Initialisation, control and readout of a nuclear-magnon quantum register

Semiconductor quantum dots (QDs) have inherited the long-standing trope: 'artificial atoms' . On one hand this does great justice to their exquisite light-matter interface, allowing the investigation of fundamental, solid-state quantum optics. On the other hand, it downplays the true complexity of the system, since a single QD electron spin is coupled to approximately 100,000 nuclear spins. Combining these two elements, we have an isolated many-body nuclear ensemble interfaced to a central, proxy qubit, which we can interrogate optically. The system then plays host to a plethora of rich spin physics and complex many-body interactions. This can be exploited in the applied physics of quantum information storage and processing, as well as the fundamental exploration of collective phenomena. This thesis begins with a pedagogical review of QD physics ranging through its bound states; their coupling to light; and the hyperfine and quadrupolar coupling of the nuclei to the electron. The interplay of these couplings becomes a tool for the initialisation, control and readout of the mesoscopic nuclear ensemble, which we use to effect the two main results of this work. The first of these is the realisation of an ultra-precise quantum sensor for the detection of the effective magnetic field of a single nuclear-spin excitation -- a nuclear magnon. In this way we readout magnon population in modes distinguished by polarity and nuclear species. This work constitutes a step towards quantum state tomography of nuclear spin-wave superposition states; a valuable tool in the operation of a magnon-based quantum memory. Moreover the sensing of coherent magnon dynamics offers hints towards emerging quantum correlations in the ensemble. The second result involves the design of a quantum-algorithm for the initialisation of the QD nuclei from infinite temperature to a purified state. This is a key requirement to observe and harness the quantum properties of the system. Importantly, our approach is demonstrably capable of purifying a general spin system down to a single macrostate. Moreover, we argue that our algorithm constitutes the optimum approach in the face of real-world dissipation. Experimentally, we achieve a reduction in the nuclear spin fluctuations of two orders of magnitude and engineer non-trivial, designer nuclear states. We further propose an extension to the algorithm for the preparation of quantum states of nuclei. This work, combined with the recent development of highly coherent QD nuclei, promises a route towards a fully fledged magnon-based quantum register.