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.

High Precision Plasma Etch for Pattern Transfer: Towards Fluorocarbon Based Atomic Layer Etching

A basic requirement of a plasma etching process is fidelity of the patterned organic materials. In photolithography, a He plasma pretreatment (PPT) based on high ultraviolet and vacuum ultraviolet (UV/VUV) exposure was shown to be successful for roughness reduction of 193nm photoresist (PR). Typical multilayer masks consist of many other organic masking materials in addition to 193nm PR. These materials vary significantly in UV/VUV sensitivity and show, therefore, a different response to the He PPT. A delamination of the nanometer-thin, ion-induced dense amorphous carbon (DAC) layer was observed. Extensive He PPT exposure produces volatile species through UV/VUV induced scissioning. These species are trapped underneath the DAC layer in a subsequent plasma etch (PE), causing a loss of adhesion. Next to stabilizing organic materials, the major goals of this work included to establish and evaluate a cyclic fluorocarbon (FC) based approach for atomic layer etching (ALE) of SiO2 and Si; to characterize the mechanisms involved; and to evaluate the impact of processing parameters. Periodic, short precursor injections allow precise deposition of thin FC films. These films limit the amount of available chemical etchant during subsequent low energy, plasma-based Ar+ ion bombardment, resulting in strongly time-dependent etch rates. In situ ellipsometry showcased the self-limited etching. X-ray photoelectron spectroscopy (XPS) confirms FC film deposition and mixing with the substrate. The cyclic ALE approach is also able to precisely etch Si substrates. A reduced time-dependent etching is seen for Si, likely based on a lower physical sputtering energy threshold. A fluorinated, oxidized surface layer is present during ALE of Si and greatly influences the etch behavior. A reaction of the precursor with the fluorinated substrate upon precursor injection was observed and characterized. The cyclic ALE approach is transferred to a manufacturing scale reactor at IBM Research. Ensuring the transferability to industrial device patterning is crucial for the application of ALE. In addition to device patterning, the cyclic ALE process is employed for oxide removal from Si and SiGe surfaces with the goal of minimal substrate damage and surface residues. The ALE process developed for SiO2 and Si etching did not remove native oxide at the level required. Optimizing the process enabled strong O removal from the surface. Subsequent 90% H2/Ar plasma allow for removal of C and F residues.

Time-Reversal Massive Multipath Effect and Bandwidth Heterogeneity

The proliferation of new mobile communication devices, such as smartphones and tablets, has led to an exponential growth in network traffic. The demand for supporting the fast-growing consumer data rates urges the wireless service providers and researchers to seek a new efficient radio access technology, which is the so-called 5G technology, beyond what current 4G LTE can provide. On the other hand, ubiquitous RFID tags, sensors, actuators, mobile phones and etc. cut across many areas of modern-day living, which offers the ability to measure, infer and understand the environmental indicators. The proliferation of these devices creates the term of the Internet of Things (IoT). For the researchers and engineers in the field of wireless communication, the exploration of new effective techniques to support 5G communication and the IoT becomes an urgent task, which not only leads to fruitful research but also enhance the quality of our everyday life. Massive MIMO, which has shown the great potential in improving the achievable rate with a very large number of antennas, has become a popular candidate. However, the requirement of deploying a large number of antennas at the base station may not be feasible in indoor scenarios. Does there exist a good alternative that can achieve similar system performance to massive MIMO for indoor environment? In this dissertation, we address this question by proposing the time-reversal technique as a counterpart of massive MIMO in indoor scenario with the massive multipath effect. It is well known that radio signals will experience many multipaths due to the reflection from various scatters, especially in indoor environments. The traditional TR waveform is able to create a focusing effect at the intended receiver with very low transmitter complexity in a severe multipath channel. TR's focusing effect is in essence a spatial-temporal resonance effect that brings all the multipaths to arrive at a particular location at a specific moment. We show that by using time-reversal signal processing, with a sufficiently large bandwidth, one can harvest the massive multipaths naturally existing in a rich-scattering environment to form a large number of virtual antennas and achieve the desired massive multipath effect with a single antenna. Further, we explore the optimal bandwidth for TR system to achieve maximal spectral efficiency. Through evaluating the spectral efficiency, the optimal bandwidth for TR system is found determined by the system parameters, e.g., the number of users and backoff factor, instead of the waveform types. Moreover, we investigate the tradeoff between complexity and performance through establishing a generalized relationship between the system performance and waveform quantization in a practical communication system. It is shown that a 4-bit quantized waveforms can be used to achieve the similar bit-error-rate compared to the TR system with perfect precision waveforms. Besides 5G technology, Internet of Things (IoT) is another terminology that recently attracts more and more attention from both academia and industry. In the second part of this dissertation, the heterogeneity issue within the IoT is explored. One of the significant heterogeneity considering the massive amount of devices in the IoT is the device heterogeneity, i.e., the heterogeneous bandwidths and associated radio-frequency (RF) components. The traditional middleware techniques result in the fragmentation of the whole network, hampering the objects interoperability and slowing down the development of a unified reference model for the IoT. We propose a novel TR-based heterogeneous system, which can address the bandwidth heterogeneity and maintain the benefit of TR at the same time. The increase of complexity in the proposed system lies in the digital processing at the access point (AP), instead of at the devices' ends, which can be easily handled with more powerful digital signal processor (DSP). Meanwhile, the complexity of the terminal devices stays low and therefore satisfies the low-complexity and scalability requirement of the IoT. Since there is no middleware in the proposed scheme and the additional physical layer complexity concentrates on the AP side, the proposed heterogeneous TR system better satisfies the low-complexity and energy-efficiency requirement for the terminal devices (TDs) compared with the middleware approach.