Single-spin quantum coherence beyond 10 seconds in an isotopically engineered silicon nanostructure*

The single-shot readout and coherent control of both the electron and the nuclear spin of a single P atom in silicon has been recently demonstrated, using ion-implanted donors in MOS nanostructures. It is known from bulk experiments that P donors in isotopically purified $^{28}$Si exhibit record coherences, but it is also suspected that the proximity to a Si/SiO$_2$ interface will deteriorate the coherence time. Here we present the first experiment on single electron and nuclear spin qubits in an isotopically engineered $^{28}$Si nanostructure. We measured exceptionally sharp electron spin resonance lines ($< 2$ kHz wide), and we obtained single-qubit control fidelities in excess of $99 \%$. We performed noise spectroscopy experiments to extract the power spectral density of the decoherence sources acting on the electron and the nucleus. Contrary to widespread belief, our data show that the ultimate limit for single-spin coherence in our nanostructure is not set by charge noise and interface effects, but simply by broadband thermal radiation coupled to the qubit through a high-bandwidth transmission line. Using dynamical decoupling, we measured coherence times up to $T_{2e} = 0.5$ s for the electron, and $T_{2n} = 18$ s for the $^{31}$P nucleus.