The aim of this thesis is to theoretically investigate two possible applications of semiconductor quantum dots for the growing field of quantum information and communication. The first one is the generation of entangled photons, which can be created by the radiative recombination of a quantum dot biexciton. This non-classical state of light is for instance used for teleportation of quantum information over distance. Although other methods of creating entangled photons exist, they suffer from problems such as inefficiency and unreliability, and an alternative which can produce an entangled photon pair on-demand within a given time interval would be most welcome. The second application is the implementation of a quantum bit using the intrinsic angular momentum of a single electron confined to a quantum dot. The quantum bit is the basic element of any quantum computer and is used to store quantum information. The work is divided into four main parts. We begin with an introduction which contains a short description about entanglement and quantum information followed by a brief review about the electron structure of semiconductors. This review aims to provide knowledge about some key methods and results from the semiconductor physics, which we will need in the following chapters. In the second part we will turn our attention to the generation of entangled light by the recombination of semiconductor biexcitons, which are composed of two excitons. We will discover that the excitons show an energy structure which requires extending the semiconductor theory from the introduction to be able to properly describe the observed effects. Once the exciton energy structure is known, we will examine a method to improve the quality of the emitted light with respect to entanglement. The third part considers effects from interactions between nuclear and electron spins. Focusing on storing one quantum bit using a single electron spin, we investigate the possible loss of information caused by interaction with the nuclear spins. We find that the temporal fluctuations of the nuclear spins give rise to an upper limit on the electron coherence time, during which quantum information can be accurately stored. We also investigate possible techniques to reduce the fluctuations and prolong the coherence time. In the fourth part we combine knowledge about the nuclear spins with the biexciton recombination process to investigate what effect exciton-nuclear spin interaction has on the entangled light. We find that the interaction with nuclear spins degrades the entanglement of the emitted light. To restore the quality of the entanglement, we investigate the effect of polarizing the nuclear spins and find that this can improve the entanglement.
The aim of this thesis is to theoretically investigate two possible applications of semiconductor quantum dots for the growing field of quantum information and communication. The first one is the generation of entangled photons, which can be created by the radiative recombination of a quantum dot biexciton. This non-classical state of light is for instance used for teleportation of quantum information over distance. Although other methods of creating entangled photons exist, they suffer from problems such as inefficiency and unreliability, and an alternative which can produce an entangled photon pair on-demand within a given time interval would be most welcome. The second application is the implementation of a quantum bit using the intrinsic angular momentum of a single electron confined to a quantum dot. The quantum bit is the basic element of any quantum computer and is used to store quantum information. The work is divided into four main parts. We begin with an introduction which contains a short description about entanglement and quantum information followed by a brief review about the electron structure of semiconductors. This review aims to provide knowledge about some key methods and results from the semiconductor physics, which we will need in the following chapters. In the second part we will turn our attention to the generation of entangled light by the recombination of semiconductor biexcitons, which are composed of two excitons. We will discover that the excitons show an energy structure which requires extending the semiconductor theory from the introduction to be able to properly describe the observed effects. Once the exciton energy structure is known, we will examine a method to improve the quality of the emitted light with respect to entanglement. The third part considers effects from interactions between nuclear and electron spins. Focusing on storing one quantum bit using a single electron spin, we investigate the possible loss of information caused by interaction with the nuclear spins. We find that the temporal fluctuations of the nuclear spins give rise to an upper limit on the electron coherence time, during which quantum information can be accurately stored. We also investigate possible techniques to reduce the fluctuations and prolong the coherence time. In the fourth part we combine knowledge about the nuclear spins with the biexciton recombination process to investigate what effect exciton-nuclear spin interaction has on the entangled light. We find that the interaction with nuclear spins degrades the entanglement of the emitted light. To restore the quality of the entanglement, we investigate the effect of polarizing the nuclear spins and find that this can improve the entanglement.
