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 ...

Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. Well known examples are crystalline solids or Coulomb crystals in ion traps. In those systems, crystallization proceeds via a classical transition, driven by thermal fluctuations. In contrast, ensembles of ultracold atoms laser-excited to Rydberg states provide a well-controlled quantum system [1], in which a crystalline phase transition governed by quantum fluctuations can be explored [2][3][4]. Here we report on the experimental preparation of the crystalline states in such a Rydberg many-body system. Fast coherent control on the many-body level is achieved via numerically optimized laser excitation pulses [2][3][4]. We observe an excitation-number staircase [2][3][4][5][6][7] as a function of the system size and show directly the emergence of incompressible ordered states on its steps. Our results demonstrate the applicability of quantum optical control techniques in strongly interacting systems, paving the way towards the investigation of novel quantum phases in long-range interacting quantum systems, as well as for detailed studies of their coherence and correlation properties [2][3][4][5][6][7][8].Rydberg atoms exhibit unique properties that are key to realize and explore novel quantum many-body Hamiltonians and their phases. The strong van der Waals interaction between them allows to create many-body systems with tailored long-range interactions in neutral ultra-cold atom samples [1,9,10]. Complete experimental control of these systems is possible using the well developed toolbox of quantum optics for the laserexcitation to the Rydberg states. The magnitude of the resulting interactions between the Rydberg atoms is determined by the choice of the excited state and it can exceed all other relevant energy scales on distances of several microns, thereby leading to an ensemble dominated by long-range interactions. In this regime, the ground state of the resulting many-body system is expected to show crystalline ordering of the Rydberg excitations, which can be understood in the limit of vanishing coupling as the classical closest packing of hard spheres [11]. The lattice constant of the crystal is set by the dipole blockade radius R b [12,13], defined as the inter-particle spacing at which the dipole interaction between two Rydberg atoms exceeds the spectral range of the optical coupling. To prepare the system in this crystalline phase, a dynamical approach has been suggested that adiabatically connects the ground state containing no Rydberg excitations with the targeted crystalline state. At the heart of this dynamical crystallization technique is the coherent control of the many-body system [2][3][4][14][15][16][17].Previous experiments showed direct or indirect evidence for correlations caused by the long-range interac- * Electronic address: peter.schauss@mpq.mpg.de tions in Rydberg many-body systems, such as a universal scaling of the Rydberg excitation number [18], subPoissonian counting statis...

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 study experimentally the far-from-equilibrium dynamics in ferromagnetic Heisenberg quantum magnets realized with ultracold atoms in an optical lattice. After controlled imprinting of a spin spiral pattern with an adjustable wave vector, we measure the decay of the initial spin correlations through singlesite resolved detection. On the experimentally accessible time scale of several exchange times, we find a profound dependence of the decay rate on the wave vector. In one-dimensional systems, we observe diffusionlike spin transport with a dimensionless diffusion coefficient of 0.22(1). We show how this behavior emerges from the microscopic properties of the closed quantum system. In contrast to the onedimensional case, our transport measurements for two-dimensional Heisenberg systems indicate anomalous superdiffusion.

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Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin-and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in the chain. DOI: 10.1103/PhysRevLett.115.035302 PACS numbers: 67.85.-d, 05.70.Ln, 37.10.Jk, 75.10.Pq Quantum many-body systems are distinct from their classical counterparts due to entanglement among their constituents [1,2]. Especially in strongly correlated regimes, such as in the vicinity of quantum phase transitions [1,3] or far away from equilibrium [4], the growth of entanglement with time or subsystem size seriously limits numerical simulations of complex quantum systems [2]. Next to its importance on this fundamental level, entanglement is a valuable resource for quantum information and its microscopic control is required for most applications [5]. Experimentally, the measurement of entanglement is difficult given that full quantum state tomography requires extraordinary control and resources making it feasible only in small systems [6][7][8]. In larger or more complex many-body systems the mere presence of entanglement can be inferred from macroscopic observables, often relying on entanglement witnesses [1,9]. Such a strategy has been applied for susceptibility measurements in solids [10], collective spin systems [11][12][13][14][15][16], or coupled superconducting qubits [17].In Hubbard systems realized with ultracold atoms, entanglement in the on-site occupation-number degree of freedom has been inferred from the visibility of a far-field interference pattern [18,19]. A spatially resolved detection of entanglement has been recently proposed using the Rényi entropy [20,21]. Extension of the Hubbard model to two components introduces a spin degree of freedom [22,23] such that spin entanglement, in the sense of the concept of entanglement of particles [24,25], can be present. First experiments with ultracold atoms showed that short-range coherent spin dynamics can be controlled in bosonic [26][27][28], as well as in fermionic systems [29]. Spin exchange collisions in state selective optical lattices have been used to realize collisional gates between neighboring atoms [30] and global measurements indicated entanglement [31,32]. However, a spatially resolved detection of either spin or occupation-number entanglement in Hubbard models has still been an outstanding experimental challenge.Inspired by recent measurements in ion chains [8], here we report on the spatially resolved detection of entanglement among spin degrees of freedom in a two-component Bose-Hubbard chain following a recent proposal [33]. Specifically, ...