Introduction

The spin projections of single electrons and holes confined in quantum dots (QDs) provide a natural two-level system that can serve as the logical basis for both classical and quantum information processing devices. When two layers of self-assembled InGaAs QDs are grown sequentially, strain propagation causes QDs in the two layers to align along the growth direction. Coherent tunneling of either electrons or holes between the two QDs leads to a variety of Coulomb and spin interactions with possible applications in optoelectronic and logic devices [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Because coherent tunneling leads to the formation of delocalized molecular states, these vertically stacked pairs of QDs have come to be known as quantum dot molecules (QDMs). One of the surprising discoveries about QDMs was that the delocalized molecular states have their own unique and tunable properties [16]. In this chapter we review the formation of delocalized molecular states of holes in QDMs and consider how the structure and symmetry of the QDM influence spin properties. Results have been obtained for molecular states charged with one, two, and three holes [9, 13, 17]. We focus here on molecular states occupied by a single hole whose spin projections could serve as the basis for optoelectronic logic devices.

Hole spins were initially discounted for spin-based devices because the complex valence-band interactions were anticipated to degrade spin storage or decoherence times.

Introduction

Most of the current semiconductor devices rely on intentional, density- and spatially controlled doping with impurities. Dopants of donor and acceptor type enable both to change locally the electronic properties (conductivity, chemical potential, built-in electric field, etc.) and to tune these properties by metallic gates. Using such doping modulation has been shown to be very fruitful in the past two decades to fabricate and investigate semiconductor quantum dots (QDs) in the Coulomb blockade regime where the number of resident charges can be deterministically tuned one by one. In parallel, incorporating magnetic dopants in a semiconductor matrix has long been motivated by the possibility of inducing new properties and developing new functionalities. Observation of ferromagnetism in diluted magnetic semiconductors like Ga1–xMnxAs (with x in the range of a few percent) by the end of the 1990s has more specifically stimulated a lot of work [14]. Even though the Curie temperature of GaMnAs below ˜ 200K is likely to limit its potential use for applications, this compound still behaves like an ideal system to investigate the setup and control of Zener-type ferromagnetism in semiconductors, where the Mn atoms incorporated in the GaAs matrix provide both localized magnetic moments and free carriers. Combining the properties of quantum dots with those induced by magnetic doping is naturally an attractive track to explore, both to tailor new spin-based quantum properties and to investigate the fundamental interactions between carriers and magnetic impurities at the microscopic level. In this perspective, the limiting case of a single magnetic atom in a single quantum dot is obviously the elementary system of highest interest.

Semiconductor quantum dots (QDs) have been extensively researched in the past 20 years or so. Over this period, the field has been stimulated by various motivating factors from fabrication of low-threshold temperature-insensitive QD lasers to the use of single spins for quantum computing and single dots for medical markers. In the past decade, refinement of fabrication and experimental techniques enabled researchers in the field to routinely use single QDs to access and control single electrons and holes and their spins, and to generate non-classical light. The focus of this book is on control of optical and transport properties of single and few QDs. The remarkable progress in this fast-developing field in the past three to five years is reported.

The term “quantum dot”, widely used from late 1980s, usually refers to a semiconductor nano-structure. Typical sizes of a quantum dot range from a few nanometers in colloidal dots (also referred to as nano-crystals) to a few hundred nanometers in lithographically fabricated electrostatic structures, so that on average they contain from 103 to 106 atoms. The small physical size is the main common characteristic feature of quantum dots made from different materials and using various fabrication methods. It is usually combined with additional methods for electron energy engineering, for example, surrounding the dot with a higher band-gap semiconductor, applying gate-voltage creating a higher potential barrier around the dot, etc. This gives rise to the most important basic property of QDs: the motion of electrons and holes in QDs is suppressed in all three dimensions.

Introduction

The advanced growth of semiconductor quantum dots (QDs) with high optical quality is one key to realizing novel devices in various research disciplines related to modern semiconductor technologies. Despite recent progress in the top-down lithographic fabrication of single semiconductor QD-like emitters [43], bottom-up fabrication methods are commonly applied for the realization of high quality light emitting QDs [7]. The exploitation of high-density QD arrays as an active material in laser diodes [17] and vertical cavity surface emitting lasers (VCSEL) resulted in a new class of devices featuring lower lasing thresholds and improved device performance (such as temperature stability) in comparison to devices with higher dimensional gain [2, 3].

