  The concept of spontaneous symmetry breaking and off-diagonal long-range
order (ODLRO) are associated with Bose-Einstein condensation. However, as in
the system of reduced dimension the effect of quantum fluctuation is
dominating, the concept of ODLRO becomes more interesting, especially for the
long-range interaction. In the present manuscript, we study the correlation
dynamics triggered by lattice depth quench in a system of three dipolar bosons
in a 1D triple-well optical lattice from the first principle using the
multiconfigurational time-dependent Hartree method for bosons (MCTDHB). Our
main motivation is to explore how ODLRO develops and decays with time when the
system is brought out-of-equilibrium by a sudden change in the lattice depth.
We compare results of dipolar bosons with contact interaction. For forward
quench $(V_{f} > V_{i})$, the system exhibits the collapse-revival dynamics in
the time evolution of normalized first- and second-order Glauber's correlation
function, time evolution of Shannon information entropy both for the contact as
well as for the dipolar interaction which is reminiscent of the one observed in
Greiner's experiment [Nature, {415}, (2002)]. We define the collapse and
revival time ratio as the figure of merit ($\tau$) which can uniquely
distinguish the timescale of dynamics for dipolar interaction from that of
contact interaction. In the reverse quench process $(V_{i} > V_{f})$, for
dipolar interaction, the dynamics is complex and the system does not exhibit
any definite time scale of evolution, whereas the system with contact
interaction exhibits collapse-revival dynamics with a definite time-scale. The
long-range repulsive tail in the dipolar interaction inhibits the spreading of
correlation across the lattice sites.
