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arXiv:0712.0141 · Physical Review Letters

Spin Echoes in the Charge Transport through Phosphorus Donors in Silicon

Hans Huebl, Felix Hoehne, Benno Grolik, Andre R. Stegner, M. Stutzmann, Martin S. Brandt

Published Apr 30, 2008• 63 citations
arXivHTMLPDF

Abstract

The electrical detection of spin echoes via echo tomography is used to observe coherent processes associated with the electrical readout of the spin state of phosphorus donor electrons in silicon near a SiO2 interface. Using the Carr-Purcell pulse sequence, an echo decay with a time constant of 1.7+/-0.2 micros is observed and discussed in terms of decoherence and recombination times. Electrical spin echo tomography thus can be used to study the dynamics of the spin-dependent transport processes, e.g., in realistic spin qubit devices for quantum information processing.

DOI
10.1103/physrevlett.100.177602

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The electrical detection of spin echoes via echo tomography is used to observe coherent processes associated with the electrical readout of the spin state of phosphorus donor electrons in silicon near a SiO2 interface. Using the Carr-Purcell pulse sequence, an echo decay with a time constant of 1.7+/-0.2 micros is observed and discussed in terms of decoherence and recombination times. Electrical spin echo tomography thus can be used to study the dynamics of the spin-dependent transport processes, e.g., in realistic spin qubit devices for quantum information processing.
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Pump-probe spectroscopy is the most common time-resolved technique for investigation of electronic dynamics, and the results provide the incoherent population decay time T1{T}_{1}T1​. Here we use a modified pump-probe experiment to investigate coherent dynamics, and we demonstrate this with a measurement of the inhomogeneous dephasing time T2∗{T}_{2}^{*}T2∗​ for phosphorus impurities in silicon. The pulse sequence produces the same information as previous coherent all-optical (photon-echo-based) techniques but is simpler. The probe signal strength is first order in the pulse area but its effect on the target state is only second order, meaning that it does not demolish the quantum information. We propose simple extensions to the technique to measure the homogeneous dephasing time T2{T}_{2}T2​, or to perform tomography of the target qubit.
Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers. Donors spins in silicon are coherent, high-performance qubits, but scale-up has been challenging. Here the authors present the first experimental demonstration of exchange-based, entangling two qubit gates between electrons bound to 31P donors in Si.
Silicon is promising for spin-based quantum computation because nuclear spins, a source of magnetic noise, may be eliminated through isotopic enrichment. Long spin decoherence times T2 have been measured in isotope-enriched silicon but come far short of the T2=2T1 limit. The effect of nuclear spins on T2 is well established. However, the effect of background electron spins from ever present residual phosphorus impurities in silicon can also produce significant decoherence. We study spin decoherence decay as a function of donor concentration, 29Si concentration, and temperature using cluster expansion techniques specifically adapted to the problem of a sparse dipolarly coupled electron spin bath. Our results agree with the existing experimental spin echo data in Si:P and establish the importance of background dopants as the ultimate decoherence mechanism in isotope-enriched silicon.
Abstract. We propose a novel optical and electrical hybrid scheme for the measurement of nuclear spin qubits in silicon. By combining the environmental insensitivity of the integer quantum Hall effect with the optically distinguishable hyperfine states of phosphorus impurities in silicon, our system can simultaneously offer nuclear spin measurement and robustness against environmental defects. 31P donor spins in isotopically purified 28Si are often discussed as very promising quantum memory qubits due to their extremely long decoherence times, and our proposed device offers an effective implementation for such a quantum memory system.