In this thesis we study the Dicke model outside the rotating wave approximation (RWA), by employing phase space techniques and the quantum trajectory theory. We present a review of the basic models of open systems in quantum optics and present an experimental proposition justifying the model to be studied. We use the phase space approach to study, among other subjects, entanglement, squeezing and fluctuations across a quantum phase transition. Three different phase space representations are used and their strengths and weaknesses compared. The quantum trajectory theory is applied to visualise the global quantum fluctuations and to learn how different measurement schemes will affect the creation of entanglement. / The University of Auckland, Department of Physics.

In this thesis we study the Dicke model outside the rotating wave approximation (RWA), by employing phase space techniques and the quantum trajectory theory. We present a review of the basic models of open systems in quantum optics and present an experimental proposition justifying the model to be studied. We use the phase space approach to study, among other subjects, entanglement, squeezing and fluctuations across a quantum phase transition. Three different phase space representations are used and their strengths and weaknesses compared. The quantum trajectory theory is applied to visualise the global quantum fluctuations and to learn how different measurement schemes will affect the creation of entanglement. / The University of Auckland, Department of Physics.

In this thesis we study the Dicke model outside the rotating wave approximation (RWA), by employing phase space techniques and the quantum trajectory theory. We present a review of the basic models of open systems in quantum optics and present an experimental proposition justifying the model to be studied. We use the phase space approach to study, among other subjects, entanglement, squeezing and fluctuations across a quantum phase transition. Three different phase space representations are used and their strengths and weaknesses compared. The quantum trajectory theory is applied to visualise the global quantum fluctuations and to learn how different measurement schemes will affect the creation of entanglement. / The University of Auckland, Department of Physics.

In this thesis we study the Dicke model outside the rotating wave approximation (RWA), by employing phase space techniques and the quantum trajectory theory. We present a review of the basic models of open systems in quantum optics and present an experimental proposition justifying the model to be studied. We use the phase space approach to study, among other subjects, entanglement, squeezing and fluctuations across a quantum phase transition. Three different phase space representations are used and their strengths and weaknesses compared. The quantum trajectory theory is applied to visualise the global quantum fluctuations and to learn how different measurement schemes will affect the creation of entanglement. / The University of Auckland, Department of Physics.

<div>Biological dynamics have been studied by many methods. Fluorescence dynamic microscopy and optical coherence tomography provided fundamental understandings of biological systems. However, their high NA optics only represent local characteristics. Biodynamic imaging (BDI) technique implements a low NA optics and acquires the statistical average of Doppler shifts that occurred by dynamic light scattering with biological dynamic subsystems provided globally averaged dynamic characteristics. </div><div>BDI is used for this study to investigate biomedical applications. The chemotherapy efficacy measurement by BDI demonstrated a good agreement between the Doppler spectral phenotypes and the preclinical outcomes. Also, dynamic responses of microbiomes by chemical stimuli demonstrated featured Doppler characteristics. The bacterial infection of epithelial spheroids showed consistent spectral responses and antibiotic-resistant E. coli infection treatment with a sensitive and resistive antibiotic showed a dramatic contrast. Furthermore, the phase-sensitive characteristics of BDI provided a clue to understanding the characteristics of the random process of biological systems. Levy-like heavy-tailed probability density functions are demonstrated and </div><div>the shape changed by infection will be discussed. </div>

Rare-earth ions in crystalline hosts have been identified as attractive media for quantum optical applications where record-high coherence times, quantum storage efficiency in solids, and quantum storage bandwidth have been demonstrated. Among rare-earth ions, Erbium uniquely possesses optical transitions at 1.5 micrometer region, making it suitable for integration with fiber telecommunication and silicon photonics. However, the intra-4f optical transitions are parity forbidden for rare-earth ions. Although, transitions are observed due to the interaction of the 4f valence electrons' energy levels with crystal fields or the lattice vibrations, the photon emission rate is prolonged for these ions. For example, Er³⁺ excited state lifetime for 1530nm transition is around 10 ms, which is about a million times longer than the excited state lifetime of alkali atoms like cesium and rubidium. There have been some recent works showing enhanced emission rate of erbium ions by about 10³ times by building a nano-photonic cavity to reach high Purcell factors. Our alternative approach to solving this problem is to use an ensemble of ions instead of a single ion to induce collective interactions in a suitable platform. In one experiment, we fabricated a SiN micro-ring resonator and implanted 10⁴ isotopically pure ¹⁶⁸Er ions in narrow segments located precisely in solids. The segments are typically separated by 0.962nm corresponding to multiples of the wavelength of Er emission at 1520nm. And we showed that when the lattice of ions is commensurate with the wavelength of the light, the scattering loss caused by the other ions is reduced. We have demonstrated for the first time that how designing atomic geometries in a solid-state photonic system can reduce the radiative loss due to spontaneous emission of ions into other photonic channels. This phenomenon is analogous to the Borrmann effect seen in x-ray transmissions of crystals at the Bragg angle of incidence. We have also shown how the interference between the optical cavity mode and atomic Bragg mode generates Fano-type resonance features. We performed these measurements using erbium ions in the SiN host. The limitations such as low coherence time and large inhomogeneous broadening in this platform prohibit observing cooperative and quantum behavior. To improve the optical property of erbium ions and study other cooperative effects, we engineered an effective ion array in an Er-doped Yttrium Orthosilicate crystal which can exhibit higher coherence time and narrower inhomogeneous broadening compared to SiN. So, we used the spectral hole burning technique to make an atomic grating in randomly distributed Er ions inside YSO. Two counter-propagating pump pulses created a standing wave inside the crystal, which enabled the creation of spectral holes only near the antinode locations. At the same time, atoms near nodes remain in the ground state. Such atomic population grating behaved like an atomic array. We have seen coherent backscattering up to 20% of the incident probe from this atomic grating resembling a mirror. To increase the reflection efficiency, we tried to increase the ion concentration in the YSO crystal. But, at high concentrations, the dipole-dipole interaction increases the broadening and decoherence rates of the ions. To increase the optical density without increasing the ion concentration, we fabricated long waveguides in SiN and LiNbO₃ with rare-earth ions implanted inside.As a future direction, we are trying to increase the reflection efficiency from the atomic grating to the point where we can see atomic mirror-assisted light trapping. We are also trying to see long-range co-operative behavior from rare-earth ion-doped crystals and rare-earth ions implanted inside long waveguides. This can open possibilities of new quantum photonic device engineering for applications in scalable and multiplexed quantum networks.

