Nonsequential double ionization (NSDI) processes of nonaligned diatomic molecules N 2 and O 2 are studied using the S -matrix theory. Our results show that the NSDI process significantly depends on the molecular symmetry and structure. The ratio of NSDI rate to single ionization rate as a function of the field intensity is obtained. It is found that N 2 behaves closely with its companion atom Ar in the ratios over the entire intensity range, while O 2 exhibits an obvious suppression effect, which is qualitatively consistent with the experiment.
With quantum calculations, we have investigated the multiphoton nonsequential double ionization of helium atoms in intense laser fields at ultraviolet wavelengths. Very surprisingly, we found a so-far unobserved double-circle structure in the correlated electron momentum spectra. The double-circle structure essentially reveals multiphoton Rabi oscillations of two electrons, which are strongly supported by the oscillating population of a certain doubly excited state and by the oscillating double ionization signals. This two-electron multiphoton Rabi effect provides a profound understanding of electronic correlations and complicated multiphoton phenomena and is expected to be a new tool for broad applications, such as quantum coherent control.
Non-sequential double ionization (NSDI) is a strong-field process involving the correlated emission of two electrons. This thesis proposes an analog quantum simulator to study NSDI in a helium atom, using ultracold trapped atoms to represent electrons. The core potential is replaced by an optical trap created by a laser. Rydberg atoms, with their strong long-range interactions, are ideal for simulating attosecond phenomena. A numerical simulation is conducted to observe the correlated two-electron momentum components after a laser pulse is applied.
With quantum calculations, we have investigated the multiphoton nonsequential double ionization of helium atoms in intense laser fields at ultraviolet wavelengths. Very surprisingly, we find a so-far unobserved double-circle structure in the correlated electron momentum spectra. The double-circle structure essentially reveals multiphoton Rabi oscillations of two electrons, which are strongly supported by the oscillating population of a certain doubly excited state and by the oscillating double ionization signals. This two-electron multiphoton Rabi effect provides profound understandings of electronic correlations and complicated multiphoton phenomena and is expected to be a new tool for broad applications, such as quantum coherent control.
The first part of this project involved continued development of theoretical models of diatomic molecular electronic level structure for application to the production of ultracold diatomic molecules via photoassociation. Recently, there has been considerable interest in producing molecules at the temperatures achieved for laser-cooled atoms, for applications to "coherent chemistry," studies of molecule-atom and molecule-molecule interactions. Bose condensates of molecules and for quantum computing. It is advantageous to produce cold molecules from laser-cooled atoms. but this requires an accurate model of the energy level structure near the dissociation limit for excited atoms, and for other intermediate states. With this in mind. we have modeled experimental photoassociation data from Rb2. spectroscopic data on the lowest excited states of Na2, and hyperfine structure of the lowest triplet state of Cs2. The second part involved continued development of experimental techniques for intense atomic beam collimation using a bichromatic laser field. We solved the equations for evolution of atoms in such a laser field, expressed the results in the form of trajectories on the Bloch sphere for a two-level atoms, and then used these results to design and perform efficient atomic beam reflection experiments. At the same time, we are developing methods to use these highly collimated beams of metastable helium atoms for precision lithography, using sensitized surfaces.
Quantum chemistry models atoms and molecules using quantum mechanics, with the electronic structure problem at its core. This problem, which determines the energy and properties of electrons in a molecule, is exponentially hard to solve exactly on classical computers. To approximate solutions, effective models introduce layers of simplifications. However, these approximations can fail for strongly correlated systems, necessitating alternative approaches. Quantum computers, capable of processing quantum information natively, offer a promising path to simulate molecular systems beyond classical reach, with potential applications in catalysis, materials science, and photochemistry. Despite rapid advancements in quantum hardware, practical quantum computations remain challenging due to limited resources. This thesis optimizes quantum resource usage in computational chemistry, introducing novel embedding techniques and exploring applications beyond ground-state energies. Chapter 1 establishes the foundation by reviewing quantum chemistry methods, from Hartree-Fock and Density Functional Theory (DFT) to active space approaches. It also provides an introduction to quantum computing for chemistry, focusing on near-term algorithms. The following chapters present novel methods aimed at reducing quantum resource requirements and tackling problems classical methods struggle with. Chapter 2 introduces a technique to reduce the
λ-norm of the electronic structure Hamiltonian, a key measure of quantum resource demand. By transforming molecular orbitals, this method enhances sampling efficiency in Noisy Intermediate-Scale Quantum (NISQ) algorithms and reduces runtime in Fault-Tolerant Quantum Computing (FTQC). Localized orbitals outperform canonical ones, and an orbital-optimization scheme is proposed to minimize the
λ-norm. Benchmarks on hydrogen chains, FeMoco, and Ruthenium complexes demonstrate its effectiveness. Chapter 3 presents the FragPT2 framework for simulating large systems with multiple interacting fragments. This method embeds each fragment in the mean field of others and applies multi-reference perturbation theory to capture inter-fragment correlations such as dispersion and charge transfer efficiently. The approach reduces computational overhead and enables scalable simulations, as shown in applications to \ce{N2} dimers, aromatic dimers, and butadiene. Chapter 4 focuses on photochemical systems, where multiple electronic states must be treated equally. The state-averaged orbital-optimized variational quantum eigensolver (SAOOVQE) is extended with analytical energy gradients and non-adiabatic couplings, enabling geometry optimizations and simulations of non-adiabatic dynamics on quantum hardware. This is demonstrated by locating the conical intersection in formaldimine, highlighting SAOOVQE’s potential for studying photoisomerization in biomolecules. Building on this, Chapter 5 develops a quantum algorithm to detect conical intersections, where the Born-Oppenheimer approximation breaks down. These intersections are characterized by a discrete Berry phase (0 or
π), representing their topological nature. The algorithm extracts this phase as a single bit of information, ensuring resilience to noise. Analytical proof and numerical validation using a toy molecular model illustrate its effectiveness for studying light-perception biochemistry and related photochemical processes. Finally, Chapter 6 explores machine learning density functionals trained on noisy quantum data. While DFT is computationally efficient, its accuracy depends on approximated exchange-correlation functionals. This work proposes a neural network-based approach to learn the exact functional from quantum data, showing that training on noisy outputs from NISQ devices can mitigate sampling errors. Applications to the Fermi-Hubbard model and other systems demonstrate its potential to generalize and provide accurate results under noise. This thesis advances quantum computational chemistry by optimizing quantum resource usage, developing new embedding strategies, and expanding the scope of quantum simulations beyond ground-state properties. These contributions pave the way for practical quantum algorithms that could revolutionize molecular simulations in the near future.