Electron Spin Coherence and Electron Nuclear Double Resonance of Bi Donors in Natural Si

George, Richard E.; Witzel, Wayne; Riemann, H.; Abrosimov, N. V.; Notzel, N.; Thewalt, M. L. W.; Morton, John J. L.

doi:10.1103/physrevlett.105.067601

Cited by 104 publications

(163 citation statements)

References 33 publications

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“…The value of T 2e = 0.7 ms is similar to T 2e found for implanted Sb donors at a lower concentration of 3 × 10 16 cm −3 (5 × 10 15 spins per line / cm 3 ) in the presence of a hydrogen passivated silicon surface [5]. The smaller Bohr radius of Bi-donors and its reduced effective gyromagnetic ratio can contribute to a smaller susceptibility to both surface noise at a given implant depth and to decoherence through coupling to neighboring donors at a given concentration [7]. This favors bismuth for implementation of quantum logic through magnetic dipolar coupling [11].…”

supporting

confidence: 78%

“…Bismuth donors in silicon are unique in exhibiting a relatively large zero field splitting of 7.4 GHz. Thus, they have attracted attention as potential nuclear spin memory and spin qubit candidates [7,8] that could be coupled to superconducting resonators [7,9,10]. Bismuth is the deepest donor in silicon with a binding energy of 70 meV and a corresponding small Bohr radius.…”

mentioning

confidence: 99%

“…The small Bohr radius and bismuth's reduced effective gyromagnetic ratio [7] can make it less susceptible to interface noise at a given implant depth and make bismuth very desirable for quantum logic implementation via magnetic dipolar coupling [11]. Furthermore, bismuth is also the heaviest donor in silicon and thus shows the least ion range straggling during ion implantation, which enables for donor qubit placement with high spatial resolution [12,13].To date, studies of spin resonance properties of bismuth in silicon have been performed with bulk doped natural silicon [7,8,[14][15][16] whereas silicon-28 material is preferable for improved spin coherence properties. Electrical activation of implanted bismuth via thermal anneals has been studied for relatively high implant doses [17][18][19][20][21], and concentrations close to the the metalinsulator transition (N c = 1.7 × 10 19 cm −3 ) [18].…”

mentioning

confidence: 99%

“…To date, studies of spin resonance properties of bismuth in silicon have been performed with bulk doped natural silicon [7,8,[14][15][16] whereas silicon-28 material is preferable for improved spin coherence properties. Electrical activation of implanted bismuth via thermal anneals has been studied for relatively high implant doses [17][18][19][20][21], and concentrations close to the the metalinsulator transition (N c = 1.7 × 10 19 cm −3 ) [18].…”

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confidence: 99%

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Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon-28

Weis

Lang

et al. 2012

Applied Physics Letters

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We have performed continuous wave and pulsed electron spin resonance measurements of implanted bismuth donors in isotopically enriched silicon-28. Donors are electrically activated via thermal annealing with minimal diffusion. Damage from bismuth ion implantation is repaired during thermal annealing as evidenced by narrow spin resonance linewidths (Bpp = 12 µT) and long spin coherence times (T2 = 0.7 ms, at temperature T = 8 K). The results qualify ion implanted bismuth as a promising candidate for spin qubit integration in silicon.Electron and nuclear spins of donor atoms in silicon are excellent qubit candidates for quantum information processing [1, 2]. Isotope engineered substrates provide a nuclear spin free host environment, resulting in long electron and nuclear spin coherence times of several seconds [3,4]. Spin properties of donor qubit candidates in silicon have been studied mostly for phosphorous and antimony [3][4][5][6]. Bismuth donors in silicon are unique in exhibiting a relatively large zero field splitting of 7.4 GHz. Thus, they have attracted attention as potential nuclear spin memory and spin qubit candidates [7,8] that could be coupled to superconducting resonators [7,9,10]. Bismuth is the deepest donor in silicon with a binding energy of 70 meV and a corresponding small Bohr radius. The small Bohr radius and bismuth's reduced effective gyromagnetic ratio [7] can make it less susceptible to interface noise at a given implant depth and make bismuth very desirable for quantum logic implementation via magnetic dipolar coupling [11]. Furthermore, bismuth is also the heaviest donor in silicon and thus shows the least ion range straggling during ion implantation, which enables for donor qubit placement with high spatial resolution [12,13].To date, studies of spin resonance properties of bismuth in silicon have been performed with bulk doped natural silicon [7,8,[14][15][16] whereas silicon-28 material is preferable for improved spin coherence properties. Electrical activation of implanted bismuth via thermal anneals has been studied for relatively high implant doses [17][18][19][20][21], and concentrations close to the the metalinsulator transition (N c = 1.7 × 10 19 cm −3 ) [18]. High implant doses ( 1 × 10 14 cm −2 for keV Bi-ions at room temperature) amorphize the silicon lattice [22]. Solid- * Please contact the corresponding author under cdweis@lbl.gov phase epitaxial regrowth (SPER) can be used to prevent diffusion of bismuth atoms and incorporate them on substitutional sites. This can lead to electrically active concentrations well above the low relatively solubility limit of bismuth in silicon (which is, e.g. 2.3 × 10 17 cm −3 at 1150 ℃ [23]). For SPER, thermal anneals at low temperatures, e.g. few minutes at 600 ℃ yield electrical activation levels of up to 90 % [20]. For low implant doses and dopant concentrations, which are desirable for long spin coherence times, no amorphization of the silicon crystal occurs during ion implantation. Thus, the electrical activation levels and annealing ...

