MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Optical Wireless Communication for Mobile Platforms

The past few decades have witnessed the widespread adaptation of wireless devices such as cellular phones and Wifi-connected laptops, and demand for wireless communication is expected to continue to increase. Though radio frequency (RF) communication has traditionally dominated in this application space, recent decades have seen an increasing interest in the use of optical wireless (OW) communication to supplement RF communications. In contrast to RF communication technology, OW systems offer the use of largely unregulated electromagnetic spectrum and large bandwidths for communication. They also offer the potential to be highly secure against jamming and eavesdropping. Interest in OW has become especially keen in light of the maturation of light-emitting diode (LED) technology. This maturation, and the consequent emerging ubiquity of LED technology in lighting systems, has motivated the exploration of LEDs for wireless communication purposes in a wide variety of applications. Recent interest in this field has largely focused on the potential for indoor local area networks (LANs) to be realized with increasingly common LED-based lighting systems. We envision the use of LED-based OW to serve as a supplement to RF technology in communication between mobile platforms, which may include automobiles, robots, or unmanned aerial vehicles (UAVs). OW technology may be especially useful in what are known as RF-denied environments, in which RF communication may be prohibited or undesirable. The use of OW in these settings presents major challenges. In contrast to many RF systems, OWsystems that operate at ranges beyond a few meters typically require relatively precise alignment. For example, some laser-based optical wireless communication systems require alignment precision to within small fractions of a degree. This level of alignment precision can be difficult to maintain between mobile platforms. Additionally, the use of OW systems in outdoor settings presents the challenge of interference from ambient light, which can be much brighter than any LED transmitter. This thesis addresses these challenges to the use of LED-based communication between mobile platforms. We propose and analyze a dual-link LED-based system that uses one link with a wide transmission beam and relaxed alignment constraints to support a more narrow, precisely aligned, higher-data-rate link. The use of an optical link with relaxed alignment constraints to support the alignment of a more precisely aligned link motivates our exploration of a panoramic imaging receiver for estimating the range and bearing of neighboring nodes. The precision of such a system is analyzed and an experimental system is realized. Finally, we present an experimental prototype of a self-aligning LED-based link.