Spintronics and quantum information processing are intensively studied fields in order to provide complementary or entirely novel routes to a future information technology [12, 5]. Single self-assembled quantum dots (QDs) grown in low-density arrays are promising candidates for realizing functional building blocks in these research fields as they allow to confine single charge carriers or spin carriers while providing a solid-state platform capable of electrical injection or manipulation. Extensive research has resulted in the realization of various devices relying on few or single QDs, for instance quantum light emitters such as single photon sources [23, 36], sources of pairs of entangled photons [1, 45], and fewto single-QD lasers [38]. Moreover, many milestone experiments have been performed with In(Ga)As QDs grown on GaAs, for instance the observation of the Purcell effect [10] or reaching the strong QD exciton–photon coupling regime [26], demonstration of the indistinguishability of photons emitted by a QD [29], or complete control of a single spin by ultrafast optical pulses [25].

Introduction

This chapter gives an overview of our recent experimental research on graphene quantum dots. We will focus on two aspects, namely transport experiments revealing the existence of excited states and how they can be used to detect the electron–hole crossover and scanninggate microscopy to reveal local information on localized states.

One of the extraordinary properties of carbon atoms is the ability to be synthesized into solid structures of any dimensionality: three-dimensional graphite and diamond, one-dimensional carbon nanotubes, and zero-dimensional fullerenes. Graphene, a twodimensional carbon allotrope, was the last to be added to this list in 2004, when K. Novoselov et al. published their results [32]. Graphene has been stimulating the physicists' imagination since then: remarkable mechanical and electronic properties make it a promising candidate for future technological advances and breakthroughs in fundamental research [10]. In particular, the linear dispersion relation of graphene (for small energies) and an additional degree of freedom due to the valley degeneracy led to new physics not observed before in a condensed-matter environment. In fact, impressive results on the so-called unconventional quantum Hall effect [33, 55] and Klein tunneling [54] were obtained. The significance of the discovery of graphene and the first experiments were acknowledged and the discoverers of graphene were rewarded the Nobel Prize in physics 2010.

It was not obvious from the very beginning of graphene research whether it is easily possible to build more complex nanostructures like quantum point contacts or quantum dots (QDs).

Introduction

This chapter is devoted to the description of the interaction of polarized light with carrier spins and nuclear spins in semiconductor quantum dots. A historical starting point of these original experiments is the close analogy between quantum dot physics and atomic physics. In 1952, Brossel Kastler and Winter investigated mercury atoms in a weak magnetic field which splits the electron Zeeman levels. By irradiation of the atoms with circularly polarized light the authors could selectively populate one of the electron Zeeman levels [9]. This process has since been referred to as optical pumping. Soon afterwards the first optical pumping of carrier spins in a semiconductor was reported [31]. The initial pumping of spin-orientated conduction electrons in silicon induced by polarized light led to polarization of the nuclear spins of the atoms of the silicon lattice via the hyperfine interaction. This dependence of the nuclear magnetization on the polarization of the absorbed light is at the heart of the experiments described in this chapter. A review of the nuclear spin effects in bulk semiconductors can be found in [37]. The hyperfine interaction between carrier and nuclear spins gives even more spectacular results in quantum dots as shown in pioneering work on optically detected nuclear magnetic resonance ODNMR [23] and orientation of one spin species will have a strong influence on the other [25, 7]. Below we detail a selection of the most remarkable consequences of nuclear spin physics on the optical properties of quantum dots.

Introduction

The ever-growing demand for fast optical data transmission calls for lasers offering high modulation rates and low energy consumption at the same time. Advances in growth and processing methods make quantum dot (QD) based lasers better candidates for this challenge than ever before. Placed in microresonators able to confine light in regions roughly the size of their wavelength, QDs pave the way to ultra-low threshold lasing. The most common resonator geometries aimed at three-dimensional light confinement are microdisks, photonic crystal membrane cavities and micropillars. The latter are especially good candidates for realizing microlasers suitable for applications as they offer directed emission and allow for parallel device processing. However, this increased efficiency also results in modified emission properties of QD lasers [8]. Semiconductor-specific processes like Pauli-blocking of states, the composite nature of the carriers involved and Coulomb interactions between carriers cause deviations from the standard atomistic laser picture. The main aim of our studies is to characterize microlaser emission in terms of photon statistics and coherence properties. Following Glauber, the most detailed description of a light field is given in a series of correlation functions describing coherence in different orders [10].

This chapter is organized as follows. Section 10.2 contains a brief review on the characteristic properties of micropillar lasers and discusses the emission properties of microlasers operated below and above threshold. Section 10.2.1 focuses on photon statistics and the classification of light fields.

Introduction

Quantum dots are often referred to as artificial atoms, since they trap carriers in discrete energy-levels due to the nanoscale three-dimensional finite potential energy well they provide. As such, dots exhibit a coherent light–matter interaction that is similar to an atom. This is evidenced by observations of atom–optics phenomena such as Rabi oscillations [43, 26], power broadening [27], Autler–Townes doublet [14, 42], Mollow triplet [42, 8], and coherent population trapping [6]. In this chapter, Rabi rotation measurements are used to examine how an exciton transition deviates from an ideal two-level atom due to its interaction with a reservoir of phonons.

