The multiple Davydov D2 Ansatz and its applications

• Main Author: Huang, Zhongkai
• Other Authors: Zhao Yang
• Format: Theses and Dissertations
• Language: English
• Published: 2019
• Subjects: DRNTU::Science::Biological sciences::Biophysics
• Online Access: https://hdl.handle.net/10356/89649; http://hdl.handle.net/10220/47718
• Institution: Nanyang Technological University

In order to accurately characterize dynamics of the Holstein polaron with simultaneous diagonal and off-diagonal exciton-phonon coupling, a series of multiple Davydov trial states, i.e., the multiple Davydov D1, D1.5, D2, and D~ ansatze, are formulated as superpositions of the correspondingly single Davydov D1, D1.5, D2, and D~ ansatze. In this thesis, the multiple Davydov D2 ansatz, also known as the multi-D2 ansatz, is demonstrated to enable numerically exact dynamics for various open quantum systems with off-diagonal coupling and is applied to study complicated dynamical quantum behaviours, such as the exciton transport in conducting polymers, Bloch oscillations dynamics in semiconductor superlattices and organic materials, singlet fission processes, and the Landau-Zener transitions in circuit quantum electrodynamics devices. We first use the Dirac-Frenkel time-dependent variational principle combined with the multi-D2 ansatz to fully quantum mechanically investigate dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling, which is treated traditionally by the Ehrenfest approximation for the description of the exciton transport in the conducting polymers. It is shown that the Ehrenfest method is equivalent to our variational method with the single D2 ansatz, and with the multi-D2 ansatz, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics. The multi-D2 ansatz is able to capture numerically accurate exciton momentum probability and help clarify the relation between the exciton momentum redistribution and the exciton energy relaxation. The results demonstrate that the exciton momentum distributions in the steady state are determined by a combination of the transfer integral and the off-diagonal coupling strength, independent of the excitonic initial conditions. We also probe the effect of the transfer integral and the off-diagonal coupling on exciton transport in both real and reciprocal space representations. Finally, the variational method with importance sampling is employed to investigate temperature effects on the exciton transport using the multi-D2 ansatz, and it is demonstrated that the variational approach is valid in both low and high temperature regimes. Next, the multi-D2 ansatz is employed to study transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal carrier-phonon coupling in an external electric field, aiming to help better understand Bloch oscillations dynamics in the semiconductor superlattices and the organic materials. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the charge carrier undergoes typical Bloch oscillations. Adding weak carrier-phonon coupling leads to a broadened carrier wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare carrier oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non-zero carrier current. For both scenarios, temporal periodicity is unchanged by carrier-phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite-sized ring within the anti-adiabatic regime. For strong diagonal coupling, the multi-D2 anstaz is found to be highly accurate, and the phonon confinement gives rise to carrier localization and decay of the Bloch oscillations. Furthermore, we adopt the multi-D2 ansatz to explore dynamics of a newly formulated microscopic model of intramolecular singlet fission with simultaneous diagonal and offdiagonal coupling to high-frequency modes. It is shown that both diagonal and off-diagonal coupling can aid efficient singlet fission if excitonic coupling is weak, and fission is only facilitated by diagonal coupling if excitonic coupling is strong. In the presence of offdiagonal coupling, it is found that high frequency modes create additional fission channels for rapid iSF. Finally, the multi-D2 ansatz is employed to examine dynamics of the Landau-Zener model with both diagonal and off-diagonal qubit-bath coupling. It is shown that steady-state transition probabilities agree with analytical predictions at long times. Landau-Zener dynamics at intermediate times is little affected by diagonal coupling, and is found to be determined by off-diagonal coupling and tunneling between two diabatic states. We investigate effects of bath spectral densities, coupling strengths and interaction angles on Laudau-Zener dynamics. Thanks to the multiple Davydov trial states, detailed boson dynamics can also be analyzed in Landau-Zener transitions. To summarize, in this thesis we adopt a time-dependent variational approach utilizing the multi-D2 ansatz, to accurately investigate dynamics of four open quantum systems with electronic and bosonic degrees of freedom. Calculations in this thesis help illustrate the effects of the transfer integral and the off-diagonal coupling on the exciton transport in off-diagonal Holstein polaron model representing the conducting polymers, and the influences of the external electric field on transient dynamics of the one-dimensional Holstein polaron modeling the semiconductor superlattices and organic materials. Results presented in the thesis may help provide guiding principles for design of efficient singlet fission materials by directly tuning singlet-triplet interstate coupling, and to manipulate the Laudau-Zener transitions in circuit quantum electrodynamics architectures by tuning off-diagonal coupling and tunneling strength. It is also our hope that the multi-D2 ansatz can be applied to more exciton-phonon coupled systems.