  We investigate a space-time crystal in a superfluid Bose gas. Using a
well-controlled periodic drive we excite only one crystalline mode in the
system, which can be accurately modeled in the rotating frame of the drive.
Using holographic imaging we observe the stability of the crystal over an
extended period of time and show the robustness of its structure in both space
and time. By introducing a fourth-order term in the Hamiltonian we show that
the crystal stabilizes at a fixed number of quanta. The results of the model
are compared to the experimental data and show good agreement, with a small
number of free parameters. The results yield insights in the long-term
stability of the crystal, which can only be obtained by the combination of the
extended control in the experiment and the nearly ab-initio character of the
model. From the model we derive a phase diagram of the system, which can be
exploited in the future to study the phase transitions for this new state of
matter in even more detail.
