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 tr
ansition, driven by thermal fluctuations. In contrast, ensembles of ultracold atoms laser-excited to Rydberg states provide a well-controlled quantum system, in which a crystalline phase transition governed by quantum fluctuations can be explored. 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. We observe an excitation-number staircase 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.
The ability to control and tune interactions in ultracold atomic gases has paved the way towards the realization of new phases of matter. Whereas experiments have so far achieved a high degree of control over short-ranged interactions, the realizatio
n of long-range interactions would open up a whole new realm of many-body physics and has become a central focus of research. Rydberg atoms are very well-suited to achieve this goal, as the van der Waals forces between them are many orders of magnitude larger than for ground state atoms. Consequently, the mere laser excitation of ultracold gases can cause strongly correlated many-body states to emerge directly when atoms are transferred to Rydberg states. A key example are quantum crystals, composed of coherent superpositions of different spatially ordered configurations of collective excitations. Here we report on the direct measurement of strong correlations in a laser excited two-dimensional atomic Mott insulator using high-resolution, in-situ Rydberg atom imaging. The observations reveal the emergence of spatially ordered excitation patterns in the high-density components of the prepared many-body state. They have random orientation, but well defined geometry, forming mesoscopic crystals of collective excitations delocalised throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realise exotic phases of matter, thereby laying the basis for quantum simulations of long-range interacting quantum magnets.
