AQUADUCT
We advance the Coupled Cluster method’s foray into the time-dependent realm, byplementing a robust solver based on the orbital-adaptive time-dependent Coupled Cluster (OATDCC) method. This involves implementing both a simplified static orbital time-dependent coupled cluster solver with single and double excitations (TDCCSD) and an orbital-adaptive scheme with double excitations (OATDCCD). To supplement the time-dependent methods we implement several ground state solvers based on the Lagrangian Coupled Cluster formulation, with single and double excitations, as well as a non-orthogonal orbital-optimised Coupled Cluster (NOCC) solver.
We construct several quantum dot basis sets with different potential functions in one- and two dimensions, including interactions with magnetic fields. What is more, we also implemet an interface with popular quantum chemistry software modules PySCF and Psi4 for extraction of additional basis sets for atoms and molecules. The quantum systems are allowed to vary with time by addition of a time-dependent addition to the Hamiltonian, with which we simulate a laser field in the dipole approximation.
As a validation we reproduce results from the scientific literature, both for atoms, molecules and quantum dots. We show that our methods leads to convergence in the ever-increasing basis set size limit, for simple quantum dot systems. For the same quantum dot system, we show the sensitivity of the system to the frequency of a driving oscillating field. Frequencies closer to the resonant frequency leads to exctiations and increased energy. We are able to simulate systems that are fairly large - quantum dots in one- and two dimensions with up to twelve electrons. For systems that meander far from the reference state, we show that the orbital-adaptive method has far superior stability, compared with the method with static orbitals.
For all quantum dot system we find strong comformity with the harmonic potential theorem, yet we see slight many-body effect for a two-dimensional double dot system. The two-dimensional quantum dots influenced by a homogoenous, static magnetic field in the form of an angular momentum operator, result in a split in the dipole spectrum of the system. This is also in accordance with the harmonic potential theorem. The difference between the two frequencies in the new spectrum is the same as the Larmor frequency of the magnetic field, within acceptable tolerance levels.