Macroscopic control of quantum states is a major theme in much of modern physics because quantum coherence enables study of fundamental physics and has promising applications for quantum information processing. The potential significance of quantum computing is recognized well beyond the physics community. For electron spins in GaAs quantum dots, it has become clear that decoherence caused by interactions with the nuclear spins is a major challenge. We propose to investigate and reduce hyperfine induced decoherence with two complementary approaches: nuclear spin state narrowing and nuclear spin polarization. We propose a new projective state narrowing technique: a large, Coulomb blockaded dot measures the qubit nuclear ensemble, resulting in enhanced spin coherence times. Further, mediated by an interacting 2D electron gas via hyperfine interaction, a low temperature nuclear ferromagnetic spin state was predicted, which we propose to investigate using a quantum point contact as a nuclear polarization detector. Estimates indicate that the nuclear ferromagnetic transition occurs in the sub-Millikelvin range, well below already hard to reach temperatures around 10 mK. However, the exciting combination of interacting electron and nuclear spin physics as well as applications in spin qubits give ample incentive to strive for sub-Millikelvin temperatures in nanostructures. We propose to build a novel type of nuclear demagnetization refrigerator aiming to reach electron temperatures of 0.1 mK in semiconductor nanostructures. This interdisciplinary project combines Microkelvin and nanophysics, going well beyond the status quo. It is a challenging project that could be the beginning of a new era of coherent spin physics with unprecedented quantum control. This project requires a several year commitment and a team of two graduate students plus one postdoctoral fellow.
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