Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Abstract

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...

Multiple-Quantum Transitions and Charge-Induced Decoherence of Donor Nuclear Spins in Silicon

“…Since this is reflected in the time evolution as p∆ν, we expect the effect of such disturbances on T 2 to be anti-proportional to p. Accordingly, the ratios T SQT 2 : T DQT 2 : T TQT 2 = 6 : 3 : 2 should be observed if the limiting process is an effective field interaction. This is in good agreement with experiment, suggesting that a field-like interaction, such as the dipolar interaction with environmental 29 Si spins [37,38] or fluctuations of the external magnetic field, is responsible for the decay of all coherences in the As + nuclear spin system. Since we have observed significantly longer coherence times in purified 28 Si samples using the same magnetic field setup [39], we can conclude that interactions with the 29 Si nuclear spin bath limit the coherence in our samples.…”

Entanglement and control of single nuclear spins in isotopically engineered silicon carbide

“…Our results underline the importance of isotopic engineering in designing materials for solid-state quantum applications. Such engineering can provide a two-fold benefit for quantum memories: it enables control of more nuclear spins by unlocking access to memories with low hyperfine coupling, while also drastically increasing the coherence of these nuclear spins 54 . Moreover, isotopic engineering enables the selection of a hyperfine distribution that can optimally trade off the effect of the "frozen core" 55 against the electron spin induced noise inherent in realistic quantum communications protocols 30 .…”

A photonic platform for donor spin qubits in silicon

“…group V) systems results in donor spin qubits' ultra-long coherence times [1]. These coherence times rely upon the removal of magnetic noise due to naturally-occurring 29 Si spin 1/2 isotope in the host lattice [23], which also removes local mass variations that inhomogeneously broaden donors' optical transitions [24].…”

“…Perturbation coupling terms, such as those arising due to electric fields ( 18 , 19 ), strain ( 20 ), and phonons ( 21 ), are weak, which in similar (that is, group V) systems result in donor spin qubits’ ultralong coherence times in enriched 28 Si ( 1 ). These coherence times rely on the removal of magnetic noise due to the naturally occurring 29 Si spin- isotope in the host lattice ( 22 ), which also removes local mass variations that inhomogeneously broaden donors’ optical transitions ( 23 ).…”