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.
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.
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.
We develop a theoretical description of a device for coherent conversion of microwave-to-optical photons. For the device, dopant ions in a crystal are used as three-level systems, and interact with the fields inside overlapping microwave and optical cavities. We develop a model for the cavity fields interacting with an ensemble of ions and model the ions using an open quantum systems approach, while accounting for the effect of inhomogeneous broadening. Numerical methods are developed to allow us to accurately simulate the device. We also further develop a simplified model, applicable in the case of small cavity fields, which is relevant to quantum information applications. This simplified model is used to predict the maximum conversion efficiency of the device. We investigate the effect of various parameters, and predict that conversion efficiency of above 80% should be possible with currently existing experimental setups inside a dilution refrigerator.
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.
When doped into solid state transparent crystals, rare-earth ions can have optically excited states with milliseconds coherence time and up to six hours coherence time for hyperfine levels after being cooled down to liquid helium temperature. This long coherence property makes them unique as solid state material and attractive for quantum information applications.The rare-earth ions have narrow homogeneous linewidths on the order of ~ kHz. When doped into a crystal, the lattice structure is slightly distorted due to the size mismatch between the dopant and the host ions, resulting in slight differences in the local crystal fields at the dopant sites. Therefore, the resonance frequencies of the rare-earth ions are shifted relatively, resulting in an inhomogeneously broadened absorption profile, typically on the order of a few GHz. This provides the possibility of addressing each group of ions individually and engineering the absorption profile for different purposes by optical pumping using a narrow linewidth laser, and makes rare-earth-ion-doped crystals suitable for ensemble based quantum memories.Quantum memories are vital components for developing longdistance quantum communication. Part of this thesis project focused on making quantum memories with high efficiency and long storage time, especially using materials with low optical depth. To achieve this goal, a low finesse, unsymmetrical cavity was employed and experiments were carried out at (or close to) the impedance matched condition. Atomic frequency comb (AFC) protocol proposed for such an inhomogeneously broadened system was used to store coherent light for a certain time. 56% overall efficiency was achieved, and the main limiting factor for reaching even higher efficiency was the inefficient coupling between incoming light and the cavity mode. Other possible loss mechanisms were analyzed as well.Long-time, on-demand, quantum memory experiments were conducted with the help of two efficient radio-frequency rephasing pulses. Storage time was extended from microseconds to milliseconds after compensating (most of) the residual earth magnetic field in the lab. The opportunities and challenges of combing the cavity assistant quantum memory and the long time, on demand quantum memory were analyzed and possible solutions were proposed. Another part of the thesis project involves slow light-based applications in rare-earth-ion-doped crystals. The strong slow light effect at the presence a spectral hole is due to the fact that the light interacts with the absorbing ions outside the spectral hole off-resonantly, and most of the light energy is stored inside the ions as a polarization. For example, with a group velocity of 300 km/s, 99.9% of the pulse energy is stored in the ions when the pulse propagates inside the crystal. The slower the light propagates, the more energy is stored inside the medium. Based on this, a frequency shifter that is capable of shifting the light frequency of ± 4 MHz was demonstrated, and frequency shift up to GHz was proposed. Group velocity control by a factor of 20 and pulse compression in time by a factor of 2 were also demonstrated. The frequency shift and group velocity of the light are solely controlled by the external electric field, which makes them ideal for weak light situation. The unique property of such a frequency shifter and group velocity controller is that they could be made to accept light from an arbitrary incoming angle and polarization, for example, scattered light.
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%.