  Synchronizing a few-level quantum system is of fundamental importance to
understanding synchronization in deep quantum regime. Whether a two-level
system, the smallest quantum system, can be synchronized has been theoretically
debated for the past several years. Here, for the first time, we demonstrate
that a qubit can indeed be synchronized to an external driving signal by using
a trapped-ion system. By engineering fully controllable gain and damping
processes, an ion qubit is synchronized to oscillate at the same frequency as
the driving signal and lock in phase. We systematically investigate the
parameter regions of synchronization and observe characteristic features of the
Arnold tongue. Our measurements agree remarkably well with numerical
simulations based on recent theory on qubit synchronization. By synchronizing
the basic unit of quantum information, our research opens up the possibility of
applying quantum synchronization to large-scale quantum networks.