<p>  Based on the multichannel quantum defect method and streamlined R-matrix treatment, this thesis studies the multi-photon ionization spectrum for atomic helium and barium, and explores the electronic correlations of these atoms. For the helium atom, the above-threshold-ionization spectra have been calculated, with two linearly polarized photons, two oppositely circularly polarized photons, and three linearly polarized photons. The propensity rules for the single-photon ionization and autoionizing decay have been extended into the multi-photon region, showing that the excitation rules are not always satisfied for the most prominent channel. In a separate project, based on the spontaneous two-photon decay of the helium 1s2s 1Se excited state that has a rather long lifetime, one can create photon pairs that are entangled in time, frequency, and polarization. Experimental schemes are proposed to use them as a laser source to ionize another helium. Finally, we considered the oneand two-photon pathway coherent control of atomic helium and barium near their autoionizing levels. For the helium atom, we proposed a controlling scheme that can flip 90 % of the photocurrent by a slight change of laser frequency. For the barium atom, we computed the phase lag between 6s1/2 and 5d3/2 ionization continua, which agrees with the experimental results that a previous phenomenological model failed to reproduce. Our treatment also develops formulas to describe the effects of hyperfine depolarization on multiphoton ionization processes, and it identifies resonances that had not been observed and classified in previous experiments. <br>  </p>

This thesis presents a means of enhancing the iterative calculation techniques used in electronic structure calculations, particularly Kohn-Sham DFT. Based on the subspace iteration method of the FEAST eigenvalue solving algorithm, this nonlinear FEAST algorithm (NLFEAST) improves the convergence rate of traditional iterative methods and dramatically improves their robustness. A description of the algorithm is given, along with the results of numerical experiments that demonstrate its effectiveness and offer insight into the factors that determine how well it performs.

Here we present the design, assembly and successful ion trapping of a room-temperature ion trap system with a custom designed and fabricated surface electrode ion trap, which allows for rapid prototyping of novel trap designs such that new chips can be installed and reach UHV in under 2 days. The system has demonstrated success at trapping and maintaining both single ions and cold crystals of ions. We achieve this by fabricating our own custom surface Paul traps in the UMass Amherst cleanroom facilities, which are then argon ion milled, diced, mounted and wire bonded to an interposer which is placed in an ultra-high vacuum chamber and baked in a conventional oven for 46 hours. We demonstrate the system’s ability to confine strontium ions and present preliminary data towards calibrating the ion trap parameters for reduced heating rates. Future work will see the system being used to study the effects of various trap geometries, process fabrication steps and surface treatments on anomalous heating rates, and for portable quantum sensing applications, as an optical atomic clock.

<div>Field-orthogonal temporal mode analysis of optical fields was recently developed to form a new framework of quantum information science. But so far, the exact profiles of the temporal modes are not known, which makes it difficult to achieve mode selection and de-multiplexing. A novel feedback-iteration method which, combined with the stimulated emission method, can give rise to the exact forms of the temporal mode structure of pulse-pumped spontaneous parametric processes both for high gain parametric process, which gives rise to quantum entanglement in continuous variables, and for the low gain case, which produces a two-photon entangled state for discrete variables.</div><div><br></div><div>For the temporal mode analysis in high gain situations, the common treatment of parametric interaction Hamiltonian does not consider the issue of time ordering problem of interaction Hamiltonian and thus leads to the inaccurate conclusion that the mode structure and the temporal mode functions do not change as the gain increases. We use an approach that is usually employed for treating nonlinear interferometers and avoids the time ordering issue. This allows us to derive an evolution equation in differential-integral form. Numerical solutions for high gain situations indicate a gain-dependent mode structure that has its mode distributions changed and mode functions broadened as the gain increases. This will enable us to have a complete picture of the mode structure of parametric processes and produce high quality quantum sources for a variety of applications of quantum technology.</div><div><br></div><div>To verify the feedback-iteration method which measures temporal mode structure directly, we measure the joint spectral density of photon pairs produced with the spontaneous parametric down-conversion process of a pulse-pumped PPKTP crystal. The measurement method is based on a stimulated emission process which significantly improves the measurement time and accuracy compared with old spectrally resolved photon coincidence measurement. With the measured joint spectral density, the amplitude of the temporal modes can be obtained with the mathematical tool of singular value decomposition and compared with those measured directly with the feedback-iteration method.</div><div><br></div><div>Because the parametric amplifier is in essence a linear four-port device, it couples and linearly mixes two inputs before amplifying and sending them to two output ports. We show that for quadrature phase amplitudes, a parametric amplifier can replace beam splitters to play the role of mixer. We apply this idea to a continuous-variable quantum state teleportation scheme in which a parametric amplifier replaces a beam splitter in the Bell measurement. We show that this scheme is loss-tolerant in the Bell measurement process and thus demonstrate the advantage of parametric amplifiers over beam splitter in the applications in quantum measurement.</div>