This thesis is devoted to the study of excitations in atomic and polariton Bose-Einstein condensates (BEC). These two specimens are prime examples for equilibrium and non equilibrium BEC. The corresponding condensate wave function of each system satisfies a particular partial differential equation (PDE). These PDEs are discussed in the beginning of this thesis and justified in the context of the quantum many-body problem. For high occupation numbers and when neglecting quantum fluctuations the quantum field operator simplifies to a semiclassical wave. It turns out that the interparticle interactions can be simplified to a single parameter, the scattering length, which gives rise to an effective potential and introduces a nonlinearity to the PDE. In both cases, i.e. equilibrium and non equilibrium, the main model corresponding to the semiclassical wave is the Gross-Pitaevskii equation (GPE), which includes certain mathematical adaptions depending on the physical context of the consideration and the nature of particles/quasiparticles, such as additional complex pumping and growth terms or terms due to motion. In the course of this work I apply a variety of state-of-the-art analytical and numerical tools to gain information about these semiclassical waves. The analytical tools allow e.g. to determine the position of the maximum density of the condensate wave function or to find the critical velocities at which excitations are expected to be generated within the condensate. In addition to analytical considerations I approximate the GPE numerically. This allows to gain the condensate wave function explicitly and is often a convenient tool to study the emergence of excitations in BEC. It is in particular shown that the form of the possible excitations significantly depends on the dimensionality of the considered system. The generated excitations within the BEC include quantum vortices, quantum vortex rings or solitons. In addition multicomponent systems are considered, which enable more complex dynamical scenarios. Under certain conditions imposed on the condensate one obtains dark-bright soliton trains within the condensate wave function. This is shown numerically and analytical expressions are found as well. In the end of this thesis I present results as part of an collaborative effort with a group of experimenters. Here it is shown that the wave function due to a complex GPE fits well with experiments made on polariton condensates, statically and dynamically.

The work presented in this thesis was submitted to The University of Manchester for the degree of Doctor of Philosophy in June 2010 by Stuart K Stubbs and is entitled “Photo-physics and applications of colloidal quantum dots”. In this thesis the results of spectroscopic studies on various colloidal quantum dots, particularly related to the measurement and characterisation of multiple exciton generation are presented. Research conducted with Nanoco Technologies Ltd. that involved the design and development of hybrid quantum dot organic light emitting diodes for use in flat panel display technology is also presented. Cadmium selenide (CdSe), indium phosphide (InP), and lead sulphide (PbS) type I and cadmium selenide/cadmium telluride type II colloidal quantum dots were characterised using steady state photoluminescence and absorption spectroscopy. The fluorescence lifetimes of the decay of single excitons was measured in these quantum dots using time correlated single photon counting. An ultrafast transient absorption spectrometer was designed, built, and used to observe the picosecond dynamics of the decay of multiexcitons. These absorption transients were analysed in order to extract the quantum efficiency of producing multiple excitons per absorbed photon. The characteristic signature for multiple exciton generation was first found in CdSe using a time correlated single photon counting set-up. Results from the transient absorption spectrometer demonstrated efficient multiple exciton generation in InP for the first time as well as in PbS, where the efficiency was found to agree with values obtained by other research groups. The absorption transients taken for the type II CdSe/CdTe type II quantum dots demonstrated some novel decay dynamics that could not be attributed to the generation of multiple excitons. Quantum dot organic light emitting diodes were fabricated using Nanoco Technologies high quality cadmium based quantum dots and were shown to demonstrate bright, colour saturated emission originating from the quantum dot layer only. Using quantum dots of different sizes and structures red, green and blue devices were made and shown to be appropriate both in terms of brightness and chromaticity for the use as the red, green and blue pixels of a flat panel display. Because heavy metals like cadmium are restricted or banned from commercial products in many countries, Nanoco Technologies heavy metal free quantum dots, made from InP, were also incorporated in devices. Devices are demonstrated that emit from the quantum dot layer only, albeit at a lower luminance and efficiency than that found in the cadmium containing devices. This was the first demonstration of a heavy metal free, hybrid quantum dot organic light emitting diode.

