Qubit coherence control in a nuclear spin bath

Coherent dynamics of localized spins in semiconductors is limited by spectral diffusion arising from dipolar fluctuation of lattice nuclear spins. Here we extend the semiclassical theory of spectral diffusion for nuclear spins I=1/2 to the high nuclear spins relevant to the III-V materials and show that applying successive qubit pi-rotations at a rate approximately proportional to the nuclear spin quantum number squared (I^2) provides an efficient method for coherence enhancement. Hence robust coherent manipulation in the large spin environments characteristic of the III-V compounds is possible without resorting to nuclear spin polarization, provided that the pi-pulses can be generated at intervals scaling as I^{-2}

Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath

Decoherence of a localized electron spin in a solid state material (the ``central spin'' problem) at low temperature is believed to be dominated by interactions with nuclear spins in the lattice. This decoherence is partially suppressed through the application of a large magnetic field that splits the energy levels of the electron spin and prevents depolarization. However, dephasing decoherence resulting from a dynamical nuclear spin bath cannot be removed in this way. Fluctuations of the nuclear field lead to uncertainty of the electron's precessional frequency in a process known as spectral diffusion. This article considers the effect of the electron's wavefunction shape upon spectral diffusion and provides wavefunction dependent decoherence time formulas for free induction decay as well as spin echoes and concatenated dynamical decoupling schemes for enhancing coherence. We also discuss dephasing of a qubit encoded in singlet-triplet states of a double quantum dot. A central theoretical result of this work is the development of a continuum approximation for the spectral diffusion problem which we have applied to GaAs and InAs materials specifically

Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins in the nuclear solid-state environment

We consider the decoherence of a single localized electron spin due to its coupling to the lattice nuclear spin bath in a semiconductor quantum computer architecture. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the electron spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The electron spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear spin bath, making the coupled decoherence problem difficult to solve. We provide a formally exact solution of this non-Markovian quantum decoherence problem which numerically calculates accurate spin decoherence at short times, which is of particular relevance in solid-state spin quantum computer architectures. A quantum cluster expansion method is developed, motivated, and tested for the problem of localized electron spin decoherence due to dipolar fluctuations of lattice nuclear spins. The method is presented with enough generality for possible application to other types of spin decoherence problems. We present numerical results which are in quantitative agreement with electron spin echo measurements in phosphorus doped silicon. We also present spin echo decay results for quantum dots in GaAs which differ qualitatively from that of the phosphorus doped silicon system. Our theoretical results provide the ultimate limit on the spin coherence (at least, as characterized by Hahn spin echo measurements) of localized electrons in semiconductors in the low temperature and the moderate to high magnetic field regime of interest in scalable semiconductor quantum computer architectures.Comment: 23 pages, 15 figure

Self-ordered nanoporous lattice formed by chlorine atoms on Au(111)

A self-ordered nanoporous lattice formed by individual chlorine atoms on the Au(111) surface has been studied with low-temperature scanning tunneling microscopy, low-energy electron diffraction, and density functional theory calculations. We have found out that room-temperature adsorption of 0.09–0.30 monolayers of chlorine on Au(111) followed by cooling below 110 K results in the spontaneous formation of a nanoporous quasihexagonal structure with a periodicity of 25–38 Å depending on the initial chlorine coverage. The driving force of the superstructure formation is attributed to the substrate-mediated elastic interaction

Electron spin as a spectrometer of nuclear spin noise and other fluctuations

This chapter describes the relationship between low frequency noise and coherence decay of localized spins in semiconductors. Section 2 establishes a direct relationship between an arbitrary noise spectral function and spin coherence as measured by a number of pulse spin resonance sequences. Section 3 describes the electron-nuclear spin Hamiltonian, including isotropic and anisotropic hyperfine interactions, inter-nuclear dipolar interactions, and the effective Hamiltonian for nuclear-nuclear coupling mediated by the electron spin hyperfine interaction. Section 4 describes a microscopic calculation of the nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flops with quasiparticle broadening included. Section 5 compares our explicit numerical results to electron spin echo decay experiments for phosphorus doped silicon in natural and nuclear spin enriched samples.Comment: Book chapter in "Electron spin resonance and related phenomena in low dimensional structures", edited by Marco Fanciulli. To be published by Springer-Verlag in the TAP series. 35 pages, 9 figure

Temperature dependence of the EPR linewidth of Yb3+ - ions in Y0.99Yb0.01Ba2Cu3OX compounds: Evidence for an anomaly near TC

Electron paramagnetic resonance experiments on doped Yb3+ ions in YBaCuO compounds with different oxygen contents have been made. We have observed the strong temperature dependence of the EPR linewidth in the all investigated samples caused by the Raman processes of spin-lattice relaxation. The spin-lattice relaxation rate anomaly revealed near TC in the superconducting species can be assigned to the phonon density spectrum changesComment: 10 pages, 4 figures Renewed versio

Theory of nuclear induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots

We propose a model for spectral diffusion of localized spins in semiconductors due to the dipolar fluctuations of lattice nuclear spins. Each nuclear spin flip-flop is assumed to be independent, the rate for this process being calculated by a method of moments. Our calculated spin decoherence time $T_{M}=0.64$ ms for donor electron spins in Si:P is a factor of two longer than spin echo decay measurements. For $^{31}$P nuclear spins we show that spectral diffusion is well into the motional narrowing regime. The calculation for GaAs quantum dots gives $T_{M}=10-50$ $\mu$s depending on the quantum dot size. Our theory indicates that nuclear induced spectral diffusion should not be a serious problem in developing spin-based semiconductor quantum computer architectures.Comment: 15 pages, 9 figures. Accepted for publication in Phys. Rev.

First-Principle Study of Phosphine Adsorption on Si(001)-2×\times1-Cl

This paper presents a DFT study for phosphine adsorption on a Si(001)-2$\times$1 surface covered by a chlorine monolayer, including adsorption on local defects, i.e. mono- and bivacancies in the adsorbate layer (Cl, Cl$_2$), and combined vacancies with removed silicon atoms (SiCl, SiCl$_2$). Activation barriers were found for the adsorbing PH$_3$ to dissociate into PH$_2$+H and PH+H$_2$ fragments; it was also established that phosphine dissociation on combined vacancies is possible at room temperature. If there is a silicon vacancy on the surface, phosphorus settles in the Si(001) lattice as PH (if the vacancy is SiCl) or as PH$_2$ (if the vacancy is SiCl$_2$). This paper suggests a method to plant a separate phosphorus atom into the silicon surface layer with atomic precision, using phosphine adsorption on defects specially created on a Si(001)-2$\times$1-Cl surface with an STM tip