There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Quantum dots embedded in photonics nanostructures provide unprecedented control over the interaction between light and matter. This review gives an overview of the theoretical principles involved, as well as applications ranging from high-precision quantum electrodynamics experiments to quantum-information processing.

Interfacing single photons and single quantum dots with photonic nanostructures

A single electron spin confined within a semiconductor nanostructure is an ideal qubit for quantum computing, as it is relatively stable against decoherence and is easily manipulated electrically or optically. Full quantum control involving initialization, spin rotation and detection, has been demonstrated previously using electrically controlled radio-frequency pulses, but this method will be too slow for the construction of quantum computing circuits operating at useful clock speeds. Optical manipulation of electron spin allows much faster operations and has the added advantage that it allows for an optical interface. Press et al. now achieve ultrafast optical control of electron spin in a quantum dot and demonstrate, in combination with optical initialization and detection, a single-qubit logic gate operation, involving a sequence of two optical pulses. Such high-speed operation could conceivably lead to quantum computing devices at gigahertz clock speeds. A basic requirement for quantum information processing systems is the ability to completely control the state of a single qubit1,2,3,4,5,6. For qubits based on electron spin, a universal single-qubit gate is realized by a rotation of the spin by any angle about an arbitrary axis. Driven, coherent Rabi oscillations between two spin states can be used to demonstrate control of the rotation angle. Ramsey interference, produced by two coherent spin rotations separated by a variable time delay, demonstrates control over the axis of rotation. Full quantum control of an electron spin in a quantum dot has previously been demonstrated using resonant radio-frequency pulses that require many spin precession periods7,8,9,10. However, optical manipulation of the spin allows quantum control on a picosecond or femtosecond timescale11,12,13,14,15,16,17,18, permitting an arbitrary rotation to be completed within one spin precession period6. Recent work in optical single-spin control has demonstrated the initialization of a spin state in a quantum dot19,20,21,22, as well as the ultrafast manipulation of coherence in a largely unpolarized single-spin state17. Here we demonstrate complete coherent control over an initialized electron spin state in a quantum dot using picosecond optical pulses. First we vary the intensity of a single optical pulse to observe over six Rabi oscillations between the two spin states; then we apply two sequential pulses to observe high-contrast Ramsey interference. Such a two-pulse sequence realizes an arbitrary single-qubit gate completed on a picosecond timescale. Along with the spin initialization and final projective measurement of the spin state, these results demonstrate a complete set of all-optical single-qubit operations.

Complete quantum control of a single quantum dot spin using ultrafast optical pulses

Pulse-excited resonance-fluorescence single-photons are generated on demand from a single quantum dot embedded in a microcavity under s-shell excitation with an ultrafast laser source.

On-demand semiconductor single-photon source with near-unity indistinguishability

Experimental and theoretical progress toward quantum computation with spins in quantum dots (QDs) is reviewed, with particular focus on QDs formed in GaAs heterostructures, on nanowire-based QDs, and on self-assembled QDs. We report on a remarkable evolution of the field, where decoherence—one of the main challenges for realizing quantum computers—no longer seems to be the stumbling block it had originally been considered. General concepts, relevant quantities, and basic requirements for spin-based quantum computing are explained; opportunities and challenges of spin-orbit interaction and nuclear spins are reviewed. We discuss recent achievements, present current theoretical proposals, and make several suggestions for further experiments.

Prospects for Spin-Based Quantum Computing in Quantum Dots

We study optically driven Rabi rotations of a quantum dot exciton transition between 5 and 50 K, and for pulse areas of up to 14 pi In a high driving field regime, the decay of the Rabi rotations is nonmonotonic, and the period decreases with pulse area and increases with temperature By comparing the experiments to a weak-coupling model of the exciton-phonon interaction, we demonstrate that the observed renormalization of the Rabi frequency is induced by fluctuations in the bath of longitudinal acoustic phonons, an effect that is a phonon analogy of the Lamb shift

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Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots.

We propose and demonstrate the sequential initialization, optical control, and readout of a single spin trapped in a semiconductor quantum dot. Hole spin preparation is achieved through ionization of a resonantly excited electron-hole pair. Optical control is observed as a coherent Rabi rotation between the hole and charged-exciton states, which is conditional on the initial hole spin state. The spin-selective creation of the charged exciton provides a photocurrent readout of the hole spin state.

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Fast optical preparation, control, and readout of a single quantum dot spin.

This thesis describes experiments on the initialisation, coherent control, and readout of a single hole spin trapped in a self assembled InGaAs semiconductor quantum dot.
High fidelity initialisation of a hole spin state is achieved by the fast ionisation of a spin polarised neutral exciton under an applied electric field and in a Faraday
geometry magnetic field. The preparation of a coherent superposition state is demonstrated by observing the precession of the hole spin about a Voigt geometry magnetic field. The hole spin dephasing time is deduced from the decay of the spin contrast. Coherent optical rotation of the hole spin state about the z-axis is demonstrated using the geometric phase shift induced by a picosecond laser pulse. By combining the precession of the spin about the x-axis, and optical rotations about the z-axis, full quantum control of a hole spin is demonstrated over the surface of the Bloch sphere. This is an important prerequisite for the use of a hole spin as a qubit for quantum information processing applications.

Coherent optical control of the spin of a single hole in an InAs/GaAs quantum dot.

The four-level exciton/biexciton system of a single semiconductor quantum dot acts as a two-qubit register. We experimentally demonstrate an exciton-biexciton Rabi rotation conditional on the initial exciton spin in a single InGaAs/GaAs dot. This forms the basis of an optically gated two-qubit controlled rotation (CROT) quantum-logic operation where an arbitrary exciton spin is selected as the target qubit using the polarization of the control laser.

Two-qubit conditional quantum-logic operation in a single self-assembled quantum dot

We report picosecond control of excitonic dressed states in a single semiconductor quantum dot. A strong laser pulse couples the exciton and biexciton states, to form an Autler-Townes doublet of the neutral exciton transition. The Rabi-splitting, and hence the admixture of the dressed states follows the envelope of the picosecond control laser. We create a superposition of dressed states, and observe the resulting beat: a direct measurement of a Rabi oscillation in time delay rather than the usual power domain.

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S. J. Boyle

Papers

Phonon-induced Rabi-frequency renormalization of optically driven single InGaAs/GaAs quantum dots.

Fast optical preparation, control, and readout of a single quantum dot spin.

Coherent optical control of the spin of a single hole in an InAs/GaAs quantum dot.

Two-qubit conditional quantum-logic operation in a single self-assembled quantum dot

Beating of exciton-dressed states in a single semiconductor InGaAs/GaAs quantum dot.