This dissertation reports on quantum state preparation of cesium atoms in a two-dimensional optical lattice, by resolved-sideband Raman cooling. An optical lattice is a periodic potential produced by the light shift interaction between an atom and light field. Laser cooled atoms can become strongly localized about the bottom of potential wells in an optical lattice, where they occupy a discrete spectrum of bound vibrational energy levels. The distribution over vibrational levels of atoms in the lattice is characterized by the mean vibrational excitation, n . In an optical lattice, absorption and emission of photons from lattice beams causes n to increase in time. This source of heating is always present, but its rate can be greatly reduced in a lattice detuned far from the atomic resonance. Sideband cooling is an efficient means of transferring atoms from higher into lower-lying vibrational levels and, thus, it reduces n for the ensemble. If the sideband cooling rate is much greater than the heating rate, then n approaches zero and virtually all atoms are in the lowest vibrational level in their potential wells. Our sideband cooling scheme involves stimulated Raman transitions between bound states in the potential wells of a pair of magnetic sublevels, followed by optical pumping, for a net loss of one quantum of vibration per cooling cycle. The process accumulates 98% of atoms in the ground vibrational level of a potential well associated with a single Zeeman substate. Each atom in the lattice is then very close to a pure state. For two-dimensional lattice with sideband cooling we find nx≈ny≈0.008 &parl0;16&parr0; . Various issues related to state preparation and sideband cooling are also discussed in the context of a one dimensional lin ⊥ lin optical lattice. These include improvement of laser cooling in a near resonance lattice by application of weak magnetic fields, transfer of atoms from near into far off-resonance lattices, and heating rates in far off-resonance lattices.

An ellipsoidal dome is a conformal optical element used to replace a hemispherical dome on a missile to enhance its performance by reducing its aerodynamic drag. Conformal optics are a general class of optical systems in which the optical elements are shaped to optimize something other than image quality, such as aerodynamics. An ellipsoidal dome has lower aerodynamic drag than a comparably sized hemispherical dome. On a missile, lower drag improves its aerodynamic performance by increasing its range and fuel efficiency but degrades the quality of the transmitted wavefront. In particular, an ellipsoidal dome introduces a varying aberration component that depends on the orientation of the aperture stop, which is pivoted about a fixed axis inside the dome. The transmitted ray bundle is incident only on a portion of the dome surface, and the included area lacks axial symmetry. To better understand the imaging characteristics of an ellipsoidal dome in this application, the first- and third-order optical properties of a constant thickness dome are investigated. Particular emphasis is placed on the geometry and symmetry of an ellipse, which impose certain constraints on the form of the aberration coefficients. The geometry is defined in terms of the aerodynamic fineness ratio, outer diameter, and center thickness of the dome. Emphasis is placed on third-order astigmatism and coma, which are shown to be the dominant aberration terms. The effects of varying the fineness ratio, thickness, and index of refraction of a dome are also investigated.

This dissertation research has focused on the design of two spectroscopic instruments that operate outside of the UV/visible region for the analysis of volatile organic hydrocarbons and hard-to-separate hydrocarbon mixtures. The first design was solid state near infrared spectrometer. The fast acquisition rate of the NIR spectrometer allowed the monitoring of the bromination of 1-hexene. The concentrations of 1-hexene and 1,2-dibromohexane were determined for the reaction using classical least squares. The root mean squared errors of prediction for 1-hexene and 1,2-dibromohexane concentrations were 0.01 and 0.003 M, respectively. This research project also focused on the investigation of the effects of instrumental parameters on partial least squares models by comparing the results obtained from four different spectrometers. The results indicate that instrumental parameters, such as resolution and wavelength coverage, have a larger effect on experimental results than the analysis method (NIR or Raman). The second instrument design investigated here was a vacuum ultraviolet ICP-AES which monitored the 130 to 200 nm wavelength range. Fifteen nonmetals were used to determine the quantitative characteristics of the design. All elements demonstrated detection limits in the ppb range. The most sensitive emission line in this work was the aluminum 167.079 nm line which had a detection limit of 200 ppt. A VUV atomic emission line database was developed to provide an analytical reference for future investigations. The database included the emission lines from 76 elements over the 130 to 195 nm wavelength region. Over 2200 lines were observed and reported. Over 1000 of the lines were previously unreported in the two major existing references for the VUV. This work is the first VUV reference to provide truly comparable intensities for a large number of elements. A GC-VUV-ICP-AES was developed to investigate the potential of VUV-ICP atomic emission spectroscopy to provide both quantitative and qualitative information for mixtures. Chlorine and carbon chromatograms were obtained simultaneously for volatile organic hydrocarbon (VOC) mixtures. The work showed that GC-VUV-ICP-AES has the potential of generating empirical formulas for compounds by simultaneously quantitating each element in the compound and determining their ratios.

