Simulation of emergent quantum phenomena for quantum information processing

In this thesis, we investigate emergent quantum phenomena in two quantum systems: vortex formation in a superfluid flow through an orifice and superradiance in emitters coupled to a cavity mode. We use computational simulations to model the time evolution of each system, taking into account the governing mathematical formalisms and relevant physical constraints. Based on the theoretical assumptions of each system, we determine how the phenomena can be observed and characterised. The thesis concludes with a summary of the main findings and a discussion of potential directions for future research.

In the first project, we simulate a rubidium-87 Bose–Einstein condensate using an effective two-dimensional Gross–Pitaevskii equation to test Feynman’s conjectures on the onset of superfluidity breakdown in liquid helium. Our results confirm Feynman’s prediction for the critical velocity (v_± = (ℏ/(md_±) ln (d_±/a_s)) determined based on the first detection of vortex pair, while deviations are observed regarding parallel vortex distances. These differences are attributed to the contrasting physical properties of liquid helium and rubidium condensates, including density, compressibility, and healing length.

In the second project, we explore Dicke superradiance in an open quantum system modelled with N spin-1/2 emitters coupled to a cavity mode, considering both the Lindblad–von Neumann quantum master equation (QME) and the non-Hermitian effective Hamiltonian (NHEH) formalisms. By analysing correlated emission, relative coherence, and entanglement, we identify temporal orderings of extremal values under each formalism. The results indicate that QME captures sequential temporal orders, whereas NHEH predicts simultaneous temporal orders due to the absence of quantum jumps. Scaling analyses show that correlated emission in both formalisms satisfy Dicke’s picture of superradiance as max(⟨C₀⟩) ∝ N² and τ_C0 ∝ (ln N)/N, and that relative coherence increases at a linear rate with N. However, the two formalisms yield quantitatively different outcomes in the presence of dissipation and decoherence, as exhibited by the analysis of entanglement witness.