Spins in a solid-state environment and photons are both promising physical systems regarding the implementation of qubits. Whereas electron and nuclear spins act very well as localized qubits that are able to store and process quantum information, photons are the primary candidates to transmit quantum information between distant locations. Entanglement, on the other hand, is a fundamental resource of quantum information processing enabling, e.g., secure communication over long distances. The generation and manipulation of entanglement are thus fundamental steps in order to leverage the benefits of quantum information processing. The aim of this dissertation is therefore to theoretically investigate entangling mechanisms for various physical systems. A functioning source of entangled photons is a basic hardware component required for quantum communication. To this end, we study a system composed of semiconductor quantum wells inside a microcavity, known as intersubband cavity system, in which the interaction of the electronic system with the cavity field can reach the ultrastrong coupling regime. The ground state contains a finite number of photons, and we find that these photons are entangled. The amount of entanglement is quantified analytically, and maximal entanglement is found to be possible. The technique of entanglement purification allows to restore maximal entanglement that has decreased, e.g. due to decoherence. Purification requires quantum memory, a role for which electron spins in electrically-defined quantum dots are well suited. However, existing purification protocols are rather unpractical in this case. Here, the concept of asymmetric bilateral two-qubit operations is introduced to purify spin entanglement by harnessing the typical interaction between electrons in neighboring quantum dots. As it turns out, this concept can be applied to a variety of qubit systems, e.g. superconducting qubits or spins in nitrogen-vacancy centers in diamond. The latter example offers several possibilities to implement a qubit, of which the intrinsic nitro- gen nuclear spin has proven its viability in many ways. We develop a scheme to deterministically couple two nuclear spin qubits, in which the interaction is mediated by an optical cavity. It is found that an entangling two-qubit gate, also required for universal quantum computation, can be implemented with operation times below 100 nanoseconds, i.e. several orders of magnitude faster compared to the decoherence time of the nuclear spin. The verification of entanglement, which is required e.g. in entanglement-based quantum com- munication to detect an eavesdropping attack, typically involves a measurement of qubit states. Using the input-output formalism, we derive a fully quantum-mechanical model of an optical readout scheme to measure the spin state of an electron in a self-assembled quantum dot.
In the last few years there has been a growing interest in the possible applications of quantum properties of different physical systems in well established technologies. This was motivated by the miniaturization of electronic devices. For very small systems, the laws of quantum mechanics start to govern their behavior and it is then to expect that for instance electronic components reach their "quantum limit". A good example of the introduction of quantum properties into conventional technologies is the case of the electron spin, which offers an alternative to electron-charge for the storage and transport of information in electronics. The idea of using electron spins in electronics gave rise to the new and exciting field of spintronics and was encouraged by experiments that showed coherent spin transport over long distances (over hundred micrometers) in semiconductors and long electron spin dephasing times. In addition to its applications in conventional technologies, the use of the electron spin as information-carrier has been suggested for the new field of quantum information processing. An important advantage of the electron spin with respect to other quantum information-carriers proposed is that it can profit from the well developed semiconductor industry and its related technologies. For the long-range transport of information, however, the highly interacting environment in solid-state devices represents a difficulty to the use of electron spins. In contrast, photons are very weekly coupled to their environment, and therefore more suitable for the transfer of information over long distances (on the order of kilometers), required, for instance, in quantum communication. Furthermore, the technology needed for the transport of photons over such long distances is well developed. Thus, an efficient transfer of quantum information between electron spins and photons is highly desirable. \n \nIn this dissertation, we show that the transfer of entanglement, a quantum correlation, from electron spins to the polarization of photons is not only theoretically possible, but also feasible under realistic experimental conditions. We study the transport of an entangled pair of electron spins through Fermi leads which split them spatially until they reach spin-LEDs, semiconductor structures containing quantum dots. In these structures, the electrons optically recombine with holes, producing then photons. We analyze the polarization state of the out-coming photons and give the conditions for which the entanglement of the electron spins is fully recovered in the photon-polarizations. We further show that it is possible to produce four-photon entanglement. \n \nWe also include in this work the study of coherent spin-transfer between quantum dots layers bridged by molecules. This study was motivated by an experiment showing that the molecules act not only as binders to construct the multilayer structures, but also as "wires" for the information through electron spins in the quantum dots. We show that a two-site Hamiltonian captures some of the essential features of the experiment. We calculate the dependence of the experimentally observed Faraday rotation (FR) signal as a function of probe energy on microscopic parameters such as spin transfer probabilities. The Faraday angle is related to the difference in the dielectric response for different polarizations of the light. We calculate the dielectric response functions of coupled quantum dots and derive an analytical expression for the FR angle in terms of electron transfer probabilities and Heisenberg exchange splittings.
