Decoherence of electron spins in isotopically enriched silicon near Clock Transitions (1509.08326v3)

Abstract: Despite the importance of isotopically purified samples in current experiments, there have been few corresponding studies of spin qubit decoherence using full quantum bath calculations. Isotopic purification eliminates the well-studied nuclear spin baths which usually dominate decoherence. We model the coherence of electronic spin qubits in silicon near so called Clock Transitions (CT) where experiments have electronic $T_{2e}$ times of seconds. Despite the apparent simplicity of the residual decoherence mechanism, this regime is not well understood: the state mixing which underpins CTs allows also a proliferation of contributions from usually forbidden channels (direct flip-flops with non-resonant spins); in addition, the magnitude and effects of the corresponding Overhauser fields and other detunings is not well quantified. For purely magnetic detunings, we identify a regime, potentially favourable for quantum computing, where forbidden channels are completely suppressed but spins in resonant states are fully released from Overhauser fields and applied magnetic field gradients. We show by a general argument that the enhancement between this regime and the high field limit is $< 8$, regardless of density, while enhancements of order 50 are measured experimentally. We propose that this discrepancy is likely to arise from strains of exclusively non-magnetic origin, underlining the potential of CTs for isolating and probing different types of inhomogeneities. We also identify a set of fields, "Dipolar Refocusing Points" (DRPs), where the Hahn echo fully refocuses the effect of the dipolar interaction.