  Topological phase transitions go beyond Ginzburg and Landau's paradigm of
spontaneous symmetry breaking and occur without an associated local order
parameter. Instead, such transitions can be characterized by the emergence of
non-local order parameters, which require measurements on extensively many
particles simultaneously - an impossible venture in real materials. On the
other hand, quantum simulators have demonstrated such measurements, making them
prime candidates for an experimental confirmation of non-local topological
order. Here, building upon the recent advances in preparing few-particle
fractional Chern insulators using ultracold atoms and photons, we propose a
realistic scheme for detecting the hidden off-diagonal long-range order
(HODLRO) characterizing Laughlin states. Furthermore, we demonstrate the
existence of this hidden order in fractional Chern insulators, specifically for
the $\nu=\frac{1}{2}$-Laughlin state in the isotropic Hofstadter-Bose-Hubbard
model. This is achieved by large-scale numerical density matrix renormalization
group (DMRG) simulations based on matrix product states, for which we formulate
an efficient sampling procedure providing direct access to HODLRO in close
analogy to the proposed experimental scheme. We confirm the characteristic
power-law scaling of HODLRO, with an exponent $\frac{1}{\nu} = 2$, and show
that its detection requires only a few thousand snapshots. This makes our
scheme realistically achievable with current technology and paves the way for
further analysis of non-local topological orders, e.g. in topological states
with non-Abelian anyonic excitations.
