1. Introduction 2. Theoretical foundations 3. Propagation and focusing of optical fields 4. Spatial resolution and position accuracy 5. Nanoscale optical microscopy 6. Near-field optical probes 7. Probe-sample distance control 8. Light emission and optical interaction in nanoscale environments 9. Quantum emitters 10. Dipole emission near planar interfaces 11. Photonic crystals and resonators 12. Surface plasmons 13. Forces in confined fields 14. Fluctuation-induced phenomena 15. Theoretical methods in nano-optics Appendices Index.

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Principles of nano-optics

The fabrication methods of the microelectronics industry have been refined to produce ever smaller devices, but will soon reach their fundamental limits. A promising alternative route to even smaller functional systems with nanometre dimensions is the autonomous ordering and assembly of atoms and molecules on atomically well-defined surfaces. This approach combines ease of fabrication with exquisite control over the shape, composition and mesoscale organization of the surface structures formed. Once the mechanisms controlling the self-ordering phenomena are fully understood, the self-assembly and growth processes can be steered to create a wide range of surface nanostructures from metallic, semiconducting and molecular materials.

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Engineering atomic and molecular nanostructures at surfaces

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

The development of colloidal quantum dots has led to practical applications of quantum confinement, such as in solution-processed solar cells1, lasers2 and as biological labels3. Further scientific and technological advances should be achievable if these colloidal quantum systems could be electronically coupled in a general way. For example, this was the case when it became possible to couple solid-state embedded quantum dots into quantum dot molecules4,5. Similarly, the preparation of nanowires with linear alternating compositions—another form of coupled quantum dots—has led to the rapid development of single-nanowire light-emitting diodes6 and single-electron transistors7. Current strategies to connect colloidal quantum dots use organic coupling agents8,9, which suffer from limited control over coupling parameters and over the geometry and complexity of assemblies. Here we demonstrate a general approach for fabricating inorganically coupled colloidal quantum dots and rods, connected epitaxially at branched and linear junctions within single nanocrystals. We achieve control over branching and composition throughout the growth of nanocrystal heterostructures to independently tune the properties of each component and the nature of their interactions. Distinct dots and rods are coupled through potential barriers of tuneable height and width, and arranged in three-dimensional space at well-defined angles and distances. Such control allows investigation of potential applications ranging from quantum information processing to artificial photosynthesis.

Colloidal nanocrystal heterostructures with linear and branched topology

The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.

Driven coherent oscillations of a single electron spin in a quantum dot

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

We demonstrate coupling and entangling of quantum states in a pair of vertically aligned, self-assembled quantum dots by studying the emission of an interacting electron-hole pair (exciton) in a single dot molecule as a function of the separation between the dots. An interaction-induced energy splitting of the exciton is observed that exceeds 30 millielectron volts for a dot layer separation of 4 nanometers. The results are interpreted by mapping the tunneling of a particle in a double dot to the problem of a single spin. The electron-hole complex is shown to be equivalent to entangled states of two interacting spins.

http://science.sciencemag.org/content/sci/291/5503/451.full.pdf

Coupling and Entangling of Quantum States in Quantum Dot Molecules

Quantum dots1,2,3,4,5,6,7 or ‘artificial atoms’ are of fundamental and technological interest—for example, quantum dots8,9 may form the basis of new generations of lasers The emission in quantum-dot lasers originates from the recombination of excitonic complexes, so it is important to understand the dot's internal electronic structure (and of fundamental interest to compare this to real atomic structure) Here we investigate artificial electronic structure by injecting optically a controlled number of electrons and holes into an isolated single quantum dot The charge carriers form complexes that are artificial analogues of hydrogen, helium, lithium, beryllium, boron and carbon excitonic atoms We observe that electrons and holes occupy the confined electronic shells in characteristic numbers according to the Pauli exclusion principle In each degenerate shell, collective condensation of the electrons and holes into coherent many-exciton ground states takes place; this phenomenon results from hidden symmetries (the analogue of Hund's rules for real atoms) in the energy function that describes the multi-particle system Breaking of the hidden symmetries leads to unusual quantum interferences in emission involving excited states

Hidden symmetries in the energy levels of excitonic 'artificial atoms'

The dark states of the heavy-hole ground-state exciton have been studied by photoluminescence spectroscopy of single self-assembled ${\mathrm{In}}_{0.60}{\mathrm{Ga}}_{0.40}\mathrm{As}$ quantum dots in magnetic fields of varying strengths and orientations. When tilting B out of the [001] crystal direction the exciton states with angular momenta $|m|=2$ are mixed with the $|m|=1$ states and become observable. In combination with a detailed analysis of the corresponding Hamiltonian a comprehensive picture of the exciton fine structure is obtained. This fine structure is characteristic for direct gap semiconductors with a twofold degenerate valence band.

Spectroscopic study of dark excitons in In x Ga 1-x As self-assembled quantum dots by a magnetic-field-induced symmetry breaking

We report results of interband spectroscopy of a single ${\mathrm{Al}}_{0.36}{\mathrm{In}}_{0.64}{\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.33}{\mathrm{Ga}}_{0.67}\mathrm{As}$ self-assembled quantum dot. The single dot spectroscopy has been carried out at low temperature as a function of the excitation power and magnetic field up to 8 T. The emission spectra as a function of excitation power show two distinct groups of transitions that we associate with the recombination from ground and excited quantum dot levels with a spacing of \ensuremath{\sim}70 meV. The application of magnetic field allows us to identify the exciton emission as well as the emission from the biexciton, and charged exciton complexes with binding energies of \ensuremath{\sim}5 meV. The binding energies compare favorably with results of calculations.

O. Stern

Papers

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

Coupling and Entangling of Quantum States in Quantum Dot Molecules

Hidden symmetries in the energy levels of excitonic 'artificial atoms'

Spectroscopic study of dark excitons in In x Ga 1-x As self-assembled quantum dots by a magnetic-field-induced symmetry breaking

Optical spectroscopy of a single Al 0.36 In 0.64 A s / A l 0.33 Ga 0.67 As quantum dot