequency transduction. This transduction is a coherent process; therefore, the narrow linewidths and long coherence times of rare-earth ions are crucial for achieving efficient frequency conversion. Particularly long coherence times can be achieved with small-spin materials, as unpaired electronic and nuclear spins introduce magnetic noise, serving as a decoherent source of the transitions. However, complete spin-free rare-earth materials cannot exist without charge compensation. Consequently, residual spins in existing rare-earth materials act as a bottleneck, limiting both their spin and optical coherence times. Rather than focusing on nearly spin-free materials, this thesis investigates the microwave and optical transitions of rare-earth ions in materials that are fully concentrated with electronic spins. Recent studies on rare-earth magnetic materials have demonstrated narrow optical linewidths resulting from magnetic ordering and a particularly strong coupling between microwave cavity modes and the collective excitations of rare-earth ions. Although these recent studies are noteworthy, the energy-level transitions, especially optical transitions, of rare-earth ions in magnetic materials remain largely unexamined. In this thesis, various spectroscopic studies are employed to characterise their transition properties and to develop a model of energy levels. The model presented is expected to be applicable to other rare-earth magnetic materials, thereby opening avenues for further investigation in this class of systems. Two types of rare-earth magnetic materials are investigated: neodymium gallate with a stoichiometric concentration of neodymium ions, and gadolinium vanadate doped with a low (ppm) concentration of erbium ions. Microwave and optical transmission spectroscopy are employed under externally applied magnetic fields to characterise the energy-state transitions of the rare-earth ions in both materials. The magnetic phases and corresponding spin configurations influence the observed spectra, making conventional approaches to spectral simulation inadequate. To address this challenge, mean field and magnon-coupled crystal-field models are developed in this thesis to predict magnon and optical transition spectra. These simulations exhibit good agreement with experimental results, allowing for the characterisation of transition properties. Following the characterisation of the material, a new transduction approach is introduced, developed, and implemented using doped rare-earth ions in a magnetic material. In this scheme, coherent conversion between microwave and optical modes is achieved by exciting an optical transition of the doped ions.
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%.
Rare-earth doped crystals have proven to be of considerable interest for quantum information processing, with demonstrations of quantum memories and the potential for coherent microwave–optical conversion as part of a quantum network. By interfacing these rare-earth based technologies with superconducting devices, they can complement existing technologies — which form the basis of many state-of-the-art quantum computers — forming a hybrid quantum information processing architecture exhibiting the advantages of fast superconducting processors alongside the extended coherence time and frequency conversion available from rare-earths. This thesis demonstrates the suitability of a widely used rare-earth doped crystal, yttrium orthosilicate (Y2SiO5 or YSO) doped with 145Nd or with 171Yb, as a substrate for fabrication of superconducting resonators. Designs for these resonators are presented with simulations of their electromagnetic modes, and their fabrication detailed. These devices are cooled to milliKelvin temperatures in a dilution refrigerator in order to investigate properties of the device and its coupling to electron spin transitions within the substrate where a coupling rate of the order gens/2π =1.2–7.1 MHz is observed. Dielectric loss due to two-level systems is measured with a loss-tangent tan δ = 4*10−6, and a coupling between resonator and spins is observed to have a high cooperativity C = 8–250. The superconducting resonator is then used to perform pulsed spectroscopy of electron spin resonance (ESR) transitions in the high-cooperativity regime, measuring two-pulse coherence times of T2 = (409 ± 14) μs for 200 ppm 145Nd:Y2SiO5 and T2 = (1170 ± 90) μs for 50 ppm 171Yb:Y2SiO5. Chirped pulses are used to invert spin magnetisation and drive arbitrary rotations, enabling the measurement of relaxation dynamics and Rabi oscillations. Dynamical decoupling sequences are explored as a method for extending coherence time. Experiments exploiting coherence-enhancing 'near-ZEFOZ' transitions in 171Yb are proposed, and continuous-wave measurements are used to demonstrate the working principle of such a scheme.