  We experimentally study the stability of a bosonic Mott-insulator against the
formation of a density wave induced by long-range interactions, and
characterize the intrinsic dynamics between these two states. The
Mott-insulator is created in a quantum degenerate gas of 87-Rubidium atoms,
trapped in a three-dimensional optical lattice. The gas is located inside and
globally coupled to an optical cavity. This causes interactions of global
range, mediated by photons dispersively scattered between a transverse lattice
and the cavity. The scattering comes with an atomic density modulation, which
is measured by the photon flux leaking from the cavity. We initialize the
system in a Mott-insulating state and then rapidly increase the global coupling
strength. We observe that the system falls into either of two distinct final
states. One is characterized by a low photon flux, signaling a Mott insulator,
and the other is characterized by a high photon flux, which we associate with a
density wave. Ramping the global coupling slowly, we observe a hysteresis loop
between the two states - a further signature of metastability. A comparison
with a theoretical model confirms that the metastability originates in the
competition between short- and global-range interactions. From the increasing
photon flux monitored during the switching process, we find that several
thousand atoms tunnel to a neighboring site on the time scale of the single
particle dynamics. We argue that a density modulation, initially forming in the
compressible surface of the trapped gas, triggers an avalanche tunneling
process in the Mott-insulating region.
