Time-Dependent Stochastic Approaches for Strong-Field Spectroscopy of Correlated Models

Student thesis: Doctoral ThesisDoctor of Philosophy


The work in this thesis aims to extend our simulation capabilities and understanding of the optical response of two-dimensional Mott insulators subject to strong-field laser pulses. These correlated systems are modelled using the Fermi-Hubbard Hamiltonian, and their real-time evolution is performed using a combination of stochastic, exact and mean-field methods. This enables their high harmonic emission to be calculated, from which we can resolve the attosecond charge dynamics of electrons in both the frequency and time domains.

The research is split into two overlapping threads, the first of which seeks to characterise the emission and understand its microscopic origins. High harmonic generation (HHG) in one-dimensional and infinite-dimensional Mott insulators has previously been investigated using a variety of techniques, but their two-dimensional analogues are almost entirely absent from the literature due to a scarcity of appropriate numerical methods. This problem is approached using the versatile time-dependent variational Monte Carlo (tVMC) algorithm, supplemented by exact diagonalisation (ED), along with mean-field methods in the metallic limit. These are combined to describe and explain the effects of correlation, dimensionality and simulation parameters on the high harmonic emission. The analysis is performed across correlation regimes, from non-interacting conductors to heavily Mott-insulating systems, with a focus on transitions between these two limits via the photo-induced breakdown of the insulating ground state.

The second research thread moves away from analysing the optical response induced by laser fields, and instead explores ways that the fields can be designed to control the response. This is achieved using so-called current tracking, for which a protocol is derived that provides a prescription for the driving pulse required to generate any predetermined current in any Fermi-Hubbard system. This is implemented using the same combination of tVMC, ED and mean-eld methods, along with further techniques that simplify the pulses to within existing experimental capabilities. These are then used to demonstrate near-arbitrary control over the HHG, including directional resolution of Mott transitions along perpendicular directions of the lattice.
Date of Award1 May 2022
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorGeorge Booth (Supervisor)

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