  Time crystals (TCs) are many-body systems displaying spontaneous breaking of
time translation symmetry. Here, we demonstrate a TC using driven-dissipative
condensates of microcavity exciton-polaritons, spontaneously formed from an
incoherent particle bath. In contrast to other realizations, the TC phases can
be controlled by the power of continuous-wave non-resonant optical drive
exciting the condensate and optomechanical interactions with phonons. Those
phases are for increasing power: (i) Larmor precession of pseudo-spins - a
signature of continuous TC, (ii) locking of the frequency of precession to
self-sustained coherent phonons - stabilized TC, (iii) doubling of TC frequency
by phonons - a discrete TC with continuous excitation. These results establish
microcavity polaritons as a platform for the investigation of time-broken
symmetry in non-hermitian systems.