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supporting

confidence: 78%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon-28

Weis

Lang

et al. 2012

Applied Physics Letters

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“…Therefore, examining the conditions for the validity of a classical Gaussian noise model is not only of fundamental interest but also highly desirable for accurate quantum control under realistic conditions. Bismuth donors in silicon (Si:Bi) have recently attracted much attention in spin-based quantum computation due to a number of favorable properties [18][19][20][21]. These include long electron spin coherence times of up to 3 s [22] observed for Bi donors (in isotopically enriched silicon-28) tuned to so-called clock transitions (CTs)-also known as optimal working points [23] or zero first-order Zeeman transitions)-whose frequency is insensitive, to first order, to magnetic field fluctuations.…”

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confidence: 99%

Classical nature of nuclear spin noise near clock transitions of Bi donors in silicon

Wolfowicz

et al. 2015

Phys. Rev. B

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Whether a quantum bath can be approximated as classical Gaussian noise is a fundamental issue in central spin decoherence and also of practical importance in designing noise-resilient quantum control. Spin qubits based on bismuth donors in silicon have tunable interactions with nuclear spin baths and are first-order insensitive to magnetic noise at so-called clock transitions (CTs). This system is therefore ideal for studying the quantum/classical Gaussian nature of nuclear spin baths since the qubit-bath interaction strength determines the back-action on the baths and hence the adequacy of a Gaussian noise model. We develop a Gaussian noise model with noise correlations determined by quantum calculations and compare the classical noise approximation to the full quantum bath theory. We experimentally test our model through a dynamical decoupling sequence of up to 128 pulses, finding good agreement with simulations and measuring electron spin coherence times approaching 1 s-notably using natural silicon. Our theoretical and experimental study demonstrates that the noise from a nuclear spin bath is analogous to classical Gaussian noise if the back-action of the qubit on the bath is small compared to the internal bath dynamics, as is the case close to CTs. However, far from the CTs, the back-action of the central spin on the bath is such that the quantum model is required to accurately model spin decoherence. Introduction. Central spin decoherence due to coupling to the environment is not only a central issue in understanding quantum-to-classical transitions [1,2], but also one of the key challenges in the realization of quantum computation [3]. There are two distinct models to describe the decoherence processes in such cases: in the semiclassical model, the central spin accumulates random phases due to thermal or quantum fluctuations of the environment [4,5], while in the quantum model, the coupling between the central spin and the environment produces entanglement and results in leakage of the which-way information from the central spin to the environment [6][7][8][9]. The fundamental difference between these two models lies in the fact that the classical noise is independent of the central spin state while the quantum noise is governed by the difference of environmental Hamiltonians conditioned on the qubit state, called the back-action from the central spin [10,11].The classical noise model of quantum baths, especially the Gaussian stochastic noise model, is a useful approximation in designing noise-resilient quantum control [12], which would otherwise require a large amount of numerical simulations of many-body dynamics of quantum baths. Dynamical decoupling has been employed to extract the noise spectra of baths [13][14][15][16][17], which are in turn used to design optimal quantum control for protecting quantum coherence and quantum gates. The viability of such methods critically

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Single Ion Implantation of Bismuth

Cassidy

Blenkinsopp

Brown

et al. 2020

Physica Status Solidi (a)

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Herein, the results from a focused ion beam instrument, designed to implant single ions with a view to the fabrication of qubits for quantum technologies, are presented. The difficulty of single ion implantation is accurately counting the ion impacts. This is achieved here through the detection of secondary electrons generated upon each ion impact. The implantation of single bismuth ions with different charge states into Si, Ge, Cu, and Au substrates is reported, and the counting detection efficiency for single ion implants and the factors that affect such detection efficiencies are determined. It is found that for 50 keV implants of Bi++ ions into silicon an 89% detection efficiency can be achieved, which is the first quantitative detection efficiency measurement for single ion implants into silicon without implanting through a thick SiO2 film. This level of counting accuracy provides implantation of single impurity ions with a success rate significantly exceeding that achievable by random (Poissonian) implantation.

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Electron Spin Coherence and Electron Nuclear Double Resonance of Bi Donors in Natural Si

Cited by 104 publications

References 33 publications

Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon-28

Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon-28

Classical nature of nuclear spin noise near clock transitions of Bi donors in silicon

Single Ion Implantation of Bismuth

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