  The quantum ground state of a massive mechanical system is a steppingstone
for investigating macroscopic quantum states and building high fidelity
sensors. With the recent achievement of ground-state cooling of a single
motional mode, levitated nanoparticles have entered the quantum domain. To
overcome detrimental cross-coupling and decoherence effects, quantum control
needs to be expanded to more system dimensions, but the effect of a decoupled
dark mode has thus far hindered cavity-based ground state cooling of multiple
mechanical modes. Here, we demonstrate two-dimensional (2D) ground-state
cooling of an optically levitated nanoparticle. Utilising coherent scattering
into an optical cavity mode, we reduce the occupation numbers of two separate
centre-of-mass modes to 0.83 and 0.81, respectively. By controlling the
frequency separation and the cavity coupling strengths of the nanoparticle's
mechanical modes, we show the transition from 1D to 2D ground-state cooling
while avoiding the effect of dark modes. Our results lay the foundations for
generating quantum-limited high orbital angular momentum states with
applications in rotation sensing. The demonstrated 2D control, combined with
already shown capabilities of ground-state cooling along the third motional
axis, opens the door for full 3D ground-state cooling of a massive object.
