Collective Decoherence of Nuclear Spin Clusters

The problem of dipole-dipole decoherence of nuclear spins is considered for strongly entangled spin cluster. Our results show that its dynamics can be described as the decoherence due to interaction with a composite bath consisting of fully correlated and uncorrelated parts. The correlated term causes the slower decay of coherence at larger times. The decoherence rate scales up as a square root of the number of spins giving the linear scaling of the resulting error. Our theory is consistent with recent experiment reported in decoherence of correlated spin clusters.Comment: 4 pages, 4 figure

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.

Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer

We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double quantum dot artificial molecule, projected to be used as a 2-qubit quantum gate in the proposed quantum dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method which is carried out analytically and the molecular orbital method which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.Comment: 12 pages, 4 figures embedded in tex

Entanglement Evolution in the Presence of Decoherence

The entanglement of two qubits, each defined as an effective two-level, spin 1/2 system, is investigated for the case that the qubits interact via a Heisenberg XY interaction and are subject to decoherence due to population relaxation and thermal effects. For zero temperature, the time dependent concurrence is studied analytically and numerically for some typical initial states, including a separable (unentangled) initial state. An analytical formula for non-zero steady state concurrence is found for any initial state, and optimal parameter values for maximizing steady state concurrence are given. The steady state concurrence is found analytically to remain non-zero for low, finite temperatures. We also identify the contributions of global and local coherence to the steady state entanglement.Comment: 12 pages, 4 figures. The second version of this paper has been significantly expanded in response to referee comments. The revised manuscript has been accepted for publication in Journal of Physics

Electron spin coherence in semiconductors: Considerations for a spin-based solid state quantum computer architecture

We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence is dominated by spin-spin interactions, through spectral diffusion and dipolar flip-flop mechanisms. These contributions lead to 1-100 $\mu$s calculated spin coherence times for a wide range of parameters, much higher than former estimates based on $T_{2}^{*}$ measurements.Comment: Role of the dipolar interaction clarified; Included discussion on the approximations employed in the spectral diffusion calculation. Final version to appear in Phys. Rev.

Interplay between Zeeman Coupling and Swap Action in Spin-based Quantum Computer Models: Error Correction in Inhomogeneous Magnetic Fields

We consider theoretically the interplay between Zeeman coupling and exchange-induced swap action in spin-based quantum dot quantum computer models in the presence of inhomogeneous magnetic fields, which are invariably present in real systems. We estimate quantitatively swap errors caused by the inhomogeneous field, establishing that error correction would, in principle, be possible in the presence of non-uniform magnetic fields in realistic structures.Comment: Revised version. To appear in Phys. Rev. Let

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

Spintronics: Fundamentals and applications

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.Comment: invited review, 36 figures, 900+ references; minor stylistic changes from the published versio