In contrast to electromagnetic fields, matter-wave fields are intrinsically interacting due to the presence of atom-atom collisions. Hence, matter-wave optics becomes effectively nonlinear as soon as the atomic densities are high enough that collisions can no longer be ignored. The goal of this dissertation is to study selected aspects of atom optics under such conditions. Specifically, Chapter 2 studies the near-resonant dipole-dipole interaction between two atoms in tailored vacua. In contrast to spontaneous emission, whose rate is known to be influenced by the type of vacuum the atom interacts with, we find that the dipole-dipole potential is determined only by the free space vacuum and is not modified either by thermal or squeezed vacua. In addition in the far off-resonance regime we find that the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground state. In the second part of the dissertation, which comprises Chapter 3, we then study several aspects of the many-body theory of atomic ultracold systems in situations where the nonlinearity arises due to the two-body dipole-dipole interaction. After a formal theoretical development we discuss the possibility of using atomic phase conjugation off Bose condensates as a diagnostic tool to access the spatial coherence properties and to measure the lifetime of the condensate. We argue that phase conjugation provides an attractive alternative to the optical methods of probing condensate proposed in the past. We further study the elementary excitations in a multicomponent Bose condensates and determine the quasi-particle frequency spectrum. We show that in that case interferences resulting from cross-coupling between the condensate components can lead to a reversal of the sign of the effective two-body interaction and to the onset of spatial instabilities.

This dissertation covers the field of atom optics and is divided into four main chapters: In Chapter 2 we investigate the effects of light forces on the center-of-mass motion of two-level atoms. This will lead to the discussion of two regimes: the "ray optic" and the "wave optic" regime. In the first case, an atom is well localized in the field which allows a comparison to be made with classical ray optics. In the second case, the atom is strongly delocalized which leads to a wave treatment and allows a comparison with diffractive optics. We finish this chapter with an example in each regime: Doppler cooling for ray optics and an atomic Fabry-Perot for wave optics. In Chapter 3 we extend the results of the previous chapter to the diffraction of atoms by a standing light field. We cover three regimes in the near resonant Kapitza-Dirac effect: the Raman-Nath, the Bragg and the optical Stern-Gerlach regime. In the Raman-Nath and Bragg regimes, the wave-packet is strongly delocalized compared to the period of the standing wave. In contrast, the Stern-Gerlach regime has a small spatial extent. The Raman-Nath and Bragg regimes are differentiated in their treatment of the kinetic energy. Initially we only discuss coherent interactions. In the later half of this chapter we introduce spontaneous emission and show how its presence affects the diffraction pattern in each of these regimes. In Chapter 4 we cover various atomic cooling schemes: strong field Sisyphus cooling, adiabatic cooling, evaporative cooling, polarization gradient cooling and velocity selective coherent population trapping. We begin with a brief discussion of atomic temperature. We then cover two cooling schemes for two-level atoms. We eventually move to multi-level atoms and end this chapter with a two-atom multi-level system. In Chapter 5 we conclude with a brief discussion of practical uses and devices that may arise from atom optics such as lenses, mirrors, gravitational interferometry, lithography and atomic clocks.

A new wavefront sensor and its application in investigating the aberrations in the human eyes are presented here. The refractive errors in human eye are discussed in detail and the need for using a wavefront sensor in quantifying these errors in detail is discussed in the context of modern refractive surgeries. The development of the new wavefront sensor from the existing ones is presented after a brief survey of existing wavefront sensors for the human eye. This wavefront sensor is based on the concept of wavefront's curvature sensing as opposed to the concept of wavefront's slope sensing which is the case for the current wavefront sensors that are being used for the human eye. Detailed theoretical analysis of the wavefront sensor along with its limitations is done. The performance is evaluated using software simulations, experimental analysis with a model human eye and with human eye in vivo. The design and implementation of a Pupillometer and its use along with a wavefront sensor is also presented.

