No abstract

Ultracold atoms in optical lattices are ideal to study fundamentally new quantum many-body systems 1,2 including frustrated or topological magnetic phases 3,4 and supersolids 5,6 . However, the necessary control of strong long-range interactions between distant ground state atoms has remained a long-standing goal. Optical dressing of ground state atoms via o -resonant laser coupling to Rydberg states is one way to tailor such interactions 5-8 . Here we report the realization of coherent Rydberg dressing to implement a two-dimensional synthetic spin lattice. Our single-atom-resolved interferometric measurements of the many-body dynamics enable the microscopic probing of the interactions and reveal their highly tunable range and anisotropy. Our work marks the first step towards the use of laser-controlled Rydberg interactions for the study of exotic quantum magnets 3,4,9 in optical lattices.Neutral ultracold atoms in optical lattices are among the most promising platforms for the implementation of analog quantum simulators of condensed matter systems. However, the simulation of magnetic Hamiltonians, often emerging as an effective model in more complex many-body systems, is difficult with contact interactions due to the low energy scale of the associated superexchange process 10 . Long-range interactions offer an alternative way to directly achieve strong effective spin-spin interactions. Such interactions emerge between magnetic atoms and between ultracold polar molecules 11 , trapped ions 12 or ground state atoms resonantly 13 or off-resonantly coupled ('dressed') to Rydberg states [5][6][7][8] . Rydberg dressing is especially appealing due to the simplicity of realizing atomic lattice systems with unity filling, combined with the great tunability of the interaction strength and shape, which might be exploited to explore exotic models of quantum magnetism 3,4 . While effects of long-range spin interactions have been observed in many-body systems of polar molecules 14 , ions [15][16][17] and resonantly excited Rydberg atoms 18,19 , none of these approaches combines the advantages of Rydberg dressing, which permits the realization of strong spin interactions in lattices with near-unity filling. So far, Rydberg dressing in a many-body system remains an experimental challenge, for which up to now only dissipative effects have been measured [20][21][22][23][24] . For two atoms, first promising experimental results have been reported recently for near-resonant strong dressing 25 , where, however, the assumption of a weak Rydberg-state admixture required for the realization of various many-body models 5,6,9,26,27 does not hold 28 .Here we demonstrate Rydberg dressing in a two-dimensional (2D) near-unity-filled atomic lattice with tailored extended range interactions between approximately 200 effective spins. In contrast to our previous experiments 18,29 on resonantly coupled Rydberg gases, all atoms participate here in the spin dynamics. We exploit the temporal control over such interactions to perform interferometric ...

By combining theory and experiments, we demonstrate that dipolar quantum gases of both 166 Er and 164 Dy support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well defined parameter range, separating the phases of a regular Bose-Einstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. In the experiment, we rely on a detailed analysis of the interference patterns resulting from the free expansion of the gas, quantifying both its density modulation and its global phase coherence. Reaching the phases via a slow interaction tuning, starting from a stable condensate, we observe that 166 Er and 164 Dy exhibit a striking difference in the lifetime of the supersolid properties, due to the different atom loss rates in the two systems. Indeed, while in 166 Er the supersolid behavior only survives a few tens of milliseconds, we observe coherent density modulations for more than 150 ms in 164 Dy. Building on this long lifetime, we demonstrate an alternative path to reach the supersolid regime, relying solely on evaporative cooling starting from a thermal gas. arXiv:1903.04375v1 [cond-mat.quant-gas]