  Quantum tunnelling is a common fundamental quantum-mechanical phenomenon that
originates from the wave-like characteristics of quantum particles. Although
the quantum-tunnelling effect was first observed 85 years ago, some questions
regarding the dynamics of quantum tunnelling remain unresolved. Here, we
realise a quantum-tunnelling system using two-dimensional ionic structures in a
linear Paul trap. We demonstrate that the charged particles in this
quantum-tunnelling system are coupled to the vector potential of a magnetic
field throughout the entire process, even during quantum tunnelling, as
indicated by the manifestation of the Aharonov-Bohm effect in this system. The
tunnelling rate of the structures periodically depends on the strength of the
magnetic field, whose period is the same as the magnetic-flux quantum $\phi_0$
through the rotor [($0.99 \pm 0.07)\times \phi_0$].