Semiconductor Quantum dots are potentially an attractive source of non-classical light. They can confine bound electron-hole pairs, excitons, in all three spatial dimensions giving them discrete optical emission energies, much like the electronic states in atomic systems. The semiconductor nature of the system allows quantum dots to be integrated into complicated device structures including optical cavities [1] and electrical injection [2]. The radiative exciton emission from a semiconductor quantum dot can provide the simplest form of quantum light, a single photon source [2]. The finite re-excitation time following the radiative decay of an exciton in a quantum dot prevents the dot from emitting more than one photon if excited with a short optical or electronic pulse. In a similar fashion excitation of the biexciton state, consisting of two electrons and holes, in the quantum dot results in the emission of a pair of photons at the energy of the biexciton and exciton transitions. The biexciton state was, in fact, proposed as a possible source of polarisation-entangled photons in 2000 by Benson et al. [3] as it consists of two polarisation-correlated decay paths which could potentially be indistinguishable. The condition of indistinguishability is fundamental to the generation of entangled photons and is, in general, not true of the two decay paths from the biexciton state in a quantum dot; physical anisotropy causes the intermediate exciton states to hybridise and separate in energy providing ‘which-path’ information about the route taken through the biexciton decay. We demonstrate how the splitting between the intermediate exciton states in a single InAs quantum dot can be controlled by growth [4], rapid thermal annealing [5] and the application of an external magnetic field [6]. Each of these three techniques can be used to make the intermediate exciton states degenerate allowing the biexciton decay to produce singe pairs of entangled photons triggered by short laser pulses [7,8]. Entangled photon pair sources are essential for applications such as entanglement based quantum key distribution, and optical quantum computing. For these applications it is important that no more than one entangled photon pair is generated in a cycle, a requirement met by our quantum dot source which is not possible with traditional methods for generating entangled pairs of photons. Entanglement also enables quantum interferometry and metrology, the basis of image resolution beyond that possible with equivalent classical light. Biphoton interferometry using entangled emission from the biexciton decay reveals fringes with half the period of classical light [9], and less that that of the laser. In addition, interferometry suggests that this type of entangled light source is not limited by decoherence, we fine the biphoton is surprising robust against dephasing, in stark contrast to the devastating effect of decoherence upon single photons emitted by similar structures.
Semiconductor quantum dots can be used as sources of entangled single photons, which constitute a crucial resource for optical quantum computing. We present theoretical research on entanglement verification and nuclear spin physics, leading to results that are relevant to both experimental work and the theory of quantum optics and mesoscopic quantum systems. Optical quantum computing requires large entangled photonic states, yet characterizing even few-photon states is a challenge in current experiments due to low photon detection efficiencies. We present a lower bound on a measure of computational usefulness of a potentially large quantum state that requires only measured values of three-photon correlations. Hence this bound provides a simple and applicable benchmarking method for quantum dot experiments. We then turn to the critical issue of the interaction between electron and nuclear spins in quantum dots. This interaction gives rise to decoherence that stands in the way of generating entangled photons as well as nuclear phenomena that might help to overcome this challenge. We formulate a quantum mechanical model of the nuclear spin system in a quantum dot driven by continuous-wave laser light. Based on the analytical steady state solution of this model we predict a novel nuclear spin effect, giving rise to nuclear spin polarization that counteracts the effect of an external magnetic field. Beyond the decoherence problem nuclear spins give rise to randomly time-varying transition energies. A quantum mechanical model of this noise as well as the effect of photon scattering is developed, leading to the insight that optical driving can continuously probe the electron transition energy and thereby prevent it from changing.
