  Highly tunable platforms for realizing topological phases of matter are
emerging from atomic and photonic systems, and offer the prospect of designing
interactions between particles. The shape of the potential, besides playing an
important role in the competition between different fractional quantum Hall
phases, can also trigger the transition to symmetry-broken phases, or even to
phases where topological and symmetry-breaking order coexist. Here, we explore
the phase diagram of an interacting bosonic model in the lowest Landau level at
half-filling as two-body interactions are tuned. Apart from the well-known
Laughlin liquid, Wigner crystal phase, stripe, and bubble phases, we also find
evidence of a phase that exhibits crystalline order at fractional filling per
crystal site. The Laughlin liquid transits into this phase when pairs of bosons
strongly repel each other at relative angular momentum $4\hbar$. We show that
such interactions can be achieved by dressing ground-state cold atoms with
multiple different-parity Rydberg states.
