Quantum simulation of fermionic models

Thesis

This work is a theoretical study of fermionic models. We focus on problems where highly controllable quantum simulators of these models have an important role, and we utilise both the analogue and the digital paradigm of quantum simulation.

In the part on analogue quantum simulation, we focus on the proposed 'spin-asymmetric' Josephson effect where Cooper-paired spins display frequency synchronized Josephson oscillations with spin-dependent amplitudes. We consider different scenarios where the phenomenon could manifest in ultracold atomic Fermi gases. We study a Fermi gas Josephson junction in the recently realized Josephson plasma oscillation regime with an additional spin-dependent potential and show that the asymmetry in the resulting spin-dependent plasma oscillation amplitudes is on the order of a couple of per cent. We also demonstrate numerically that spin-asymmetric Josephson-like currents occur in a one-dimensional spin-dependent optical superlattice, with amplitude asymmetries up to 39%. Finally, we show that at zero temperature the tunable critical current in ferromagnetic Josephson junctions can be explained by the spin-asymmetric Josephson effect.

In the part where digital quantum simulation is used, we propose a hybrid quantum-classical approach to studying strongly correlated fermion models. In this approach, a digital quantum simulator works in conjunction with a classical feedback loop to solve the infinite-dimensional Hubbard model directly in the thermodynamic limit. The scheme implements the well-established dynamical mean-field theory (DMFT) method, such that the digital quantum simulator solves the classically hard DMFT impurity problem and self-consistency is taken care of in a classical computer. We first present a few-qubit proof-of-principle setup for equilibrium systems that implements the simplified 'two-site' DMFT. This few-qubit setup is used for a qualitative description of the Mott transition in the half-filled infinite-dimensional Hubbard model. We then describe a scalable setup for simulating non-equilibrium many-body quantum dynamics by proposing the implementation of the non-equilibrium extension of DMFT with the hybrid device.

Authors: Kreula, J

• DOI: 10.5287/ora-wvbkgaojp
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford