Mathematical Transform of Traveling-Wave Equations and Phase Aspects of Quantum Interaction

The traveling wave equation is an essential tool in the study of vibrations and oscillating systems. This paper introduces an important extension to the Fourier/Laplace transform that is needed for the analysis of signals that are represented by traveling wave equations. Another objective of the paper is to present a mathematical technique for the simulation of the behavior of large systems of optical oscillators

Journeys from quantum optics to quantum technology

Sir Peter Knight is a pioneer in quantum optics which has now grown to an important branch of modern physics to study the foundations and applications of quantum physics. He is leading an effort to develop new technologies from quantum mechanics. In this collection of essays, we recall the time we were working with him as a postdoc or a PhD student and look at how the time with him has influenced our research

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology

Microscopy of spin hydrodynamics and cooperative light scattering in atomic Hubbard systems

Wechselwirkungen zwischen quantenmechanischen Teilchen können zu kollektiven Phänomenen führen, deren Eigenschaften sich vom Verhalten einzelner Teilchen stark unterscheiden. Während solche Quanteneffekte im Allgemeinen schwierig zu beobachten sind, haben sich ultrakalte, in optischen Gittern gefangene atomare Gase als vielseitige experimentelle Plattform zur Erforschung der Quantenvielteilchenphysik erwiesen. In dieser Arbeit setzten wir ein Gitterplatz- und Einzelatom-aufgelöstes Quantengasmikroskop für bosonische Rb-87 Atome ein, um Vielteilchensysteme im und außerhalb des Gleichgewichts zu untersuchen. Zunächst betrachteten wir den quantenmechanischen Phasenübergang zwischen dem suprafluiden und dem Mott-isolierenden Zustand im Bose-Hubbard-Modell, das nativ durch kalte Atome in optischen Gittern realisiert wird, und zeigten, dass sich die Brane-Parität eignet, um nichtlokale Ordnung im konventionell als ungeordnet erachteten zweidimensionalen Mott-Isolator zu identifizieren. Mithilfe eines mikroskopischen Ansatzes zur Realisierung einstellbarer Gittergeometrien und programmierbarer Einheitszellen implementierten wir Quadrats-, Dreiecks-, Kagome- und Lieb-Gitter und beobachteten die Skalierung des Phasenübergangspunkts mit der mittleren Koordinationszahl des Gitters. In einem eindimensionalen Gitter untersuchten wir zudem den Hochtemperatur-Spintransport im Heisenberg-Modell, das durch Superaustausch in der Mott-isolierenden Phase eines zwei-Spezies Bose-Hubbard-Modells realisiert wurde. Durch Betrachten der Relaxationsdynamik eines als Domänenwand präparierten Anfangszustandes fanden wir eine superdiffusive Raum-Zeit-Skalierung mit einem anomalen dynamischen Exponenten von 3/2. Anschließend untersuchten wir die theoretisch vorhergesagten mikroskopischen Voraussetzungen für Superdiffusion, indem wir reguläre Diffusion im nicht-integrablen, zweidimensionalen Heisenberg-Modell und ballistischen Transport für SU(2)-Symmetrie-gebrochene magnetisierte Anfangszustände nachwiesen. Weiterhin maßen wir die Zählstatistik der durch die Domänenwand transportierten Spins; die sich daraus ergebende schiefe Verteilung deutete auf einen nichtlinearen zugrundeliegenden Transportprozess hin, der an die dynamische Kardar-Parisi-Zhang Universalitätsklasse erinnert. Mittels Mott-Isolatoren im Limit tiefer Gitter konnten wir darüber hinaus die durch Photonen vermittelten Wechselwirkungen in einem Spinsystem untersuchen, das aus zwei über einen geschlossenen optischen Übergang gekoppelten Zuständen besteht. Durch spektroskopische Untersuchung der Reflexion und Transmission konnten wir die direkte Anregung einer subradianten Eigenmode und kohärente Spiegelung beobachten, was auf die Realisierung einer effizienten, im freien Raum operierenden, paraxialen Licht-Materie-Schnittstelle hindeutet.The interplay of quantum particles can give rise to collective phenomena whose characteristics are distinct from the behavior of individual particles. While quantum effects are generally challenging to observe, ultracold atomic gases trapped in optical lattices have emerged as a versatile experimental platform to study quantum many-body physics. In this thesis, we employed a site– and single-atom–resolved quantum gas microscope of bosonic Rb-87 atoms to explore many-body systems in and out of equilibrium. We first considered the ground-state quantum phase transition between the superfluid and Mott-insulating state in the Bose–Hubbard model, natively realized by cold atoms in optical lattices, for which we found brane parity to be suitable for detecting nonlocal order in the conventionally unordered two-dimensional Mott insulator. Using a microscopic approach to realizing tunable lattice geometries and programmable unit cells, we implemented square, triangular, kagome and Lieb lattices, and observed the mean-field scaling of the phase transition point with average coordination number. In a one-dimensional lattice, we furthermore studied high-temperature spin transport in the Heisenberg model, realized by superexchange in the Mott-insulating phase of a two-species Bose–Hubbard model. By tracking the relaxation dynamics of an initial domain-wall state, we found superdiffusive space–time scaling with an anomalous dynamical exponent of 3/2. We then probed the predicted microscopic requirements for superdiffusion, verifying regular diffusion for the integrability-broken two-dimensional Heisenberg model and ballistic transport for SU(2)-symmetry–broken net magnetized initial states. Subsequently, we measured the full counting statistics of spins transported across the domain wall; the resulting skewed distribution implied a nonlinear underlying transport process, reminiscent of the Kardar–Parisi–Zhang dynamical universality class. Moving to Mott insulators in the deep-lattice limit, we could moreover study photon-mediated interactions on a subwavelength-spaced, array-ordered spin system consisting of states coupled by a closed optical transition. By spectroscopically probing the reflectance and transmittance, we demonstrated the direct excitation of a subradiant eigenmode and observed specular reflection, indicating the realization of an efficient free-space paraxial light–matter interface

