Fabrication of a quantum well heterostructure based on plasma polymerized aniline and its characterization using STM/STS

Two-dimensional electronic systems play a crucial role in modern electronics and offer a multitude of opportunities to study the fundamental phenomena at low dimensional physics. A quantum well heterostructure based on polyaniline (P) and iodine doped polyaniline (I) thin films were fabricated using radio frequency plasma polymerization on indium tin oxide coated glass plate. Scanning probe microscopy and scanning electron microscopy studies were employed to study the morphology and roughness of the polymer thin films. Local electronic density of states (LDOS) of the P–I–P heterostructures is probed using scanning tunnelling spectroscopy (STS). A step like LDOS is observed in the P–I–P heterostructure and is attributed to the quantum well confinement of electrons in the polymer heterostructure.

Thermo- Optic and Nonlinear-Optical studies on CdSe Quantum Dots for Photonic Applications

In general, linear- optic, thermo- optic and nonlinear- optical studies on CdSe QDs based nano uids and their special applications in solar cells and random lasers have been studied in this thesis. Photo acous- tic and thermal lens studies are the two characterization methods used for thermo- optic studies whereas Z- scan method is used for nonlinear- optical charecterization. In all these cases we have selected CdSe QDs based nano uid as potential photonic material and studied the e ect of metal NPs on its properties. Linear optical studies on these materials have been done using vari- ous characterization methods and photo induced studies is one of them. Thermal lens studies on these materials give information about heat transport properties of these materials and their suitability for applica- tions such as coolant and insulators. Photo acoustic studies shows the e ect of light on the absorption energy levels of the materials. We have also observed that these materials can be used as optical limiters in the eld of nonlinear optics. Special applications of these materials have been studied in the eld of solar cell such as QDSSCs, where CdSe QDs act as the sensitizing materials for light harvesting. Random lasers have many applications in the eld of laser technology, in which CdSe QDs act as scattering media for the gain.

Model calculations on the influence of quantum electrodynamical effects on the chemistry of superheavy elements.

Using a phenomenological model, the influence of quantum electrodynamical effects on the prediction of the chemical behavior of superheavy elements within a relativistic Dirac-Slater calculation was investigated. This influence will be small and nondetectable for elements up to Z = 114. For elements near Z = 164 some changes in the ground state configurations occur but the chemical behavior will not change. Using this heuristic model, it is also possible to calculate elements beyond Z = 175. As an example we have chosen element E184 and are now able to make more valid speculations about the chemical behavior of the element than Penneman and co-workers could.

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

Effect of Auger recombination and leakage on the droop in InGaN/GaN quantum well LEDs

We investigate the effect of the epitaxial structure and the acceptor doping profile on the efficiency droop in InGaN/GaN LEDs by the physics based simulation of experimental internal quantum efficiency (IQE) characteristics. The device geometry is an integral part of our simulation approach. We demonstrate that even for single quantum well LEDs the droop depends critically on the acceptor doping profile. The Auger recombination was found to increase stronger than with the third power of the carrier density and has been found to dominate the droop in the roll over zone of the IQE. The fitted Auger coefficients are in the range of the values predicted by atomistic simulations.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Optimizing Robust Quantum Gates in Open Quantum Systems

