When light exhibits particle properties, and when matter exhibits wave properties quantum mechanics is needed to describe physical phenomena. A two-photon source produces nonmaximally entangled photon pairs when the source is small enough to diffract light. It is shown that diffraction degrades the entanglement. Quantum states produced in this way are used to probe the complementarity between path information and interference in Young's double slit experiment. When two photons have a nonmaximally entangled polarization it is shown that the Pancharatnam phase is dependent on the entanglement in a nontrivial way. This could be used for implementing simple quantum logical circuits. Magnetic traps are capable of holding cold neutral atoms. It is shown that magnetic traps and guides can be generated by thin wires etched on a surface using standard nanofabrication technology. These atom chips can hold and manipulate atoms located a few microns above the surface with very high accuracy. The potentials are very versatile and allows for highly complex designs, one such design implemented here is a beam splitter for neutral atoms. Interferometry with these confined de Broglie is also considered. These atom chips could be used for implementing quantum logical circuits.

Comparisons between measurements of the ground-state hyperfine structure and gravitational acceleration of hydrogen and antihydrogen could provide a test of fundamental physical theories such as CPT (charge conjugation, parity, time-reversal) and gravitational symmetries. Currently, antihydrogen traps are based on Malmberg-Penning traps. The number of antiprotons in Malmberg-Penning traps with sufficiently low energy to be suitable for trappable antihydrogen production may be reduced by the electrostatic space charge of the positrons and/or collisions among antiprotons. Alternative trap designs may be needed for future antihydrogen experiments. A computational tool is developed to simulate charged particle motion in customizable magnetic fields generated by combinations of current loops and current lines. The tool is used to examine charged particle confinement in two systems consisting of dual, levitated current loops. The loops are coaxial and arranged to produce a magnetic null curve. Conditions leading to confinement in the system are quantified and confinement modes near the null curve and encircling one or both loops are identified. Furthermore, the tool is used to examine and quantify charged particle motion parallel to the null curve in the large radius limit of the dual, levitated current loops. An alternative to new trap designs is to identify the effects of the positron space in existing traps and to find modes of operation where the space charge is beneficial. Techniques are developed to apply the Boltzmann density relation along curved magnetic field lines. Equilibrium electrostatic potential profiles for a positron plasma are computed by solving Poisson's equation using a finite-difference method. Equilibria are computed in a model Penning trap with an axially varying magnetic field. Also, equilibria are computed for a positron plasma in a model of the ALPHA trap. Electric potential wells are found to form self-consistently. The technique is expanded to compute equilibria for a two-species plasma with an antiproton plasma confined by the positron space charge. The two-species equilibria are used to estimate timescales associated with three-body recombination, losses due to collisions between antiprotons, and temperature equilibration. An equilibrium where the three-body recombination rate is the smallest is identified.