Barker leads the UCL Optomechanics Group, focusing on levitated nano/micro-oscillators in vacuum. Research directions: (1) Six-degree-of-freedom cooling — demonstrated simultaneous cavity cooling of all 6 DOF of a levitated nanoparticle (Nature Physics 2023, with Monteiro); (2) Sympathetic cooling of two nanoparticles via Coulomb interaction, squeezing transfer (Phys. Rev. Research 2023); (3) Dark matter searches — levitated nanoparticles as directional dark matter sensors sensitive to nuclear recoil and momentum transfer; QTFP-funded project 'Development of Levitated Quantum Optomechanical Sensors for Dark Matter Detection'; (4) Controlling mode orientations for directional force sensing near the quantum limit; (5) Quantum macroscopic superposition tests. Closely collaborates with Monteiro (theory), Bose (quantum entanglement tests), and Ghag (dark matter).