Diagnosis and application of laser wakefield accelerators

This thesis is concerned with experimental diagnostic methods of the laser-plasma interaction in laser wakefield accelerators, and how high energy photon beams from such accelerators may be exploited in a potential application. Raman scattered light from the 20 TW Astra laser pulse was found to have shorter wavelength than expected given the interferometrically-measured plasma density, due to the relativistic motion of plasma electrons. Simulations indicated that the scattering helps to shape the pulse, removing laser energy not trapped in the wake. The signature of Raman scatter from the 200 TW Astra-Gemini pulse was instead the generation of extended plasma filaments, the direction of which indicated weaker relativistic effects. Altering the focal spot position or quality generated more filaments and reduced electron beam charge, linking Raman scattering, pulse focussing, and accelerator performance. When a low intensity (10¹⁰ W/cm²) probe pulse crossed a high intensity (10¹⁹ W/cm²) drive pulse of equal frequency, the probe was observed to be amplified in intensity by up to 10⁵ over a distance of tens of microns. No frequency shift of the probe was observed, and the effect required the polarisations of the pulses to be parallel. In simulations the pulses created a ponderomotive grating, trapping electrons which were able to scatter the drive into the probe in the superradiant regime of Raman amplification. Laser wakefield-driven x-ray beams were used to perform a microtomographic scan of a human femoral trabecular bone sample. Under optimal conditions x-ray beams containing 1.3 ± 0.5 × 10⁹ photons were produced on 97% of laser shots, with critical energy 33 ± 12 keV and source size of 2-3 μm. Image resolution was 36 ± 7 μm and after 180 image acquisitions the 3D resolution of the tomogram was up to 50 μm. The average photon flux between 10 and 100 keV was 5.9 ± 2.4 × 10⁵ ph/s/mrad² which is comparable to microfocus sources capable of few-micron source sizes.Open Acces

Ab initio approaches to x-ray cavity QED : From multi-mode theory to nonlinear dynamics of Mössbauer nuclei