We are currently at the cusp of a revolution in quantum technology that relies not just on the passive use of quantum effects, but on their active control. At the forefront of this revolution is the implementation of a quantum computer. Encoding information in quantum states as “qubits” allows to use entanglement and quantum superposition to perform calculations that are infeasible on classical computers. The fundamental challenge in the realization of quantum computers is to avoid decoherence – the loss of quantum properties – due to unwanted interaction with the environment. This thesis addresses the problem of implementing entangling two-qubit quantum gates that are robust with respect to both decoherence and classical noise. It covers three aspects: the use of efficient numerical tools for the simulation and optimal control of open and closed quantum systems, the role of advanced optimization functionals in facilitating robustness, and the application of these techniques to two of the leading implementations of quantum computation, trapped atoms and superconducting circuits. After a review of the theoretical and numerical foundations, the central part of the thesis starts with the idea of using ensemble optimization to achieve robustness with respect to both classical fluctuations in the system parameters, and decoherence. For the example of a controlled phasegate implemented with trapped Rydberg atoms, this approach is demonstrated to yield a gate that is at least one order of magnitude more robust than the best known analytic scheme. Moreover this robustness is maintained even for gate durations significantly shorter than those obtained in the analytic scheme. Superconducting circuits are a particularly promising architecture for the implementation of a quantum computer. Their flexibility is demonstrated by performing optimizations for both diagonal and non-diagonal quantum gates. In order to achieve robustness with respect to decoherence, it is essential to implement quantum gates in the shortest possible amount of time. This may be facilitated by using an optimization functional that targets an arbitrary perfect entangler, based on a geometric theory of two-qubit gates. For the example of superconducting qubits, it is shown that this approach leads to significantly shorter gate durations, higher fidelities, and faster convergence than the optimization towards specific two-qubit gates. Performing optimization in Liouville space in order to properly take into account decoherence poses significant numerical challenges, as the dimension scales quadratically compared to Hilbert space. However, it can be shown that for a unitary target, the optimization only requires propagation of at most three states, instead of a full basis of Liouville space. Both for the example of trapped Rydberg atoms, and for superconducting qubits, the successful optimization of quantum gates is demonstrated, at a significantly reduced numerical cost than was previously thought possible. Together, the results of this thesis point towards a comprehensive framework for the optimization of robust quantum gates, paving the way for the future realization of quantum computers.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Exploiting non-Markovianity for quantum control

Quantum technology, exploiting entanglement and the wave nature of matter, relies on the ability to accurately control quantum systems. Quantum control is often compromised by the interaction of the system with its environment since this causes loss of amplitude and phase. However, when the dynamics of the open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Interaction with the environment is then not necessarily detrimental. We show that the back-flow of amplitude and phase can be exploited to carry out quantum control tasks that could not be realized if the system was isolated. The control is facilitated by a few strongly coupled, sufficiently isolated environmental modes. Our paradigmatic example considers a weakly anharmonic ladder with resonant amplitude control only, restricting realizable operations to SO(N). The coupling to the environment, when harnessed with optimization techniques, allows for full SU(N) controllability.

Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.

A Computational Model for Observation in Quantum Mechanics

A computational model of observation in quantum mechanics is presented. The model provides a clean and simple computational paradigm which can be used to illustrate and possibly explain some of the unintuitive and unexpected behavior of some quantum mechanical systems. As examples, the model is used to simulate three seminal quantum mechanical experiments. The results obtained agree with the predictions of quantum mechanics (and physical measurements), yet the model is perfectly deterministic and maintains a notion of locality.

Room-temperature continuous-wave operation of GaInNAs/GaAs quantum dot laser with GaAsN barrier grown by solid source molecular beam epitaxy

We present the results of GaInNAs/GaAs quantum dot structures with GaAsN barrier layers grown by solid source molecular beam epitaxy. Extension of the emission wavelength of GaInNAs quantum dots by ~170nm was observed in samples with GaAsN barriers in place of GaAs. However, optimization of the GaAsN barrier layer thickness is necessary to avoid degradation in luminescence intensity and structural property of the GaInNAs dots. Lasers with GaInNAs quantum dots as active layer were fabricated and room-temperature continuous-wave lasing was observed for the first time. Lasing occurs via the ground state at ~1.2μm, with threshold current density of 2.1kA/cm[superscript 2] and maximum output power of 16mW. These results are significantly better than previously reported values for this quantum-dot system.

Java Applets for teaching quantum mechanics: Particle in a box

These Java Applets help to illustrate some of the difficult to grasp concepts of quantum mechanics. To run this Applet, use the 'Download as zip files' option. Make sure you extract the files first, then double click on the .html file to run the Applet. These are released as open access resources for the purpose of testing, and are to be deployed at the users own risk. Please report any errors you find.