Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.

Optical Control of Magnetic Feshbach Resonances by Closed-Channel Electromagnetically Induced Transparency

Optical control of interactions in ultracold gases opens new fields of research by creating ``designer" interactions with high spatial and temporal resolution. However, previous optical methods using single optical fields generally suffer from atom loss due to spontaneous scattering. This thesis reports new optical methods, employing two optical fields to control interactions in ultracold gases, while suppressing spontaneous scattering by quantum interference. In this dissertation, I will discuss the experimental demonstration of two optical field methods to control narrow and broad magnetic Feshbach resonances in an ultracold gas of $^6$Li atoms. The narrow Feshbach resonance is shifted by $30$ times its width and atom loss suppressed by destructive quantum interference. Near the broad Feshbach resonance, the spontaneous lifetime of the atoms is increased from $0.5$ ms for single field methods to $400$ ms using our two optical field method. Furthermore, I report on a new theoretical model, the continuum-dressed state model, that calculates the optically induced scattering phase shift for both the broad and narrow Feshbach resonances by treating them in a unified manner. The continuum-dressed state model fits the experimental data both in shape and magnitude using only one free parameter. Using the continuum-dressed state model, I illustrate the advantages of our two optical field method over single-field optical methods.

Using Coding to Improve Localization and Backscatter Communication Performance in Low-Power Sensor Networks

Backscatter communication is an emerging wireless technology that recently has gained an increase in attention from both academic and industry circles. The key innovation of the technology is the ability of ultra-low power devices to utilize nearby existing radio signals to communicate. As there is no need to generate their own energetic radio signal, the devices can benefit from a simple design, are very inexpensive and are extremely energy efficient compared with traditional wireless communication. These benefits have made backscatter communication a desirable candidate for distributed wireless sensor network applications with energy constraints.

The backscatter channel presents a unique set of challenges. Unlike a conventional one-way communication (in which the information source is also the energy source), the backscatter channel experiences strong self-interference and spread Doppler clutter that mask the information-bearing (modulated) signal scattered from the device. Both of these sources of interference arise from the scattering of the transmitted signal off of objects, both stationary and moving, in the environment. Additionally, the measurement of the location of the backscatter device is negatively affected by both the clutter and the modulation of the signal return.

This work proposes a channel coding framework for the backscatter channel consisting of a bi-static transmitter/receiver pair and a quasi-cooperative transponder. It proposes to use run-length limited coding to mitigate the background self-interference and spread-Doppler clutter with only a small decrease in communication rate. The proposed method applies to both binary phase-shift keying (BPSK) and quadrature-amplitude modulation (QAM) scheme and provides an increase in rate by up to a factor of two compared with previous methods.

Additionally, this work analyzes the use of frequency modulation and bi-phase waveform coding for the transmitted (interrogating) waveform for high precision range estimation of the transponder location. Compared to previous methods, optimal lower range sidelobes are achieved. Moreover, since both the transmitted (interrogating) waveform coding and transponder communication coding result in instantaneous phase modulation of the signal, cross-interference between localization and communication tasks exists. Phase discriminating algorithm is proposed to make it possible to separate the waveform coding from the communication coding, upon reception, and achieve localization with increased signal energy by up to 3 dB compared with previous reported results.

The joint communication-localization framework also enables a low-complexity receiver design because the same radio is used both for localization and communication.

Simulations comparing the performance of different codes corroborate the theoretical results and offer possible trade-off between information rate and clutter mitigation as well as a trade-off between choice of waveform-channel coding pairs. Experimental results from a brass-board microwave system in an indoor environment are also presented and discussed.