As a consequence of degeneracies arising from crystal symmetries, it is possible for electron states at band-edges ('valleys') to have additional spin-like quantum numbers. An important question is whether coherent manipulation can be performed on such valley pseudospins, analogous to that implemented using true spin, in the quest for quantum technologies. Here, we show that valley coherence can be generated and detected. Because excitons in a single valley emit circularly polarized photons, linear polarization can only be generated through recombination of an exciton in a coherent superposition of the two valley states. Using monolayer semiconductor WSe2 devices, we first establish the circularly polarized optical selection rules for addressing individual valley excitons and trions. We then demonstrate coherence between valley excitons through the observation of linearly polarized luminescence, whose orientation coincides with that of the linearly polarized excitation, for any given polarization angle. In contrast, the corresponding photoluminescence from trions is not observed to be linearly polarized, consistent with the expectation that the emitted photon polarization is entangled with valley pseudospin. The ability to address coherence, in addition to valley polarization, is a step forward towards achieving quantum manipulation of the valley index necessary for coherent valleytronics.

http://depts.washington.edu/xulab/wordpress/wp-content/uploads/2012/03/nnano.2013.151.pdf

Optical generation of excitonic valley coherence in monolayer WSe2

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

Emission of single photons can be achieved by using defects in two-dimensional crystals as a source of luminescence.

Single quantum emitters in monolayer semiconductors

The spin of a single electron subject to a static magnetic field provides a natural two-level system that is suitable for use as a quantum bit, the fundamental logical unit in a quantum computer. Semiconductor quantum dots fabricated by strain driven self-assembly are particularly attractive for the realization of spin quantum bits, as they can be controllably positioned, electronically coupled and embedded into active devices. It has been predicted that the atomic-like electronic structure of such quantum dots suppresses coupling of the spin to the solid-state quantum dot environment, thus protecting the 'spin' quantum information against decoherence. Here we demonstrate a single electron spin memory device in which the electron spin can be programmed by frequency selective optical excitation. We use the device to prepare single electron spins in semiconductor quantum dots with a well defined orientation, and directly measure the intrinsic spin flip time and its dependence on magnetic field. A very long spin lifetime is obtained, with a lower limit of about 20 milliseconds at a magnetic field of 4 tesla and at 1 kelvin.

Optically programmable electron spin memory using semiconductor quantum dots

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

The fine structure of excitons is studied by magnetophotoluminescence spectroscopy of single self-assembled In(Ga)As/(Al)GaAs quantum dots. Both strength and orientation of the magnetic field are varied. In a combination with a detailed theoretical analysis, these studies allow us to develop a comprehensive picture of the exciton fine structure. Symmetry of the dot structures as well as its breaking cause characteristic features in the optical spectra, which are determined by the electron-hole exchange and the Zeeman interaction of the carriers. The symmetry breaking is either inherent to the dot due to geometry asymmetries, or it can be obtained by applying a magnetic field with an orientation different from the dot symmetry axis. From data on spin splitting and on polarization of the emission we can identify neutral as well as charged exciton complexes. For dots with weakly broken symmetry, the angular momentum of the neutral exciton is no longer a good quantum number and the exchange interaction lifts degeneracies within the fine-structure manifold. The symmetry can be restored by a magnetic field due to the comparatively strong Zeeman interactions of electron and hole. For dots with a strongly broken symmetry, bright and dark excitons undergo a strong hybridization, as evidenced by pronounced anticrossings when states within the manifold are brought into resonance. The fine structure can no longer be described within the frame developed for structures of higher dimensionality. In particular, the hybridization cannot be broken magnetically. For charged excitons, the exchange interaction vanishes, demonstrating that the exchange splitting of a neutral exciton can be switched off by injecting an additional carrier.

Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots

Self-assembled ${\mathrm{In}}_{0.60}{\mathrm{Ga}}_{0.40}\mathrm{As}$ quantum dots (QD's) have been studied by single dot magnetophotoluminescence spectroscopy ( $B\ensuremath{\le}8\mathrm{T}$). At $B\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ a splitting of the exciton ( $X$) emission is observed which we ascribe to an asymmetry of the confinement potential. With increasing $B$ the emission splits into a quadruplet corresponding to the $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}2$ and $\ifmmode\pm\else\textpm\fi{}1X$ states, which originates from a reduction of the cubic symmetry of the QD's. From the spectroscopic data we obtain values for the electron ( $e$) and hole ( $h$) $g$ factors. We also determine the $X$ singlet-triplet splitting which is found to be enhanced over bulk values by about an order of magnitude due to the increase of the $e\ensuremath{-}h$ overlap in the QD's.

Electron and Hole g Factors and Exchange Interaction from Studies of the Exciton Fine Structure in In 0.60 Ga 0.40 As Quantum Dots

A method is presented for calculating the diamagnetic coefficient of an exciton in a semiconductor nanostructure. The diamagnetic coefficient characterizes the response of a confined exciton to a weak magnetic field, and gives information about the roles of confinement and of the Coulomb interaction in determining the optical properties. A general formulation is presented for nanostructures of arbitrary size, shape, and dimensionality. We introduce a generalized gauge transformation that allows us to express the diamagnetic coefficient in terms of two characterizations of the size of an exciton, one involving confinement and the other involving the Coulomb interaction. Calculations of the diamagnetic coefficient are given for quantum well, wire, and dot geometries.

Exciton diamagnetic shift in semiconductor nanostructures

A facade assembly for an electric socket consists of a support for mounting to the socket, a cover plate to provide a raised decorative area that covers the socket, and a wallplate to surround the raised area and snap onto the cover plate. The facade assembly provides an attractive "designer-style" appearance that permits easy replacement of modular elements that determine the aesthetic qualities of the assembly.

Scott N. Walck

Papers

Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots

Electron and Hole g Factors and Exchange Interaction from Studies of the Exciton Fine Structure in In 0.60 Ga 0.40 As Quantum Dots

Exciton diamagnetic shift in semiconductor nanostructures

Wallbox electric device assembly

Exciton binding energies and diamagnetic shifts in semiconductor quantum wires and quantum dots