Spin readout and addressability of phosphorus-donor clusters in silicon

The spin states of an electron bound to a single phosphorus donor in silicon show remarkably long coherence and relaxation times, which makes them promising building blocks for the realization of a solid-state quantum computer. Here we demonstrate, by high-fidelity (93%) electrical spin readout, that a long relaxation time T1 of about 2 s, at B=1.2 T and T≈100 mK, is also characteristic of electronic spin states associated with a cluster of few phosphorus donors, suggesting their suitability as hosts for spin qubits. Owing to the difference in the hyperfine coupling, electronic spin transitions of such clusters can be sufficiently distinct from those of a single phosphorus donor. Our atomistic tight-binding calculations reveal that when neighbouring qubits are hosted by a single phosphorus atom and a cluster of two phosphorus donors, the difference in their electron spin resonance frequencies allows qubit rotations with error rates ≈10(-4). These results provide a new approach to achieving individual qubit addressability.