Optics with external surfaces that deviate from conventional forms to better satisfy the needs of host platform are known as conformal optics. These external surfaces generate significant amounts of aberration that may be compensated with additional corrector elements. This dissertation introduces a new tool for the design of correctors for non-rotationally symmetric optical systems. This is accomplished through the derivation of two new differential equations using an approach similar to that of Wassermann and Wolf. The new aspheric design equations are derived without the assumption of axial symmetry and may be used to precisely control a ray bundle. Solving the new design equations produces the surface profiles of two aspheric optical surfaces which make a non-rotationally symmetric system aplanatic. The aplanatic system may contain tilted and decentered elements, or optical elements without rotational symmetry before and after the two aspheric surfaces. As coma and spherical aberration can be significant in conformal windows, these equations are powerful for producing starting points and developing a design. To validate the new equations, they were implemented in a Code V RTM macro called the Generalized Aspheric design Program (GAP). This macro is used in the design of a variety of non-rotationally symmetric optical systems to create a diffraction limited field of view. These include a system with an elliptical dome with a decentered inside surface, a system containing cylindrical elements, and a system with a toroidal conformal window. In all cases, GAP is able to directly generate corrector surfaces. For comparison, the classical Wassermann-Wolf equations were also implemented in a Code V macro for the design of rotationally symmetric systems.

The topic of dissertation is on the development of a miniature imaging device named as multi-modal miniature microscope [a.k.a. 4M Device]. Generally speaking, the development of an optical imaging device involves three main processes: optical design, fabrication and metrology. They are interdependent and often comprise a feedback loop. This dissertation will address these three processes sequentially. The 4M device is miniature compound microscope consisting of miniature optics, electronic imaging device, and mechanical device. Every component is integrated on single silicon substrate. The main purpose of 4M device is to provide an imaging capability for the detection of pre-cancer without biopsy. It uses a novel optics called hybrid lens that is fabricated by using a grayscale photomask and photolithographic technique. The hybrid lens is made of sot-gel material and glass substrate. It has 1.2mm of diameter and its surface is conic. Given lens design constraints from the fabrication, the series of lens design for 4M device are implemented and presented. Each design delivers diffraction-limited imaging performance with N.A ranging from 0.4 to 0.7. The 4M device that is currently built has 0.4 of N.A. The imaging quality assessments of 4M device are also implemented in quantitative and qualitative ways. There are two instruments for imaging quality assessment: Multi-modal imaging testbed for entire imaging device and Shack-Hartmann wavefront sensor for individual element. The qualitative assessment includes multi-modal imaging experiments under different illumination modes. The object is a cervical cancer cell prepared by Dr. Kortum's Group at Univ. of Texas at Austin. The qualitative assessment includes the surface characterization and wavefront measurement of individual optics and the MTF measurement of entire device. The results of imaging quality assessment show the potential of 4M device for medical imaging device. They also explain the degradation of imaging quality.

A complete description of the quantum state of a physical system is the fundamental knowledge necessary to statistically predict the outcome of measurements. In turning this statement around, Wolfgang Pauli raised already in 1933 the question, whether an unknown quantum state could be uniquely determined by appropriate measurements--a problem that has gained new relevance in recent years. In order to harness the prospects of quantum computing, secure communication, teleportation, and the like, the development of techniques to accurately control and measure quantum states has now become a matter of practical as well as fundamental interest. However, there is no general answer to Pauli's very basic question, and quantum state reconstruction algorithms have been developed and experimentally demonstrated only for a few systems so far. This thesis presents a novel experimental method to measure the unknown and generally mixed quantum state for an angular momentum of arbitrary magnitude. The (2F + 1) x (2F + 1) density matrix describing the quantum state is hereby completely determined from a set of Stern-Gerlach measurements with (4F + 1) different orientations of the quantization axis. This protocol is implemented for laser cooled Cesium atoms in the 6S₁/₂(F = 4) hyperfine ground state manifold, and is applied to a number of test states prepared by optical pumping and Larmor precession. A comparison of the input and the measured states shows successful reconstructions with fidelities of about 0.95.

Conventional methods of aspheric surface production utilize sub-diameter rigid tooling. The spherical tool has a slight misfit with respect to the aspheric optic being produced. This misfit leads to long working times due to minimal surface contact. It also leads to high frequency zones due to the mechanics of grinding and polishing. To remedy both of these problems, a non-rigid tool is employed. A thin membrane (∼1 mm) of aluminum or plastic is machined or pressed to the correct radius and grinding/polishing pads are glued to the lap. These semi-flexible laps make better contact with the work surface, thus reducing production time. They also make much smoother surfaces than does conventional tooling. This thesis details the theoretical analysis and simulations as well as experimental results and conclusions. The experimental results include: static deflection testing, removal rate testing as a function of spatial frequency, and production data from two fabrication projects.