Non-Perturbative Approaches to Linear and Nonlinear Responses of Atoms, Molecules, and Molecular Aggregates: A Theoretical Approach to Molecular Quantum Information and Quantum Biology

Non-perturbative approaches to linear and nonlinear responses (NLR) of atoms, molecules, and molecular aggregates are reviewed in relation to low and high harmonic generations (HG) by laser fields. These response properties are effective for the generation of entangled light pairs for quantum information processing by spontaneous parametric downconversion (SPDC) and stimulated four-wave mixing (SFWM). Quasi-energy derivative (QED) methods, such as QED Møller–Plesset (MP) perturbation, are reviewed as time-dependent variational methods (TDVP), providing analytical expressions of time-dependent linear and nonlinear responses of open-shell atoms, molecules, and molecular aggregates. Numerical Liouville methods for the low HG (LHG) and high HG (HHG) regimes are reviewed to elucidate the NLR of molecules in both LHG and HHG regimes. Three-step models for the generation of HHG in the latter regime are reviewed in relation to developments of attosecond science and spectroscopy. Orbital tomography is also reviewed in relation to the theoretical and experimental studies of the amplitudes and phases of wave functions of open-shell atoms and molecules, such as molecular oxygen, providing the Dyson orbital explanation. Interactions between quantum lights and molecules are theoretically examined in relation to derivations of several distribution functions for quantum information processing, quantum dynamics of molecular aggregates, and future developments of quantum molecular devices such as measurement-based quantum computation (MBQC). Quantum dynamics for energy transfer in dendrimer and related light-harvesting antenna systems are reviewed to examine the classical and quantum dynamics behaviors of photosynthesis. It is shown that quantum coherence plays an important role in the well-organized arrays of chromophores. Finally, applications of quantum optics to molecular quantum information and quantum biology are examined in relation to emerging interdisciplinary frontiers.