Electron spins in semiconductor structures are quantum bits with good prospects, but the information stored in the spin states tends to degrade quickly owing to interactions with nuclei in the host material. A study of GaAs quantum dots now provides a fuller understanding of this memory loss and how it can be suppressed. Quantum-memory times exceeding 200 μs are demonstrated, two orders of magnitude longer than previously reported for this system.

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Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs

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.

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 review the progress and main challenges in implementing large-scale quantum computing by optical control of electron spins in quantum dots (QDs). Relevant systems include self-assembled QDs of III–V or II–VI compound semiconductors (such as InGaAs and CdSe), monolayer fluctuation QDs in compound semiconductor quantum wells, and impurity centres in solids, such as P-donors in silicon and nitrogen-vacancy centres in diamond. The decoherence of the electron spin qubits is discussed and various schemes for countering the decoherence problem are reviewed. We put forward designs of local nodes consisting of a few qubits which can be individually addressed and controlled. Remotely separated local nodes are connected by photonic structures (microcavities and waveguides) to form a large-scale distributed quantum system or a quantum network. The operation of the quantum network consists of optical control of a single electron spin, coupling of two spins in a local nodes, optically controlled quantum interfacing ...

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Quantum computing by optical control of electron spins

Theory of Optical Spin Orientation of Electrons and Nuclei in Semiconductors

Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.

https://iopscience.iop.org/article/10.1088/0034-4885/80/1/016001/pdf

Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths.

Nuclear acoustic resonance (NAR) and nuclear magnetic resonance (NMR) are used to study the line-widths, second moments, and line shapes of nuclear-spin systems of InAs, InSb, GaAs, GaSb, and AlSb. These cw measurements are made at frequencies of 8-10 MHz and at 300\ifmmode^\circ\else\textdegree\fi{}K in single crystals with intrinsic or near intrinsic concentrations of impurities. Different NAR and NMR linewidths for the same nuclear-spin system are explained by the different interaction Hamiltonians for spin-phonon and spin-photon couplings to the nuclear-spin system. When the magnetic field is along $〈001〉$ directions, the resonance line shapes are broadened by dipole-dipole and isotropic nuclear-exchange interactions. When the magnetic field is rotated from $〈001〉$ directions, increased broadening of the resonance line shapes is explained by small anisotropic dipole-dipole and much larger anisotropic quadrupole interactions. The measured like-spin and unlike-spin exchange constants agree with an exchange-constant dependence on the inverse fourth power of the internuclear distance. Like-spin and unlike-spin exchange constants are determined at the nuclear positions in each compound and used with a theory for indirect nuclear-spin exchange to predict the $s$-character electronic wave-function density. The strongly anisotropic quadrupole broadening is explained by electric field gradients produced by the electric fields associated with ionized substitutional impurities. From the measured field gradients, antishielding constants at the In, Sb, Ga, and As nuclear positions are determined relative to each other.

R. K. Sundfors

Papers

Exchange and Quadrupole Broadening of Nuclear Acoustic Resonance Line Shapes in the III-V Semiconductors