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 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

1 aGraß, Tobias1 aBienias, Przemyslaw1 aGullans, Michael1 aLundgren, Rex1 aMaciejko, Joseph1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1809.0449301495nas a2200181 4500008004100000245006100041210006000102260001500162300001100177490000800188520098100196100002001177700001801197700002101215700001901236700002101255856003701276 2017 eng d00aLight-induced fractional quantum Hall phases in graphene0 aLightinduced fractional quantum Hall phases in graphene c2017/12/15 a2474030 v1193 aWe show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

1 aGhazaryan, Areg1 aGraß, Tobias1 aGullans, Michael1 aGhaemi, Pouyan1 aHafezi, Mohammad uhttps://arxiv.org/abs/1612.08748