  Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical
many-body states, that are characterized by robust self-sustained oscillations,
emerging via spontaneous breaking of discrete or continuous time translation
symmetry. DTCs are periodically driven systems that oscillate with a
subharmonic of the external drive, while CTCs are continuously driven and
oscillate with a frequency intrinsic to the system. Here, we explore a phase
transition from a continuous time crystal to a discrete time crystal. A CTC
with a characteristic oscillation frequency $\omega_\mathrm{CTC}$ is prepared
in a continuously pumped atom-cavity system. Modulating the pump intensity of
the CTC with a frequency $\omega_{\mathrm{dr}}$ close to
$2\,\omega_\mathrm{CTC}$ leads to robust locking of $\omega_\mathrm{CTC}$ to
$\omega_{\mathrm{dr}}/2$, and hence a DTC arises. This phase transition in a
quantum many-body system is related to subharmonic injection locking of
non-linear mechanical and electronic oscillators or lasers.