We present a comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments. Signals in both the probe and conjugate directions are discussed. The effects of recombination, non-radiative scattering and spatial and orientational diffusion are included. The analysis is applied to both a molecular and to a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. The theory is used to explain our recent observations in germanium. Included are discussions of picosecond transient grating self-diffraction measurements that can be understood in terms of an orientational grating produced by anisotropic (in k-space) state-filling. Though there have been predictions and indirect experimental evidence for isotropic state-filling in germanium, this is the first direct experimental indication of anisotropic state-filling in a semiconductor.

Beginning with the discovery of graphene, two-dimensional materials have amassed a strong interest. Like graphene, transition metal dichalcogenides (TMDs) can be coaxed into atomically thin sheets which have some impressive properties. Unlike graphene, TMDs also has a change in their electronic band structure causing an indirect band gap to a direct gap transition in its monolayer form. Additionally, these materials lose their inversion symmetry as a monolayer. These unique properties make TMDs a strong candidate for being used in optoelectronic and valleytronic devices. In order for these devices to be successful, the optical properties of TMDs must be thoroughly understood. Due to this class of material's strong Coulomb interaction, the optical properties are dominated by excitons, a quasiparticle made up of an electron-hole pair. Therefore, the success of these devices relies, in part, on understanding and manipulating excitons. One key parameter of excitons is their dephasing rate which characterizes the lifetime of the coherent superposition of two states (i.e. how the coherence decays which is caused by excitons interacting with their environment). In this work, two optical properties are investigated: (1) How the linear absorption of the TMDs A-exciton peak varies as the material increases in thickness. By looking at how the absorption varies by sample thickness, the interaction between emitters can be understood. Experimental results for the diamagnetic shift are presented which are used to determine the lateral excitonic size. Through theoretical calculations, based on the semiconductor Maxwell-Bloch equations, additional insight into the radiative coupling of the systems are obtained. (2) How the coherence prole of the exciton changes in the presence of an external magnetic eld and specic valley excitation. By varying the polarization scheme in the four wave mixing measurement, specic valley excitation can be selected, allowing for insight into the dephasing mechanisms. By applying an external magnetic eld, the energy levels of the electron and hole can be discretized and the corresponding eects on the system's coherence seen. In conjunction with time-dependent density function theory calculations and the experimental results, a deeper understanding of exciton dynamics and multi-exciton complexes was obtained. Finally, a new system is proposed in which complex spectroscopic techniques can be performed on micron sized samples as well as devices in the presence of an external magnetic eld at cryogen temperatures. This system will allow for the investigation of the optical properties of stacked monolayers (heterostructures) as well as devices.

Title: Dynamics of photoexcited charge carriers in diamond Author: Bc. Tomas Popelar Department: KCHFO MFF UK Supervisor: prof. RNDr. Petr Maly DrSc., KCHFO MFF UK Abstract: In this work we examine the luminescence from diamond in the strong excitation regime by one-photon or two-photon absorption of femtosecond laser beam. Measured sample was very pure type IIa diamond prepared by CVD method which was held in cryostat in order to measure temperature dependant luminescence in range from 12 K to 300 K. The signal was collected and analyzed either by spectrograph or streak camera so we gained time-integrated and time-resolved results. We analyzed only the part of the spectrum containing contributions from electron-hole liquid (for low temperatures), free excitons and probably exciton complexes. For higher temperatures where the condensation is not possible the contribution from e-h plasma was too weak compared to free excitons and was only detectable by time-resolved measurements. Other time-dependant results were obtained by pump and probe experiment with which we examined a change of life- times based on mode of excitation (one-photon or two-photon one) and also an influence of other beams on the condensation into electron-hole drops. Keywords: CVD diamond, dynamics, e-h liquid, excitons

