Spectral diffusion arising from29 Si nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on 31 P nuclear spin coherence is measured as a function of 29 Si concentration using X-band pulsed electron nuclear double resonance (ENDOR). The 31 P nuclear spin echo decays show that decoherence is controlled by 29 Si flip-flops resulting in both fast (exponential) and slow (non-exponential) spectral diffusion processes. The decay times span a range from 100 ms in crystals containing 50%29 Si to 3 s in crystals containing 1% 29 Si. These nuclear spin echo decay times for neutral donors are orders of magnitude longer than those reported for ionized donors in natural silicon. The electron spin of the neutral donors 'protects' the donor nuclear spins by suppressing 29 Si flip-flops within a 'frozen core', as a result of the detuning of the 29 Si spins caused by their hyperfine coupling to the electron spin.Donors in silicon have been considered for use in quantum information since the early days of the field. 1,2Donors have both electron and nuclear spins which can be manipulated independently, and both have been considered for use as potential quantum bits (qubits). While donor electron spins have received a majority of the attention, 3-6 the nuclear spins are capable of much longer coherence times.7-9 This characteristic was utilized in the original Kane proposal for quantum computing 1 and gained attention later for building a quantum memory. 7While exceptionally long T 2 times of donor nuclear spins in silicon have already been demonstrated, 7,8 the mechanics of nuclear spin decoherence are not yet fully understood. In this study, we focus on neutral 31 P donor nuclear spin decoherence arising from interactions with 29 Si nuclear spins in the silicon host environment.Spectral diffusion due to spin 1/2 29 Si nuclei is a major source of decoherence for donor electron spins in silicon [10][11][12][13] and is predicted to be a major source of decoherence for donor nuclear spins as well.10 While the predicted coherence time for neutral 31 P donor nuclear spins in natural silicon (containing 4.7% 29 Si) was 0.5 s, several experimental works reported much shorter times (from hundreds of microseconds to tens of milliseconds). 14-17Coherence times presented here and by Wolfowicz et al. 18show that the limit from 29 Si spectral diffusion is actually longer than inferred from those previous experiments. To resolve the role of 29 Si spectral diffusion, we measure neutral 31 P nuclear spin coherence times in silicon crystals with 29 Si concentrations ranging from 1% to 50%. 12We find an inverse linear dependence of 31 P nuclear spin coherence time on 29 Si concentration (f), ranging from 100 ms at 50% 29 Si to 3 s at 1% 29 Si. The nuclear spin coherence time is about 1 second in natural silicon at 1.7 K; close to predictions of central spin stochastic models.10 Howeve...
We use the nuclear spin coherence of 31 P donors in 28 Si to determine flip-flop rates of donor electron spins. Isotopically purified 28 Si crystals minimize the number of 29 Si flip-flops, and measurements at 1.7 K suppress electron spin relaxation. The crystals have donor concentrations ranging from 1.2 × 10 14 to 3.3 × 10 15 P/cm 3 , allowing us to detect how electron flip-flop rates change with donor density. We also simulate how electron spin flip-flops can cause nuclear spin decoherence.We find that when these flip-flops are the primary cause of decoherence, Hahn echo decays have a stretched exponential form. For our two higher donor density crystals (> 10 15 P/cm 3 ), there is excellent agreement between simulations and experiments. In lower density crystals (< 10 15 P/cm 3 ), there is no longer agreement between simulations and experiments, suggesting a different, unknown mechanism is limiting nuclear spin coherence. The nuclear spin coherence in the lowest density crystal (1.2 × 10 14 P/cm 3 ) allows us to place upper bounds on the magnitude of noise sources in bulk crystals such as electric field fluctuations that may degrade silicon quantum devices. I. INTRODUCTIONQuantum devices utilizing spins, electron spin resonance (ESR) and nuclear magnetic resonance (NMR) in solids, and magnetic resonance imaging (MRI) can all be affected by electron spin flip-flops. This decoherence mechanism causes errors in spin-based quantum devices, 1 affects electron and nuclear coherence times in ESR and NMR, and can be utilized for dynamic nuclear polarization 2 to enhance signal strength in MRI. 3 A flip-flop occurs when two dipole-dipole coupled electron spins, one spin up and the other spin down, swap their spin states. This is possible so long as the combined energy of the spins does not change. The rates of flip-flops (spin diffusion) can be calculated in
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