The understanding of weak measurements and interaction-free measurements has greatly expanded the conceptual and experimental toolbox to explore the quantum world. Here we demonstrate single-shot variable-strength weak measurements of the electron an
d the nuclear spin states of a single $^{31}$P donor in silicon. We first show how the partial collapse of the nuclear spin due to measurement can be used to coherently rotate the spin to a desired pure state. We explicitly demonstrate that phase coherence is preserved throughout multiple sequential single-shot weak measurements, and that the partial state collapse can be reversed. Second, we use the relation between measurement strength and perturbation of the nuclear state as a physical meter to extract the tunneling rates between the $^{31}$P donor and a nearby electron reservoir from data, conditioned on observing no tunneling events. Our experiments open avenues to measurement-based state preparation, steering and feedback protocols for spin systems in the solid state, and highlight the fundamental connection between information gain and state modification in quantum mechanics.
Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual 31-P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmar
king of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized 31-P nucleus of a single P donor in isotopically purified 28-Si. We find average gate fidelities of 99.95 % for the electron, and 99.99 % for the nuclear spin. These values are above certain error correction thresholds, and demonstrate the potential of donor-based quantum computing in silicon. By studying the influence of the shape and power of the control pulses, we find evidence that the present limitation to the gate fidelity is mostly related to the external hardware, and not the intrinsic behaviour of the qubit.
Enhanced electron cooling is demonstrated in a strained-silicon/superconductor tunnel junction refrigerator of volume 40 um^3. The electron temperature is reduced from 300 mK to 174 mK, with the enhancement over an unstrained silicon control (300 mK
to 258 mK) being attributed to the smaller electron-phonon coupling in the strained case. Modeling and the resulting predictions of silicon-based cooler performance are presented. Further reductions in the minimum temperature are expected if the junction sub-gap leakage and tunnel resistance can be reduced. However, if only tunnel resistance is reduced, Joule heating is predicted to dominate.
A small magnetic field is found to enhance relaxation processes in a superconductor thus stabilizing superconductivity in non-equilibrium conditions. In a normal-metal (N) - insulator - superconductor (S) tunnel junction, applying a field of the orde
r of 100 mu T leads to significantly improved cooling of the N island by quasiparticle (QP) tunneling. These findings are attributed to faster QP relaxation within the S electrodes as a result of enhanced QP drain through regions with locally suppressed energy gap due to magnetic vortices in the S leads at some distance from the junction.
We demonstrate significant modification of the electron-phonon energy loss rate in a many-valley semiconductor system due to lattice mismatch induced strain. We show that the thermal conductance from the electron system to the phonon bath in strained
n + Si, at phonon temperatures between 200 mK and 450 mK, is more than an order of magnitude lower than that for a similar unstrained sample.