Electronic structure methods enable first-principles calculations of the properties of molecules and materials. But numerically exact calculations of systems relevant to chemistry are computationally intractable due to the exponentially scaling cost of solving the associated Schrödinger equation. This thesis describes the application of quantum Monte Carlo (QMC) methods that enable the accurate solution of this equation at reduced computational cost. Chapter 2 introduces the fast randomized iteration (FRI) framework for analyzing discrete-space QMC methods for ground-state electronic structure calculations. I analyze the relative advantages of applying different strategies within this framework in terms of statistical error and computational cost. Chapter 3 discusses the incorporation of strategies from related stochastic methods to achieve further reductions in statistical error. Chapter 4 presents a general framework for extending these FRI-based approaches to calculate energies of excited electronic states. Chapter 5 demonstrates that leveraging the best of these ground- and excited-state techniques within the FRI framework enables the calculation of very accurate electronic energies in large molecular systems. In contrast to Chapters 2–5, which describe discrete-space QMC methods, Chapter 6 describes a continuous-space approach, based on diffusion Monte Carlo, for calculating optical properties of materials with a particular layered structure. I apply this approach to calculate exciton, trion, and biexciton binding energies of hybrid organic-inorganic lead-halide perovskite materials using a semiempirical Hamiltonian.

In the past decade, research in the field of singlet fission, the process in which one high energy singlet fission exciton forms two lower energy triplet excitons, has seen a resurgence as a process that has the potential to improve solar energy conversion efficiency and contribute to a push for renewable energy. While an impressive motivation, there is still much progress in terms of understanding the physics of the process as well as improving molecular design for actual applications that needs to be made before this motivation can be fully realized. Two significant current hurdles in this field are the extraction of the newly formed triplet excitons from their entangled triplet pair state before recombination, and the lack of stable chromophores with viable energetics for singlet fission and high triplet energies for application purposes. Over the past five years, we have addressed these issues with targeted molecular design. Only a couple of studies have successfully separated the triplet pair state in intramolecular singlet fission systems. We create an intramolecular singlet fission system, a PDI-pentacene-pentacene-PDI tetramer, in which a charge transfer state is utilized to separate an electronically entangled triplet pair. We have also shown that singlet fission can be controlled as well as actually induced in chromophores by employing molecular contortion to tune the energetics. With this work, we have contributed to the motivation of using singlet fission in real-life applications.

