Optical sensing and imaging inside heavily scattering media are of intense interest because of their importance in biomedical, environmental, and material inspection applications. When coherent light interacts with scatterers, bright and dark intensity regions form, a phenomenon known as speckle. Often viewed as being detrimental, speckle can be exploited to yield useful information with a correlation analysis.<br> <br>A coherent method is presented for the imaging of a hidden object moving within thick and randomly scattering media using speckle intensity correlations over object position, with the possibility of accessing super-resolution information. With prior information about the moving object's motion, spatial speckle intensity correlations as a function of object position can reveal the hidden object's relative refractive index distribution. Our experimental evidence shows that it is feasible to image complex aperture-type moving objects and circular patches inside scatter that is a magnitude of order heavier than other comparable imaging modalities. Images of the moving object were obtained from speckle intensity correlation data using phase retrieval. Biological tissue was used to demonstrate the possibility of in vivo deep-tissue imaging. Speckle intensity correlations are shown to be sensitive to both the scattering strength of the embedded object and the environment, both of which are useful for sensing. We present a general theory that describes this influence of the background scattering medium and allows for imaging a hidden moving object. Additionally, we present a method to improve the sensitivity of speckle correlography in remote optical metrology. By placing a scattering slab in front of the detector, we demonstrate enhanced sensitivity, detecting the subwavelength in-plane displacement of a remote diffuse object.

<p>Metasurfaces are broadly defined as artificially engineered material interfaces that have the ability to determinately control the amplitude and phase signatures of an incident electromagnetic wave. Subwavelength sized optical scatterers employed at the planar interface of two media, introduce abrupt modifications to impinged light characteristics. Arbitrary engineering of the optical interactions and the arrangement of the scatterers on plane, enable ultra-compact, miniaturized optical systems with a wide array of applications (e.g. nanoscale and nonlinear optics, sensing, detection, energy harvesting, information processing and so on) realizable by the metasurfaces. However, maturation from the laboratory to industry scale realistic systems remain largely elusive despite the expanding reach and vast domains of functionalities demonstrated by researchers. A large part of this multi-faceted problem stems from the practical constraints posed by the commonly used plasmonic materials that limit their applicability in devices requiring high temperature stability, robustness in varying ambient, mechanical durability, stable growth into nanoscale films, CMOS process compatibility, stable bio-compatibility, and so on. </p> <p>Aiming to create a whole-some solution, my research has focused on developing novel, high-performance, functional plasmonic metasurface devices that utilize the inherent benefits of various emerging and alternative material platforms. Among these, the two-dimensional MXenes and the refractory transition metal nitrides are of particular importance. By exploiting the plasmonic response of thin films of the titanium carbide MXene (Ti₃C₂T_x) in the near infrared spectral window, a highly broadband metamaterial absorber has been designed, fabricated and experimentally demonstrated. In another work, high efficiency photonic spin Hall Effect has been experimentally realized in robust phase gradient metasurface devices based on two different refractory transition metal nitrides –titanium nitride (TiN) and zirconium nitride (ZrN). Further, taking advantage of the refractory nature of these plasmonic nitrides, a metasurface based temperature sensor has been developed that is capable of remote, optical sensing of very high temperatures ranging up to 1200^oC.</p>

<pre>Bridging the gap between the classical and quantum regimes has consequences not only for fundamental tests of quantum theory, but for the relation between quantum mechanics and gravity. The field of levito-dynamics provides a promising platform for testing the hypotheses of the works investigating these ideas. By manipulating a macroscopic particle's motion to the scale of its ground state wavefunction, levito-dynamics offers insight into the macroscopic-quantum regime.</pre><pre><br></pre><pre>Ardent and promising research has brought the field of levito-dynamics to a state in which these tests are available. Recent work has brought a mesoscopic particle's motion to near the ground state. Several factors of decoherence are limiting efficient testing of these fundamental theories which implies the need for alternative strategies for achieving the same goal. This thesis is concerned with investigating alternative methods that may enable a mesoscopic particle to reach the quantum regime. </pre><pre><br></pre><pre><pre>In this thesis, three theoretical proposals are studied as a means for a mesoscopic particle to reach the quantum regime as well as a detailed study into one of the most important factors of heating and decoherence for optical trapping. The first study of cooling a particle's motion highlights that the rotational degrees of freedom of a levitated symmetric-top particle leads to large harmonic frequencies compared to the translational motion, offering a more accessible ground state temperature after feedback cooling is applied. An analysis of a recent experiment under similar conditions is compared with the theoretical findings and found to be consistent. <br></pre> <pre>The second method of cooling takes advantage of the decades long knowledge of atom trapping and cooling. By coupling a spin-polarized, continuously Doppler cooled atomic gas to a magnetic nanoparticle through the dipole-dipole interaction, motional energy is able to be removed from the nanoparticle. Through this method, the particle is able to reach near its quantum ground state provided the atoms are at a temperature below the nanoparticle ground state temperature and the atom number is sufficiently large.</pre> <pre>The final investigation presents the dynamics of an optically levitated dielectric disk in a Gaussian standing wave. Though few studies have been performed on disks both theoretically and experimentally, our findings show that the stable couplings between the translational and rotational degrees of freedom offer a possibility for cooling several degrees of freedom simultaneously by actively cooling a single degree freedom.</pre></pre>

