Decoherence of nuclear spins in the frozen core of an electron spin

Guichard, Roland; Balian, S. J.; Wolfowicz, Gary; Mortemousque, Pierre-André; Monteiro, T. S.

doi:10.1103/physrevb.91.214303

Cited by 19 publications

(26 citation statements)

References 46 publications

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“…31 The longer coherence time for our isolated neutral 31 P donors supports the "frozen core" picture [19][20][21] where most 29 Si pairs near a central spin are too detuned by the donor electron spin to flip-flop.…”

Section: Fig 3 (Color Online)supporting

confidence: 63%

“…[19][20][21] The main difference between electron and 31 P nuclear spins is the strength of their interactions to the 29 Si spin bath. Contact hyperfine interactions for an electron spin are much stronger than dipolar interactions for a 31 P nuclear spin, therefore the same 29 Si bath decoheres the electron spin faster than the nuclear spin.…”

Section: Fig 3 (Color Online)mentioning

confidence: 99%

“…[19][20][21] This protection might not be required in high purity isotopically enriched silicon, with a low content of 29 Si, where 29 Siinduced spectral diffusion is no longer a dominant source of decoherence.…”

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confidence: 99%

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Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Petersen¹,

Tyryshkin²,

Morton³

et al. 2016

Phys. Rev. B

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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...

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Section: Fig 3 (Color Online)supporting

confidence: 63%

Section: Fig 3 (Color Online)mentioning

confidence: 99%

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Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Petersen¹,

Tyryshkin²,

Morton³

et al. 2016

Phys. Rev. B

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“…Nevertheless, we shall admit that a deeper insight into the nuclear spin dynamics in the presence of polarizing electronic spins can be reached only with the developing of specific theoretical models. Quite advanced theoretical models have already been developed for donors in silicon, NV-centers in diamond and quantum dots [49][50][51]. For the case of RE-doped crystals only simple model was numerically studied [26].…”

Section: Temperature Dependence Of Optical Dephasingmentioning

confidence: 99%

Optical coherence of¹⁶⁶Er:⁷LiYF₄crystal below 1 K

et al. 2018

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We explore optical coherence and spin dynamics of an isotopically purified 166 Er: 7 LiYF 4 crystal below 1 K and at weak magnetic fields < 0.3T. Crystals were grown in our lab and demonstrate narrow inhomogeneous optical broadening down to 16MHz. Solid-state atomic ensembles with such narrow linewidths are very attractive for implementing of off-resonant Raman quantum memory and for the interfacing of superconducting quantum circuits and telecom C-band optical photons. Both applications require a low magnetic field of ∼10mT. However, at conventional experimental temperatures T>1.5K, optical coherence of Er:LYF crystal attains m 10 s time scale only at strong magnetic fields above 1.5 T. In the present work, we demonstrate that the deep freezing of Er:LYF crystal below 1 K results in the increase of optical coherence time to m 100 s at weak fields.

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“…The distant 29 Si spin pairs have negligible hyperfine interaction with the donor electron spin and are therefore not significantly detuned from one another, allowing for flipflops [35]. Their small coupling with the measured nuclear spin is compensated by the very large number of pairs involved in the process (≈10 8 [36]). The second type of 29 Si spin pair, recently identified in [36], consists of the few spin pairs that are much closer to the donor and are located at lattice sites that are equivalent by symmetry.…”

Section: Coherence Measurementsmentioning

confidence: 99%

²⁹Si nuclear spins as a resource for donor spin qubits in silicon

et al. 2016

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Nuclear spin registers in the vicinity of electron spins in solid state systems offer a powerful resource to address the challenge of scalability in quantum architectures. We investigate here the properties of 29 Si nuclear spins surrounding donor atoms in silicon, and consider the use of such spins, combined with the donor nuclear spin, as a quantum register coupled to the donor electron spin. We find the coherence of the nearby 29 Si nuclear spins is effectively protected by the presence of the donor electron spin, leading to coherence times in the second timescale-over two orders of magnitude greater than the coherence times in bulk silicon. We theoretically investigate the use of such a register for quantum error correction (QEC), including methods to protect nuclear spins from the ionisation/neutralisation of the donor, which is necessary for the re-initialisation of the ancillae qubits. This provides a route for multi-round QEC using donors in silicon.

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Decoherence of nuclear spins in the frozen core of an electron spin

Cited by 19 publications

References 46 publications

Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Optical coherence of¹⁶⁶Er:⁷LiYF₄crystal below 1 K

²⁹Si nuclear spins as a resource for donor spin qubits in silicon

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Decoherence of nuclear spins in the frozen core of an electron spin

Cited by 19 publications

References 46 publications

Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Nuclear spin decoherence of neutralP31donors in silicon: Effect of environmentalSi29nuclei

Optical coherence of166Er:7LiYF4crystal below 1 K

29Si nuclear spins as a resource for donor spin qubits in silicon

Contact Info

Product

Resources

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Optical coherence of¹⁶⁶Er:⁷LiYF₄crystal below 1 K

²⁹Si nuclear spins as a resource for donor spin qubits in silicon