Chromophore is a molecule or a part of a molecule which is responsible for its appearance color. This definition has been evolving over time with the progress of science. Contemporary scientific advances have expanded its meaning: to an inclusive level, chromophore is an irreducible collective of fundamental particles, which can represent the photophysical (optical physical) properties of the macroscopic matter. Previous studies have already found that the same molecule can have different photophysical properties under different condensed states. Therefore, it is straight forward to conclude that the definition of chromophore should take such extrinsic influencing interactions of this given molecule into consideration, thus simply taking the smallest unit such as a molecule is not accurate. A good example is quantum dots. Same species of quantum dots possess the identical smallest chemical unit but can emit very differently due to quantum confinement effect, thus defining the smallest unit as the chromophore is apparently fallacious. In solid polymeric compositions, the chemical unit or building blocks may differ from the spectroscopic unit depending on how these chemical units interacts within their ensemble to evolve new properties such as a new transition dipole. As thus, understanding the evolution of photophysical behaviors between the targeted unit and neighbors is of much importance to determine whether they should be considered as one chromophore or many. This requires a thorough understanding towards the evolution of photophysical properties of a collective, and the construction of such collective will need to pay extra attention to, as any structural factor could have changed some photophysical interactions of the collective. The introductory chapter discusses the material platform and fundamental photophysics investigated in this dissertation. Chromophore assembly (CA) as a sylloge of several classes of self-assembled materials, including metal-organic frameworks (MOFs), covalent-organic frameworks (COFs), porous organic polymers (POPs). Among them, MOF-based CAs (MOF-CAs) featuring with the ease of synthesis, demonstrate incomparable promises to construct such collective with several appealing characteristics, including component diversity, chemical stability, structural porosity, and post-synthetic versatility (Chapter 1.1). As for here, the main target to achieve using these assemblies is to understand the interaction between adjacent chemical monomeric units, therefore their spatial arrangements are of the paramount importance. As modern theory discovered, both ordered and random systems can be very important for novel quantum material developments. Both crystalline and amorphous arrangements of monomeric units can be achieved by adopting different classes of materials. MOF-CAs could achieve the precise control of spatial arrangement including distance, direction, and dihedral angle by its crystalline structures, whereas porous organic polymer-based CAs (POP-CAs) could feature a total randomness. Photophysics, as the research topic targeting the firsthand knowledge gained by interrogating the information provided by the propagating light after its interaction with matters, could provide crucial knowledge of the targeted matter. Hence, photophysical properties could provide fundamental understanding of the targeted matter (Chapter 1.2). State-of-the-art spectroscopic methods and instrumentation have made it possible to critically examine new structures to correlate photophysics with the chemical structure of their assemblies. By combining multiple spectroscopic techniques along with theoretical study, several correlations between the electronic properties of the matter, such as structural features, have been investigated. To illustrate, some unique topology-dependent photophysical behaviors found in chromophore assemblies are introduced (Chapter 1.3). In this dissertation, the feasibility of using specific types of MOF-CAs to conduct unique photophysical studies has been carefully chosen and verified (Chapter 2). Next, with the help of first principles computations, the nature of several electronic excited states as a function of different extent of Van der Waals or electronic interaction in MOF-CAs is unveiled, and experimentally studied with several environmental variates (Chapter 3). The knowledge was then articulated to devise a strategy to improve resonance energy transfer process in MOF-CAs. Here, low electronic symmetry of linker and directionally aligned transition dipoles of their collective ensembled are found beneficial to improve such photophysical process in a bottom-up manner (Chapter 4). Then, a series of MOFs were rationally designed to examine the feasibility and extent of a nonlinear excitonic process, singlet fission, to promote the generation of carriers usable for many applications including light-harvesting applications. The outcome demonstrated MOF-CA is a powerful tool to design such materials and is more capable in terms of its tunability (Chapter 5). At last, a set of randomly oriented CAs in POP were examined for underlying excited state dynamic process that highlights a thermal activated delayed fluorescence (TADF) involving S1 and low-lying T2 excited states (Chapter 6). This dissertation has highlighted unique yet tunable excited-state features and photophysical processes within the well-defined molecular ensemble realized via porous frameworks. These photophysical properties differ from those of their respective molecular system in their solubilized forms. Studies in this dissertation demonstrates a reliable platform to investigate multibody chromophore systems and suggested several valuable discoveries and lights the way for the study of novel chromophore assembly systems.

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Plants and bacteria both have specialized light-harvesting pigment-protein complexes, composed of a network of chromophores encompassed by a protein scaffold, that are involved in photosynthesis. While chromophore, as well as protein, composition and arrangement vary in these light-harvesting complexes, chromophores transfer energy as molecular excitation energy through their complex multi-chromophoric network with near perfect efficiency. Understanding the efficiency of this excitation energy transfer process has been the focus of many interdisciplinary studies. By elucidating the mechanisms involved in efficient excitation energy transfer in biological systems, we are able to guide the design of novel organic materials for their application in photovoltaic systems. Interdisciplinary studies of light-harvesting biological systems leverage advanced spectroscopic techniques and theoretical models to help explain the interaction be- tween excited electronic states. Difficulties in assigning the origin of spectral features in spectroscopy experiments arise from both homogeneous and inhomogeneous effects. Various computational studies have been able to provide theoretical models that help disentangle these effects and provide insight into the origin of some these spectral features. In this work, we present a computational approach that is used to calculate an ensemble of model Hamiltonians for a light-harvesting pigment-protein complex found in algae. To verify the reliability of our model, we compare various computed spec- tra with experimental measurements. Next, we extend our computational approach for parameterizing an ensemble of Hamiltonians for two configurationally unique or- ganic dimers. Finally, we examine the error of some of the approximations made while partitioning “system” and “bath” degrees of freedom when computing molecu- lar properties. Using these methods we are able to provide mechanistic interpretations and explanations of spectral signatures observed in various linear and nonlinear ex- perimental spectra.