Quantum Computing Hardware based on Rare-Earth-Ion Doped Whispering-Gallery Mode Resonators

Abstract

Rare-earth-ion doped crystals are an interesting system for quantum computing investigations due to their long optical and hyperfine coherence times. In particular, the ground-state coherence times can be longer than one second, which makes them perfect for long-term storage of quantum states. They also have the advantage of being a solid-state system. At present, many of the fundamental requirements for quantum computing have been demonstrated using rare-earth-ions; however, quantum state readout has yet to be achieved. The strong-coupling regime is of great importance in cavity quantum electrodynamics, as in this regime interactions between single atoms and single photons can be realized. Strong coupling thereby provides a method of enabling qubit-qubit interactions. It is desirable to achieve this regime with rare-earth-ion doped resonators, as it would enable on-demand readout of quantum states, a necessity for quantum computing, and provide the scalability required for implementation of quantum networks. This thesis describes the work that has gone into investigating the suitability of rare-earth-ion doped whispering-gallery mode resonators for quantum computing applications. A theoretical analysis of the strong-coupling regime is performed, followed by experiments investigating the properties of ions in resonators, and of new rare-earth-ion materials. A final set of experiments studies a new quantum memory protocol for use with rare-earth-ions. A theoretical investigation is undertaken to determine whether the strong-coupling regime will be attainable with rare-earth-ion doped whispering-gallery mode resonators. Emphasis is given to determining which rare-earth-ion materials will have the best properties when used as resonators. Specific applications of the strong-coupling regime are examined for this system; in particular, whether it will be possible to demonstrate the reversible transfer of quantum states, and detection of single dopants. Experiments are performed, measuring the properties of millimetre-sized Pr3+:Y2SiO5 resonators. Direct measurements of cavity quantum electrodynamics parameters are made using photon echoes, giving good agreement with theoretical predictions. Interactions between the atom and cavity are observed and a theoretical model is presented to describe these effects. Thus, a more realistic picture is obtained of the experimental requirements for achieving the strong-coupling regime. The properties of different rare-earth-ion doped materials are measured and analysed to determine their suitability for quantum computing applications. The spin Hamiltonian parameters of Pr3+:YAG are measured using Raman heterodyne spectroscopy, and then used to find the optical transitions with zero first-order Zeeman shift, as this should allow the coherence time to be extended to a point where this system is useful for resonator applications. Hyperfine transitions with zero first-order Zeeman shift are also calculated for Er3+:Y2SiO5, with the aim of enabling long-term storage in a telecommunication-wavelength memory. The thesis concludes with an experimental investigation into a new quantum memory technique that does not require spectral hole burning. The hybrid photon echo rephasing protocol uses strong optical pulses to perform rephasing, thus utilizing the advantageous properties of the two-pulse photon echo. Furthermore, the use of external broadening fields removes the usual problem of noise from amplified spontaneous emission. The properties of this memory are examined using a Pr3+:Y2SiO5 crystal.