Electron spin relaxation times of phosphorus donors in silicon

Donor electron spins in phosphorus-doped silicon (Si:P) are a candidate two-level system (qubit) for quantum information processing. Spin echo measurements of isotopically purified ${}^{28}\mathrm{S}\mathrm{i}:\mathrm{P}$ are presented that show exceptionally long transverse relaxation (decoherence) times, ${T}_{2},$ at low temperature. Below $\ensuremath{\sim}10\mathrm{K}$ the spin decoherence is shown to be controlled by instantaneous diffusion and at higher temperatures by an Orbach process. ${T}_{2}$ for small pulse turning angles is 14 ms at 7 K and extrapolates to $\ensuremath{\sim}60\mathrm{ms}$ for an isolated spin, over 2 orders of magnitude longer than previously demonstrated.