



02085nas a2200169   4500008004100000245004300041210004300084260001300127520161100140100002001751700002501771700002401796700002101820700001801841700001901859856003701878       2021                        eng d00aCrystallography of Hyperbolic Lattices0 aCrystallography of Hyperbolic Lattices  c5/3/20213 a<p>Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch&#39;s theorem precludes a simple understanding of their band structure. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive, for the first time, a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. Our results find application for both finite and infinite hyperbolic lattices. We describe a method to efficiently generate finite hyperbolic lattices of arbitrary size and explain why the present crystallography is the first step towards a complete band theory of hyperbolic lattices and apply it to construct Bloch wave Hamiltonians. This work lays the foundation for generalizing some of the most powerful concepts of solid state physics, such as crystal momentum and Brillouin zone, to the emerging field of hyperbolic lattices and tabletop simulations of gravitational theories, and reveals the connections to concepts from topology and algebraic geometry.</p>1 aBoettcher, Igor1 aGorshkov, Alexey, V.1 aKollár, Alicia, J.1 aMaciejko, Joseph1 aRayan, Steven1 aThomale, Ronny  uhttps://arxiv.org/abs/2105.0108701617nas a2200157   4500008004100000245012800041210006900169520105700238100001801295700002401313700002101337700001801358700002101376700002501397856003701422       2018                        eng d00aFractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal0 aFractional quantum Hall phases of bosons with tunable interactio3 a<p>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.</p>1 aGraß, Tobias1 aBienias, Przemyslaw1 aGullans, Michael1 aLundgren, Rex1 aMaciejko, Joseph1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/1809.04493