Numerical stability of time-dependent coupled-cluster methods for many-electron dynamics in intense laser pulses

We investigate the numerical stability of time-dependent coupled-cluster theory for many-electron dynamics in intense laser pulses, comparing two coupled-cluster formulations with full configuration interaction theory. Our numerical experiments show that orbital-adaptive time-dependent coupled-cluster doubles (OATDCCD) theory offers significantly improved stability compared with the conventional Hartree-Fock-based time-dependent coupled-cluster singles-and-doubles (TDCCSD) formulation. The improved stability stems from greatly reduced oscillations in the doubles amplitudes, which, in turn, can be traced to the dynamic biorthonormal reference determinants of OATDCCD theory. As long as these are good approximations to the Brueckner determinant, OATDCCD theory is numerically stable. We propose the reference weight as a diagnostic quantity to identify situations where the TDCCSD and OATDCCD theories become unstable.Comment: 5 pages, 6 figures (supplemental material, 7 pages, 11 figures

Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States

We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion coupled-cluster theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for the He and Be atoms, and for the LiH, CH$^+$, and LiF molecules, show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration-interaction theory provided all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorate. Observing that populations computed from the linear-response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.Comment: 58 pages, 14 figure

Real-time quantum many-body dynamics

Solutions to the time-dependent Schrödinger equation are central to the understanding of the interaction between particles and external probes. The increasing availability of intense laser fields in experiments has spawned an interest in the study of the dynamics of many-body systems interacting with strong laser pulses. However, the complexity of the many-body problem quickly becomes a significant roadblock in the exploration of larger atoms and molecules, thus limiting the size of the systems that can be explored. Real-time ab initio electronic structure theory provides promising methods for investigating the dynamics of matter-field interactions and we have implemented several many-body methods which we use to analyze atoms and molecules subject to intense laser fields. We implement three different ab initio real-time methods: Hartree-Fock, configuration interaction, and coupled-cluster which we apply to systems of atoms and molecules. A thorough theory section outlines the foundation of our work. We demonstrate the strengths of the implemented methods and highlight the applicability of the orbital-adaptive time-dependent coupled-cluster method with doubles excitations by showcasing how this method is stable where the more conventional time-dependent coupled-cluster method with singles-and-doubles excitations fail. We demonstrate the first dipole allowed transition energy for Neon and Argon in the aug-cc-pVDZ basis to be 19.4327 eV and 12.7275 eV, respectively. Finally, we end this thesis demonstrating the versatility of our implemented methods by exhibiting simulations of exotic systems with spin-dependent laser fields and ionization of the one-dimensional Beryllium atom

Predicting solid state material platforms for quantum technologies

Semiconductor materials provide a compelling platform for quantum technologies (QT). However, identifying promising material hosts among the plethora of candidates is a major challenge. Therefore, we have developed a framework for the automated discovery of semiconductor platforms for QT using material informatics and machine learning methods. Different approaches were implemented to label data for training the supervised machine learning (ML) algorithms logistic regression, decision trees, random forests and gradient boosting. We find that an empirical approach relying exclusively on findings from the literature yields a clear separation between predicted suitable and unsuitable candidates. In contrast to expectations from the literature focusing on band gap and ionic character as important properties for QT compatibility, the ML methods highlight features related to symmetry and crystal structure, including bond length, orientation and radial distribution, as influential when predicting a material as suitable for QT.ISSN:2057-396

Linear and Nonlinear Optical Properties from TDOMP2 Theory

We present a derivation of real-time (RT) time-dependent orbital-optimized Møller–Plesset (TDOMP2) theory and its biorthogonal companion, time-dependent non-orthogonal OMP2 theory, starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in the time-independent molecular electronic structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from RT simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation, TDCC2. We also compare our results with those from CCSD and CC2 linear and quadratic response theories. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, including core excitations where optimized orbitals might be particularly important, frequency-dependent polarizabilities and hyperpolarizabilities from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations