Techniques for quantum simulation with ultracold gases, paraxial optics and electric circuits

Oliver, Christopher ORCID: 0009-0003-3135-5592 (2023). Techniques for quantum simulation with ultracold gases, paraxial optics and electric circuits. University of Birmingham. Ph.D.

Preview

Oliver2023PhD.pdf
Text - Accepted Version
Available under License All rights reserved.
Download (10MB) | Preview

Abstract

Quantum simulation refers to the use of controllable physical systems to simulate quantum mechanical models. Since the concept was proposed in the early 1980s, quantum simulation has grown into a major field, with important applications both within physics and in the wider world. In this thesis, we present three works of quantum simulation. Firstly, in an ultracold atom setting, we present the experimental realisation of a synthetic dimension formed from the energy eigenstates of a harmonic trap when the system is driven with a time-periodic potential. We characterise the scheme using Bloch oscillations of the cloud up-and-down the ladder of trap states, and demonstrate a long synthetic dimension of several tens of sites. Secondly, we theoretically propose the use of the temporal dynamics of an optical pulse in a 1D array of waveguides to engineer quantum Hall physics. We show that the photonic band structure of a realistic model of a waveguide array can be engineered to share some key features of a relevant quantum Hall model, and then highlight a number of specific effects that could be observed in experiment, namely a controllable optical delay and the steering of a wavepacket back-and-forth across the array. Finally, we propose the use of lattices formed from commercially-available coaxial cables as a quantum simulator. We calculate the dispersion of Bloch waves in a 2D brick wall lattice of identical cables and three-port connector elements, and show that we find dispersive bands that touch at Dirac points, and a flat band that is not isolated. The lower dispersive band is conical for small momenta, suggesting we are in the nearly-free-photon limit. We then show that we can control the location and gap of the Dirac points, suggesting connections with the theory of artificial magnetic fields in strained graphene. We further show that we can introduce energetically-isolated flat bands. These works have many interesting future research directions, including the realisation of quantum Hall physics using our shaken trap synthetic dimension scheme; the investigation of the interplay between photon-photon interactions and topology using the optical pulse/waveguide array techniques, and the exploration of interacting physics in the coaxial cable lattice.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):