Electron spin coherence exceeding seconds in high-purity silicon.

Silicon is one of the most promising semiconductor materials for spin-based information processing devices. Its advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of a (28)Si form with no magnetic nuclei overcomes a primary source of spin decoherence in many other materials. Nevertheless, the coherence lifetimes of electron spins in the solid state have typically remained several orders of magnitude lower than that achieved in isolated high-vacuum systems such as trapped ions. Here we examine electron spin coherence of donors in pure (28)Si material (residual (29)Si concentration <50 ppm) with donor densities of 10(14)-10(15) cm(-3). We elucidate three mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime T(2) up to 2 s. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. A magnetic field gradient suppresses such interactions, producing an extrapolated electron spin T(2) of 10 s at 1.8 K. These coherence lifetimes are without peer in the solid state and comparable to high-vacuum qubits, making electron spins of donors in silicon ideal components of quantum computers, or quantum memories for systems such as superconducting qubits.

[1]  H. Riemann,et al.  Electron spin coherence and electron nuclear double resonance of Bi donors in natural Si. , 2010, Physical Review Letters.

[2]  T. Castner Raman Spin-Lattice Relaxation of Shallow Donors in Silicon , 1963 .

[3]  L Frunzio,et al.  High-cooperativity coupling of electron-spin ensembles to superconducting cavities. , 2010, Physical review letters.

[4]  Ian Appelbaum,et al.  Electronic measurement and control of spin transport in silicon , 2007, Nature.

[5]  C. Kittel,et al.  Dipolar Broadening of Magnetic Resonance Lines in Magnetically Diluted Crystals , 1953 .

[6]  B. E. Kane A silicon-based nuclear spin quantum computer , 1998, Nature.

[7]  T. Ichikawa,et al.  Effect of spin flip-flop on electron-spin-echo decay due to instantaneous diffusion , 1992 .

[8]  W. Rhim,et al.  Analysis of multiple pulse NMR in solids. II , 1973 .

[9]  Jacob M. Taylor,et al.  Nanoscale magnetic sensing with an individual electronic spin in diamond , 2008, Nature.

[10]  W. Mims,et al.  Phase Memory in Electron Spin Echoes, Lattice Relaxation Effects in CaW O 4 : Er, Ce, Mn , 1968 .

[11]  E. A. Gere,et al.  Electron Spin Resonance Experiments on Donors in Silicon. II. Electron Spin Relaxation Effects , 1959 .

[12]  Todd A. Brun,et al.  Quantum Computing , 2011, Computer Science, The Hardware, Software and Heart of It.

[13]  K. B. Whaley,et al.  Electrical activation and electron spin coherence of ultralow dose antimony implants in silicon , 2005, cond-mat/0507318.

[14]  G. M. Zhidomirov,et al.  Contribution to the Theory of Spectral Diffusion in Magnetically Diluted Solids , 1969 .

[15]  J Wrachtrup,et al.  Strong coupling of a spin ensemble to a superconducting resonator. , 2010, Physical review letters.

[16]  Amir Yacoby,et al.  Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs , 2011 .

[17]  S. Sarma,et al.  Theory of nuclear-induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots , 2002, cond-mat/0211567.

[18]  S. Hartmann,et al.  Theory of spectral diffusion decay using an uncorrelated-sudden-jump model , 1974 .

[19]  B. E. Kane Silicon‐Based Quantum Computation , 2000, quant-ph/0003031.

[20]  E. Haller,et al.  Electron spin coherence of phosphorus donors in silicon: Effect of environmental nuclei , 2010 .

[21]  R J Schoelkopf,et al.  Quantum computing with an electron spin ensemble. , 2009, Physical review letters.

[22]  Quantum theory of spectral diffusion induced electron spin decoherence , 2005, cond-mat/0501503.

[23]  K. Salikhov,et al.  The theory of electron spin-echo signal decay resulting from dipole-dipole interactions between paramagnetic centers in solids , 1981 .

[24]  Jacob M. Taylor,et al.  Suppressing Spin Qubit Dephasing by Nuclear State Preparation , 2008, Science.

[25]  S. A. Lyon,et al.  Electron spin relaxation times of phosphorus donors in silicon , 2003 .

[26]  Archil Avaliani,et al.  Quantum Computers , 2004, ArXiv.

[27]  Philip W. Anderson,et al.  Spectral Diffusion Decay in Spin Resonance Experiments , 1962 .

[28]  J. P. Gordon,et al.  Microwave Spin Echoes from Donor Electrons in Silicon , 1958 .

[29]  Andrea Morello,et al.  Electron spin decoherence in isotope-enriched silicon. , 2010, Physical review letters.

[30]  H. Riemann,et al.  Enrichment of silicon for a better kilogram , 2010 .

[31]  U. Haeberlen,et al.  Coherent Averaging Effects in Magnetic Resonance , 1968 .

[32]  Pedram Khalili Amiri,et al.  Quantum computers , 2003 .

[33]  C Langer,et al.  Long-lived qubit memory using atomic ions. , 2005, Physical review letters.