  We study quantum particles at zero temperature in an optical lattice coupled
to a resonant cavity mode. The cavity field substantially modifies the particle
dynamics in the lattice, and for strong particle-field coupling leads to a
quantum phase with only every second site occupied. We study the growth of this
new order out of a homogeneous initial distribution for few particles as the
microscopic physics underlying a quantum phase transition. Simulations reveal
that the growth dynamics crucially depends on the initial quantum many-body
state of the particles and can be monitored via the cavity fluorescence.
Studying the relaxation time of the ordering reveals inhibited tunnelling,
which indicates that the effective mass of the particles is increased by the
interaction with the cavity field. However, the relaxation becomes very quick
for large coupling.