In this thesis, a theoretical framework for x-ray cavity QED with Mössbauer nuclei is developed. First, it is shown how Jaynes-Cummings-like few-mode models for open resonators can be derived from first principles, which has been an open question in the quantum optics literature. The resulting ab initio few-mode theory is applied to the x-ray cavity case, generalizing a previous phenomenological model. In addition, a second orthogonal approach is developed to enable the numerically efficient treatment of complex cavity geometries. It is shown that one can thereby directly derive a nuclear ensemble Master equation using Green’s functions to encode the cavity environment. This approach provides an ab initio quantum theory for the system, which resolves previous discrepancies and allows to semianalytically calculate cavity-modified nuclear level schemes without the need for a fitting procedure. On the basis of the two developed theories, multi-mode effects resulting from large losses in leaky resonators are investigated. A general criterion is introduced to identify and classify such multi-mode effects, which demonstrates that they are responsible for previously observed signatures in x-ray cavity experiments and can be harnessed to artificially tune nuclear quantum systems. Further interesting cusp features in nuclear Fano interference trajectories of x-ray cavities with overlapping modes are reported. Finally, the gained insights are employed to investigate nonlinear excitation dynamics of Mössbauer nuclei in the presence of strong x-ray driving fields. The feasibility of inverting nuclear ensembles at upcoming facilities and the possibility of using focused pulses in combination with x-ray cavities for intensity boosting is analyzed

Foundation experiments in quantum atom optics with ultracold metastable helium

The field of atom optics has progressed rapidly over the past 20 years since the realisation of Bose-Einstein condensation, such that the wave behaviour of atomic gases is now routinely demonstrated. Furthermore, the study of quantum atom optics, which goes beyond a ‘mean-field’ description of quantum systems to consider the behaviour of single particles, has demonstrated both the similarities between photons and massive species, and their differences as a result of the internal structure and external interactions of atoms. An important class of observable quantities which allow such effects to be measured are nth order correlation functions, which can be interpreted as a result of either particle or wave behaviour. These functions provide a statistical description of fluctuations in n-tuples of particles in a source, which rigorously defines concepts such as coherence. The quantum statistics of a Bose-Einstein condensate should be the same as that for an optical laser, while an ideal thermal Bose gas matches the behaviour of incoherent light. However, correlation measurements can also be used to quantify the influence of interactions, dimensionality, confining potentials and waveguides, and the difference in quantum statistics between fermions and bosons, which illustrates the rich range of behaviour exhibited by atomic gases. In this thesis, several aspects of quantum atom optics are explored with experiments using ultracold metastable helium, a species with the unique advantage of facilitating simple single-atom detection with high resolution, while still allowing Bose-Einstein condensates to be formed. The coherence of atomic systems is shown to be maintained when outcoupled as pulsed atom lasers, and the long-range order characteristic of Bose-Einstein condensates is demonstrated to third order for the first time. Conversely, thermal bunching is observed for a variety of atomic systems, including the measurement of correlation functions up to sixth order with near-ideal interference contrast. These results clearly demonstrate the correspondence between the quantum statistics of photons and atoms as was formalised by Glauber, as well as confirming the validity of applying Wick’s theorem to simplify the statistics of atomic gases. Correlation functions are also shown to be an ideal tool to probe the quantum state of an ultracold gas, and were used to observe the phenomenon of transverse condensation in an elongated Bose gas, as well as characterise the mode occupancy of matter waves guided by an optical potential. Ultracold metastable helium is also suitable for exploring other fundamental topics in quantum optics such particle/wave duality. The notion of complementarity stimulated long running philosophical discussions about how apparently mutually exclusive behaviours can coexist, which culminated in Wheeler devising his famous ‘delayed choice’ gedankenexperiment. A proposed experimental method to realise Wheeler’s experiment with ultracold atoms is discussed, and preliminary measurements presented which indicate that the completion of this experiment could be achieved in the near future. Not only is this of interest in its own right, but the implementation of this experiment has also developed techniques which may enable further studies in quantum atom optics such as investigations of the Hong-Ou-Mandel effect and quantum entanglement with massive particles