Thompson leads the Ion Trapping Group at Imperial using RF (Paul) traps with laser-cooled Ca-40 ions and Penning traps. Research foci: (1) High-fidelity quantum logic gates — optimal control techniques for single-ion state manipulation and two-qubit gates; demonstrated >1 s coherence times via Ramsey interferometry in a Penning trap; (2) Precision spectroscopy — ytterbium ion optical clock uncertainty characterisation at 2.2×10^−18 fractional uncertainty (NPL collaboration); proposed precision laser spectrometer for highly charged ions (HCI) in cylindrical Penning traps for QED tests; (3) Axion sensing — collaborating with Devlin on the Penning-trap single-electron photon counter for axion searches; (4) Coulomb crystals — ultrahigh resolution spectroscopy of ion crystals. Past work includes SPECTRAP project at GSI Darmstadt for HCI spectroscopy.

Uses MBE thin-film growth combined with equilibrium and non-equilibrium ARPES to sense electronic structure at material interfaces. Directions: (1) non-equilibrium photoemission (tr-ARPES) to map ultrafast electron dynamics in topological and superconducting materials; (2) MBE engineering of interfacial superconductivity and topological orders at oxide and chalcogenide interfaces; (3) light-induced phase transitions probed by ultrafast ARPES as a sensing modality for correlated electron dynamics.