<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>

<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>

<p>Partition density functional theory (P-DFT) is a density-based embedding method used to calculate the electronic properties of molecules through self-consistent calculations on fragments. P-DFT features a unique set of fragment densities that can be used to define formal charges and local dipoles. This dissertation is concerned mainly with establishing how the optimal fragment densities and energies of P-DFT depend on the specific methods employed during the self-consistent fragment calculations. First, we develop a procedure to perform P-DFT calculations on three-dimensional heteronuclear diatomic molecules, and we compare and contrast two different approaches to deal with non-integer electron numbers: Fractionally occupied orbitals (FOO) and ensemble averages (ENS). We find that, although both ENS and FOO methods lead to the same total energy and density, the ENS fragment densities are less distorted than those of FOO when compared to their isolated counterparts. Second, we formulate partition spin density functional theory (P-SDFT) and perform numerical calculations on closed- and open-shell diatomic molecules. We find that, for closed-shell molecules, while P-SDFT and P-DFT are equivalent for FOO, they partition the same total density of a molecule differently for ENS. For open-shell molecules, P-SDFT and P-DFT yield different sets of fragment densities for both FOO and ENS. Finally, by considering a one-electron system, we investigate the self-interaction error (SIE) produced by approximate exchange-correlation functionals and find that the molecular SIE can be attributed mainly to the non-additive Hartree-exchange-correlation energy.</p>

<p>Developing a hybrid platform that combines nanophotonic circuits and atomic physic may provide new chip-scale devices for quantum application or versatile tools for exploring photon-mediated long-range quantum systems. However, this challenging project demands the excellent integration of cold atom trapping and manipulation technology with cutting-edge nanophotonics circuit design and fabrication. In this thesis project, we aim to develop a novel suspended membrane platform that serves as a quantum interface between laser-cooled, trapped atoms in an ultrahigh vacuum and the photons guided in the nanophotonic circuits based on high-quality silicon nitride microring resonators fabricated on a transparent membrane substrate. </p> <p><br></p> <p>The proposed platform meets the stringent performance requirements imposed by nanofabrication and optical physics in an ultra-high vacuum. These include a high yield rate for mm-scale suspended dielectric photonic devices, minimization of the surface roughness to achieve ultrahigh-optical quality, complete control of optical loss/in-coupling rate to achieve critical photon coupling to a microring resonator, and high-efficiency waveguide optical input/output coupler in an ultrahigh vacuum environment. This platform is compatible with laser-cooled and trapped cold atoms. The experimental demonstration of trapping and imaging single atoms on a photonic resonator circuit using optical tweezers has been demonstrated. Our circuit design can potentially reach a record-high cooperativity parameter C$>$500 for single atom-photon coupling, which is of high importance in realizing a coherent quantum nonlinear optical platform and holds great promise as an on-chip atom-cavity QED platform.</p>

<p>This dissertation discusses the theoretical methods for quantum scattering in the context of x-ray scattering from electrons and classical scattering in the context of collisions between Rydberg atoms.</p> <p><br></p> <p>A method for describing non-relativistic x-ray scattering from bound electrons is presented. The approach described incorporates the full spatial dependence of the incident x-ray field and is non-perturbative in the incident x-ray field. The x-ray scattering probability obtained by numerical solution for the case of free-electrons is bench-marked with well known analytical free-electron results.</p> <p><br></p> <p>A recent investigation by Fuchs \emph{et al.} [Nat. Phys. 11, 964 (2015)] revealed an anomalous frequency shift of at least 800 eV in non-linear Compton scattering of high-intensity x-rays by electrons in solid beryllium. The x-ray scattering approach described is used to explore the role of binding energy, band structure, electron-electron correlation and a semi-Compton channel in the frequency shift of scattered x-rays for different scattered angles. The results of the calculation do not exhibit an additional redshift for the scattered x-rays beyond the non-linear Compton shift predicted by the free-electron model. </p> <p><br></p> <p>The interference between Compton scattering and nonlinear Compton scattering from a two-color field in the x-ray regime is theoretically analyzed for bound electrons. A discussion of the underlying phase shifts and the dependence of the interference effect on the polarizations of the incident and outgoing fields are presented. </p> <p><br></p> <p>The problem of using x-ray scattering to image the dynamics of an electron in a bound system is examined. Previous work on imaging electronic wave-packet dynamics with x-ray scattering revealed that the scattering patterns deviate substantially from the notion of instantaneous momentum density of the wave packet. Here we show that the scattering patterns can provide clear insights into the electronic wave packet dynamics if the final state of the scattered electron and the scattered photon momentum are determined simultaneously. The scattering probability is shown to be proportional to the modulus square of the Fourier transform of the instantaneous electronic spatial wave function weighted by the final state of the electron.</p> <p><br></p> <p>Collisional ionization between Rydberg atoms is examined. The dependence of the ionization cross section on the magnitude and the direction of orbital angular momentum of the electrons and the direction of the Laplace-Runge-Lenz vector of the electrons is studied. The case of exchange ionization is examined and its dependence on the magnitude of angular momentum of the electrons is discussed.</p> <p><br></p>