New technologies based on the properties of quantum mechanics promise to revolutionise the way information is processed by outperforming what is possible using classical devices. Examples include massively parallel processing using quantum computers, verifiably secure communication using quantum cryptography, and measurement with sensitivity beyond classical limitation with quantum metrology. Realising the full potential of these technologies necessitates the ability to communicate quantum information over large distances, a key requirement for future quantum networks. However, developing practical implementations of long-distance quantum communication is challenging as it necessitates three major ingredients: light-matter interfaces, elementary quantum operations, and quantum memories. This thesis describes work that has been undertaken to address these requirements using semiconductor nanotechnology. We have first demonstrated that single InAs quantum dots embedded inside conventional diode structures constitute high-fidelity controllable interfaces between optical qubits and solid-state qubits. Indeed, the polarisation state of a photon was transferred into the spin state of an electron-hole pair and eventually restored through radiative recombination of the electron and the hole with a fidelity up to 95%. Moreover, spins were manipulated using subnanosecond modulation of a vertical electric field applied to the quantum dots. By controlling this electrical modulation, we demonstrated elementary phase-shift and spin-flip gate operations with near-unity fidelities. An electron-hole pair confi ned in a single quantum dot has a short radiative lifetime limiting therefore its use as an excitonic quantum memory. The solution we proposed was to use a quantum dot molecule to control the spatial separation of the electron and the hole and therefore prevent their recombination. Comprehensive studies of electric field eff ects upon the photoluminescence of quantum dot molecules lead to a clear understanding and a good control over their physical properties. Single photons were stored in individual quantum dot molecules up to 1μs and read out on a subnanosecond time scale. Moreover, the circular polarisation of individual photons was transferred into the spin state of electron-hole pairs with a fidelity above 90%, which does not degrade for storage times up to the 12.5 ns repetition period of the experiment. Our work on single quantum dots could be extended in the near future to allow for two-qubits quantum operations by con fining a second electron-hole pair to be electrically manipulated. Storage of a superposition of spin states in a quantum dot molecule should also be possible if the spin states are made degenerate, which is feasible using the electric fi eld dependence of the energy splitting between the spin states discussed in this thesis. We believe that combining both approaches will lead to the development of a controllable multi-qubit quantum memory for polarised light, a building block for long distance quantum communication based on semiconductor nanotechnology.
Electron spins confined in quantum dots (QDs) are among the leading contenders for implementing quantum information processing. In this Thesis we address two of the most significant technological challenges towards developing a scalable quantum information processor based on spins in quantum dots: (i) decoherence of the electronic spin qubit due to the surrounding nuclear spin bath, and (ii) long-range spin-spin coupling between remote qubits. To this end, we develop novel strategies that turn the unavoidable coupling to the solid-state environment (in particular, nuclear spins and phonons) into a valuable asset rather than a liability. In the first part of this Thesis, we investigate electron transport through single and double QDs, with the aim of harnessing the (dissipative) coupling to the electronic degrees of freedom for the creation of coherence in both the transient and steady-state behaviour of the ambient nuclear spins. First, we theoretically show that intriguing features of coherent many-body physics can be observed in electron transport through a single QD. To this end, we first develop a master-equation-based formalism for electron transport in the Coulomb-blockade regime assisted by hyperfine (HF) interaction with the nuclear spin ensemble in the QD. This general tool is then used to study the leakage current through a single QD in a transport setting. When starting from an initially uncorrelated, highly polarized state, the nuclear system experiences a strong correlation buildup, due to the collective nature of the coupling to the central electron spin. We demonstrate that this results in a sudden intensity burst in the electronic tunneling current emitted from the QD system, which exceeds the maximal current of a corresponding classical system by several orders of magnitude. This gives rise to the new paradigm of electronic superradiance. Second, building upon the insight that the nuclear spin dynamics are governed by collective interactions giving rise to coherent effects such as superradiance, we propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics is shown to lead to intriguing effects such as multistability and criticality in the steady-state solutions. In the second part of this Thesis, our focus turns towards the realization of long-range spin-spin coupling between remote qubits. We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezo-active materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range, can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitations can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits. In summary, this thesis provides contributions towards developing a scalable quantum information processor based on spins in quantum dots in two different aspects. The first part is dedicated to a deeper understanding of the nuclear spin dynamics in quantum dots. In the second part we put forward a novel sound-based strategy to realize long-range spin-spin coupling between remote qubits. This completes a broad picture of spin-based quantum information processing which integrates different perspectives, ranging from the single-qubit level to a broader quantum network level.