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.
Long coherence times and fast gate operations are desirable but often conflicting requirements for physical qubits. This conflict can be resolved by resorting to fast qubits for operations, and by storing their state in a `quantum memory while idle.
The $^{31}$P donor in silicon comes naturally equipped with a fast qubit (the electron spin) and a long-lived qubit (the $^{31}$P nuclear spin), coexisting in a bound state at cryogenic temperatures. Here, we demonstrate storage and retrieval of quantum information from a single donor electron spin to its host phosphorus nucleus in isotopically-enriched $^{28}$Si. The fidelity of the memory process is characterised via both state and process tomography. We report an overall process fidelity of $F_p =$81${pm}$7%, a memory fidelity ($F_m$) of over 90%, and memory storage times up to 80 ms. These values are limited by a transient shift of the electron spin resonance frequency following high-power radiofrequency pulses.
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.
We experimentally investigate the non-resonant feeding of photons into the optical mode of a zero dimensional nanocavity by quantum dot multiexciton transitions. Power dependent photoluminescence measurements reveal a super-linear power dependence of
the mode emission, indicating that the emission stems from multiexcitons. By monitoring the temporal evolution of the photoluminescence spectrum, we observe a clear anticorrelation of the mode and single exciton emission; the mode emission quenches as the population in the system reduces towards the single exciton level whilst the intensity of the mode emission tracks the multi-exciton transitions. Our results lend strong support to a recently proposed mechanism mediating the strongly non-resonant feeding of photons into the cavity mode.
We report the design, fabrication and optical investigation of electrically tunable single quantum dot - photonic crystal defect nanocavities operating in both the weak and strong coupling regimes of the light matter interaction. Unlike previous stud
ies where the dot-cavity spectral detuning was varied by changing the lattice temperature, or by the adsorption of inert-gases at low temperatures, we demonstrate that the quantum confined Stark effect can be employed to quickly and reversibly switch the dot-cavity coupling simply by varying a gate voltage. Our results show that exciton transitions from individual dots can be tuned by ~4 meV relative to the nanocavity mode before the emission quenches due to carrier tunneling escape. This range is much larger than the typical linewidth of the high-Q cavity modes (~0.10 meV) allowing us to explore and contrast regimes where the dots couple to the cavity or decay by spontaneous emission into the 2D photonic bandgap. In the weak coupling regime, we show that the dot spontaneous emission rate can be tuned using a gate voltage, with Purcell factors >=7. New information is obtained on the nature of the dot-cavity coupling in the weak coupling regime and electrical control of zero dimensional polaritons is demonstrated for the highest-Q cavities (Q>=12000). Vacuum Rabi splittings up to ~0.13 meV are observed, much larger than the linewidths of either the decoupled exciton or cavity mode. These observations represent a voltage switchable optical non-linearity at the single photon level, paving the way towards on-chip dot based nano-photonic devices that can be integrated with passive optical components.