The neutral exciton transition may be regarded as a two-level system, or qubit, composed of the crystal ground-state ∣0〉 and a single electron-hole pair ∣X〉. The state-vector of a qubit can be described as a pseudo spin-half. When an oscillating electro-magnetic field resonantly excites the two-level transition it drives an oscillation in the population inversion known as a Rabi oscillation. This results from the oscillations of the driving field and the dipole of the two-level system being synchronous, such that in its rotating frame, the driving field acts as a static magnetic field that causes the pseudo-spin to rotate. Coherent control of the pseudo-spin can be achieved by applying well-defined driving fields, enabling the preparation, and manipulation of superposition states. Such coherent control concepts have found widespread use in electron spin, and nuclear magnetic resonance spectroscopy.

Scalability requirements in future device application of self-assembled quantum dots for non-classical light generation necessitate control of the quantum dot nucleation site. In this chapter we discuss a site-control technique based on directed self-assembly of InAs/InP quantum dots emitting at telecommunication wavelengths. The site-control method preserves the high optical quality inherent in self-assembled quantum dots and the characteristic signatures of a strongly confined system are observed in the emission spectra. The efficacy of site-control manifests in the coupling of single quantum dots to microcavities required for the fabrication of efficient devices. The a priori knowledge of the quantum dot position is used to deterministically couple single dots to high-finesse microcavities with the assurance that one and only one quantum dot is coupled to each cavity. Such devices form the basis of efficient sources of single photons and entangled photon pairs for telecommunications applications that can be manufactured in a scalable manner using conventional semiconductor processing.

Introduction

Self-assembled quantum dots possess the two-level emitter characteristics required for non-classical light generation [37] in quantum information processing and quantum key distribution. The performance of a quantum dot-based single photon source or entangled photon pair source will depend on how well the dot can be coupled to a high-quality factor Q, small volume Veff microcavity [44]. The cavity is required to channel photons from the exciton decay into an optical mode that can be collected by an external optical system.

Introduction

Quantum dots have proven to be exciting systems to study light-matter interaction [32, 9]. Self-assembled quantum dots obtained by the Stranski–Krastanow growth mode have been the main system to date [32, 9]. Here we introduce a new type of quantum dot embedded in a one-dimensional nanowire. Quantum dots in nanowires offer a range of advantages over strain-driven Stranski–Krastanov quantum dots. In the case of quantum dots in nanowires, the light extraction efficiency can be very high for the quantum dot emission due to a waveguide effect in the nanowire [14, 45], theoretically approaching 100% according to simulations [14]. Since strain is not the driving mechanism during growth, unprecedented material freedom is available to the quantum engineer in the choice of materials for the quantum dot and the barrier material. At the scale of nanowires, both zincblende and wurtzite crystal structures can coexist, opening the door to a new type of confinement based not only on the material composition, but also on the phase of the crystal lattice [1]. The ability to electrically contact a single nanowire implies that all the current injected in a nanowire will flow through a single quantum dot, enabling an efficient interface between single electrons and single photons [33, 44]. In addition, electrostatic gating is highly versatile, allowing for coherent spin manipulation [36], charge state control [54], and the ability to control the exciton–biexciton splitting by an in-plane electric field [43].

Introduction

In 1998, Daniel Loss and David DiVincenzo published a seminal paper describing how semiconductor quantum dots could be used to create spin qubits for quantum information processing [28]. They recognized that a single spin in a magnetic field forms a natural two-level system that can serve as a quantum bit. Moreover, owing to the weak magnetic moment of the electron, the spin is relatively well isolated from the environment leading to long coherence times. To confine single spins, Loss and DiVincenzo envisioned the quantum dot architecture shown in Fig. 15.1. A GaAs/AlGaAs heterostructure confines electrons to a two-dimensional electron gas (2DEG). Depletion gates are fabricated on top of the structure to provide a tunable confinement potential, trapping a single electron in each quantum dot. Neighboring quantum dots are tunnel coupled, with the coupling strength controlled by the electrostatic potential. The orientation of a single spin can be controlled by using electron spin resonance (ESR), while nearest-neighbor coupling is mediated by the depletion gate tunable exchange interaction.

It is fair to say that in 1998 many of the requirements of the Loss–DiVincenzo proposal had not been implemented, starting with the most basic necessity of a single electron lateral quantum dot [8]. The purpose of this chapter is to describe several experiments inspired by the Loss–DiVincenzo proposal. Many powerful experiments have been performed since 1998 and, given the space constraints here, we cannot give each experiment the attention it deserves.