A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site-resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.

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 ...

Coherent many-body quantum dynamics lies at the heart of quantum simulation and quantum computation. Both require coherent evolution in the exponentially large Hilbert space of an interacting many-body system [1,2]. To date, trapped ions have defined the state of the art in terms of achievable coherence times in interacting spin chains [3][4][5][6]. Here, we establish an alternative platform by reporting on the observation of coherent, fully interaction-driven quantum revivals of the magnetization in Rydberg-dressed Ising spin chains of atoms trapped in an optical lattice. We identify partial many-body revivals at up to about ten times the characteristic time scale set by the interactions. At the same time, single-site-resolved correlation measurements link the magnetization dynamics with inter-spin correlations appearing at different distances during the evolution. These results mark an enabling step towards the implementation of Rydberg atom based quantum annealers [7], quantum simulations of higher dimensional complex magnetic Hamiltonians [8,9], and itinerant long-range interacting quantum matter [10][11][12].arXiv:1705.08372v1 [physics.atom-ph]

We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to dynamically deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.

We investigate thermal relaxation of superfluid turbulence in a highly oblate Bose-Einstein condensate. We generate turbulent flow in the condensate by sweeping the center region of the condensate with a repulsive optical potential. The turbulent condensate shows a spatially disordered distribution of quantized vortices and the vortex number of the condensate exhibits nonexponential decay behavior which we attribute to the vortex pair annihilation. The vortex-antivortex collisions in the condensate are identified with crescent-shaped, coalesced vortex cores. We observe that the nonexponential decay of the vortex number is quantitatively well described by a rate equation consisting of one-body and two-body decay terms. In our measurement, we find that the local two-body decay rate is closely proportional to T 2 /µ, where T is the temperature and µ is the chemical potential.