The initialization and manipulation of quantum information stored in silicon by bismuth dopants

The initialization and manipulation of quantum information stored in silicon by...

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Temperature (K)

Si:BiSi:P

TS from fit to exp (¬ 2t/T2¬ (2t)n/TnS) CPMG decay

Fit to T1 T1 for higher concentration (ref. 24)

Figure 4 | Storage times for classical (T1) and quantum (T2) information. Electron spin relaxation times as a function of temperature for Si:Bi, with measurements of Si:P for comparison. Our Si:Bi sample has a concentration of ∼3×1015 Bicm−3. The blue squares are the T1, the yellow circles are the monoexponential T2 values, the red circles and the purple hexagons are the T2 and TS values respectively from the fit to the function e−2t/T −(2t) /T and the green triangles are the CPMG decays. The blue line is a fit to our T1 measurements described in the main text. For comparison, the same set of measurements with Si:P (concentration ∼1015 cm−3) is shown with smaller shapes. The grey filled squares are T1 measurements from ref. 24 for a more concentrated (4×1016 cm−3) sample of Si:Bi.

to access the excited 1s(T2) states where two-phonon Orbach spin-lattice relaxation occurs strongly25. This means that in the

LETTERS NATUREMATERIALSDOI:10.1038/NMAT2828 temperature regime where Orbach effects dominate, the T1 time of

Bi is longer than all other group v donors in Si (ref. 24). The T1 times measured here follow the same temperature dependence as those in ref. 24, but the higher spin concentration of 4×1016 cm−3 used in that work led to shorter relaxation times. A similar concentration-dependenteffecthasbeendescribedforSi:P(ref.26).

For temperatures below 14K, the spin echo decay in Si:Bi is limited by the 4.7% of Si nuclei with spin 1/2 that provide the TS decay. With an isotopically pure sample of 28Si:Bi this contribution would not have been present, revealing the magnitude of other interactions such as the weak dipolar coupling to other Si:Bi electron spins. To remove some of the effects of the 29Si decoherence at temperatures between 8 and 12K, we applied a train of 1,020 pi pulses23,27 (Fig. 3c). With this Carr–Purcell–Meiboom– Gill (CPMG) sequence, sources of decoherence can be dynamically decoupled, including not only the coupling to 29Si nuclei, but also instrumental imperfections in the spectrometer.

The CPMG decay at 8K shown in Fig. 3c has an exponential decay time of 17ms. Some CPMG decays have been attributed to a collective response of spin ensembles to pi pulses that are not short enough28. We consider this possibility in the Supplementary Information. The CPMG decays we measure in Si:P are shorter than for Si:Bi in our temperature range, and limited by the T1 time. The T2 time of isotopically pure 28Si:P has been measured11 as 14ms at 6.9K with a Hahn echo sequence, the longest electron spin T2 time in the literature for a solid-state system. A Hahn echo decay of 1.8ms has been reported for the nitrogen–vacancy centre in diamond29; this measurement was at room temperature but required isotopically pure diamond and there is no deterministic fabrication paradigm here to rival those already working in silicon2. Furthermore, although the diamond results were obtained with a single electron spin, electrical detection is moving in the direction of single electron spin readout of donors in silicon4,9. The differing resonant frequencies of dopants in slightly different environments maypermitselectiveaddressing13.Ourresultsare clearlysufficiently promising to warrant the fabrication of high-quality crystals of isotopically pure 28Si : Bi. Such a sample would be particularly exciting in light of a presentation at a recent workshop30 reporting an unpublished measurement of T2 =0.6s for isotopically purified 28Si:P. In analogy with the observations in 28Si:P, the Si:Bi T2 should increase towards the limiting value of 2T1. The very long spin coherence times we measure show that Si:Bi is well suited for storing quantum information. We have flipped the electron spin in a time of 13ns, and find T2 = 2ms: over 105 times longer. We conclude that quantum information processing in silicon can be based not only on phosphorus dopants, but also bismuth dopants and combinations of the two, as required in schemes13,15 where the dopants with higher binding energies function as qubits and the others are the control bits, regulated for example by terahertz radiation5.

Note added in proof: We discuss some of the extra possibilities for Si:Bi quantum information processing in ref 31. Also, while carrying out further experiments and preparing our manuscript for resubmission following initial refereeing, an online preprint appeared reporting pulsed ESR and ENDOR of bismuth dopants in non-isotopically purified silicon with low magnetic fields of up to 0.6 T (ref. 32).

Methods

The samples used here are single float-zone crystals of silicon, bulk doped in the melt with bismuth atoms. A 2×2×4mm sample with a concentration estimated as 3×10 Bicm was used for the 9.7GHz measurements, whereas a ∼4×10 Bicm sample (1×2×4mm) was used for the measurements at 240GHz. For the pulsed ENDOR measurement (Fig. 2a) we applied white light to shorten the electron spin T time , enabling a shorter shot repetition time. The same light source was used in Fig. 1b.

The highest field ESR resonance was used for all of the relaxation times presented here, and short (16ns) pi/2 pulses were used to excite the entire EPR resonance. To measure the Hahn echo decays (such as Fig. 3a), single shots were collected and the magnitudes of the echo signals were averaged . Our calibrated Cernoxthermometerwasusedtocontrolthetemperatureto±0.1K.

Received 15 July 2009; accepted 6 July 2010; published online 15 August 2010

References

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Acknowledgements

We thank B. Pajot for supplying the Si:Bi samples. Our research was supported by the RCUK Basic Technologies programme, the EPSRC programme grant COMPASSS and a Wolfson Royal Society Research Merit Award. The National High Magnetic Field

Laboratory is supported by NSF Cooperative Agreement No. DMR-0654118, and by the State of Florida. G.W.M. is supported by an 1851 Research Fellowship.

Author contributions

G.W.M., M.W. and C.W.M.K. carried out the experiments at 9.7GHz; G.W.M. and J.v.T. carried out the experiments at 240GHz. G.W.M. and P.T.G. carried out the simulations. G.W.M. analysed the data, which were interpreted by G.W.M., A.M.S., J.v.T., C.W.M.K. andG.A.TheLetterwaswrittenbyG.W.M.,A.M.S.,J.v.T.,C.W.M.K.andG.A.

Additional information

The authors declare no competing financial interests. Supplementary information accompanies this paper on w.nature.com/naturematerials. Reprints and permissions information is available online at http://npg.nature.com/reprintsandpermissions. CorrespondenceandrequestsformaterialsshouldbeaddressedtoG.W.M.

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