SciPost Thesis Link
| Title: | Signatures of many-body localisation in a two-dimensional lattice of ultracold polar molecules with disordered filling | |
| Author: | Timothy J. Harris | |
| As Contributor: | Timothy Harris | |
| Type: | Master's | |
| Field: | Physics | |
| Specialties: |
|
|
| Approaches: | Theoretical, Computational | |
| URL: | https://espace.library.uq.edu.au/view/UQ:5aaa580 | |
| Degree granting institution: | The University of Queensland | |
| Supervisor(s): | Matthew J. Davis | |
| Defense date: | 2023-09-08 |
Abstract:
An isolated quantum many-body system driven far from equilibrium will tend to relax back to an equilibrium state described by the predictions of quantum statistical mechanics, in analogy with more familiar classical systems. In the quantum case, this relaxation is typically characterised by a rapid growth of entanglement, resulting in a loss of memory of the initial state. However, in some scenarios thermalisation is prohibited, causing the system to remain out of equilibrium and retain memory of its initial state indefinitely. Many-body localisation (MBL) is one example of such behaviour, resulting from the presence of strong spatial disorder in the system. Owing to recent advances in the field of analogue quantum simulation, experiments with ultracold atoms and molecules trapped in optical lattices are now able to probe non-equilibrium dynamics of isolated quantum systems in microscopic detail. In particular, signatures of MBL and the absence of thermalisation have been observed in several experiments with ultracold quantum gases. In this thesis we take a computational approach to exploring quantum thermalisation and MBL in systems of ultracold polar molecules trapped in optical lattices. Specifically, we focus on characterising a novel ergodicity breaking mechanism that emerges in molecular quantum simulators when a fraction of the lattice sites are left unoccupied. This scenario is of particular relevance, as to date no experiment has achieved a lattice filling fraction greater than ~30%. We consider a dilute gas of ultracold polar molecules pinned in a deep optical lattice (1D, ladder and 2D geometries are investigated) with at most one molecule per lattice site. The physics of these systems is well described by a dipolar spin-1/2 Hamiltonian, with effective on-site disorder arising from the dilute, randomised configurations of molecules in the lattice. Experimentally, such a model may be realised by encoding a spin-1/2 degree of freedom in two of the molecules' rotational states, with effective spin couplings arising from the dipolar interactions. The microscopic parameters of the model (including the strength of the effective on-site disorder) can be precisely controlled by varying the choice of rotational states, altering the intensities of the lattice lasers, and through the application of external DC electric and microwave fields. We perform extensive exact diagonalisation calculations to explore the non-equilibrium dynamics and eigenstate properties for systems of up to N = 16 molecules at 50% lattice filling. We observe several essential signatures of MBL, including retention of initial state memory in the system's long-time dynamics, logarithmic growth of bipartite entanglement entropy, divergent entanglement fluctuations close to the critical disorder strength and a transition to Poissonian level-spacing statistics. Our results are realisable in current quantum gas microscope experiments with ultracold molecules in optical lattices. In particular, it should be possible to probe dynamical signatures such as initial state memory retention via observables such as one and two-body correlators, and through measures such as out-of-time order correlators. Our results also open up further avenues to explore many-body physics with molecules, including investigating fundamental questions about the nature of thermalisation in isolated quantum many-body systems, and the existence of MBL in spatial dimensions d > 1.