# Project Area D:

Rydberg Many Body Physics

Over the last few decades an amazing level of control has been achieved over essentially all properties of ensembles of ultracold atoms in their electronic ground state, making them versatile model systems for exploring the physics of strongly correlated matter. This includes their motion, density, spatial geometry, coherence properties, as well as the strength of the interactions. So far, however, the nature of the inter-atomic potential could hardly be controlled. At the same time, new laser sources capable of spanning almost the complete wavelength range (from ultraviolet to infrared), have made it possible to achieve full quantum control over the single-atom electronic properties, including highly excited Rydberg states. By exploiting the extreme properties of Rydberg states it is now possible to introduce and control totally new types of non-local and strong interactions between ultracold atoms.

For quantum simulation, ultracold Rydberg atoms potentially harness the best features of both ultracold neutral atom (1) and trapped ion (2) systems, which represent the state-of-the-art. The current generation of experiments is able to control essentially all single-atom properties, including preparing single atoms and small ensembles of atoms in tailored geometries. By tuning electric fields, for example it is possible to modify the Rydberg-Rydberg interactions, not only in strength but also in character, range and angular dependence (including van-der-Waals and dipolar interactions). In comparison to trapped ions, Rydberg atom systems can potentially be scaled to hundreds or thousands of particles each strongly interacting with one another. These interactions can be many orders of magnitude larger than those between ground-state atoms (3), leading to effects over distances considerably larger than the typical inter-atomic separation. This offers new possibilities to create and control atomic interactions which go far beyond usual (short-range) two-body scattering.

Having mastered the single- and few-atom properties of these systems, attention has started to turn to the study of genuine many-body effects. In the pioneering papers of ultracold Rydberg gases (3) (4), many-body effects were identified in the transport of excitations using Förster resonances. In 2004, the first experimental evidence was given for the so-called Rydberg blockade effect in which the presence of one Rydberg atom strongly suppresses the subsequent excitation of other atoms giving rise to strong spatial and temporal correlations (5) (6). Associated with the Rydberg blockade is an enhancement of the atom-light interaction similar to that observed in cavity quantum electrodynamics. Non-equilibrium effects can also arise due to the strong interactions, including mechanical forces (7) and coupling between internal and external degrees of freedom (8), the evolution of individual impurities to a quantum gas (9), and the rapid dipole mediated transport of Rydberg excitations (10). In 2007 it was shown that the Hamiltonian governing the combined Rydberg-light system has a close relation to the well-known Ising model (11), but in a new universality class, thereby providing a test bed for studying novel magnetic phenomena. Combined theoretical and experimental work has helped to elucidate the phase diagram and universal critical properties of this system. In 2010 it was predicted that by chirping the laser excitation pulses one could realize a crystalline state of Rydberg atoms (12). Recent experiments have demonstrated the emergence of spatially correlated structures in excellent agreement with the theory (13). The latest theoretical investigations suggest that ground state atoms dressed with Rydberg character exhibit novel soft-core interactions (14) giving rise to phenomena such as supersolidity (15) (16).

1. R. Blatt, C. F. Roos. Quantum simulations with trapped ions. *Nature Physics (Review) 8, 277–284 (2012)*.

2. I. Bloch, J. Dalibard and S. Nascimbène. Quantum simulations with ultracold quantum gases. *Nature Physics (Review) 8, 267–276 (2012)*.

3. I. Mourachko, D. Comparat, F. deTomasi, A. Fioretti, P. Nosbaum, V. M. Akulin, and P. Pillet. Many-body effects in a frozen Rydberg gas. *Phys. Rev. Lett. 80, 249-253 (1998)*.

4. W .R. Anderson, J. R. Veale, and T.F. Gallagher. Resonant dipole-dipole energy transfer in a nearly frozen Rydberg gas. *Phys. Rev. Lett. 80, 249 (1998)*.

5. D. Tong, S. M. Farooqi, J. Stanojevic, S. Krishnan, Y. P. Zhang, R. Côté, E. E. Eyler, and P. L. Gould. Local blockade of Rydberg excitation in an ultracold gas. *Phys. Rev. Lett. 93, 063001 (2004)*.

6. K. Singer, M. Reetz-Lamour, T. Amthor, L. G. Marcassa, and **M. Weidemüller**. Suppression of excitation and spectral broadening induced by interactions in a cold gas of Rydberg atoms. *Phys. Rev. Lett. 93, 16003 (2004)*.

7. T. Amthor, M. Reetz-Lamour, S. Westermann, J. Denskat, and **M. Weidemüller**. Mechanical effect of van der Waals interactions observed in real time in an ultracold Rydberg gas. *Phys. Rev. Lett. 98, 023004 (2007)*.

8. S. Wüster, A. Eisfeld, and **J.M. Rost**. Conical intersections in an ultracold gas. *Phys. Rev. Lett. 106, 153002 (2011)*.

9. J. B. Balewski, A. T. Krupp, A. Gaj, D. Peter, H. P. Büchler, R. Löw, S. Hofferberth and **T. Pfau**. Coupling a single electron to a Bose–Einstein condensate. *Nature 502, 664–667 (2013)*.

10. G. Günter, H. Schempp, M. Robert-de-Saint-Vincent, V. Gavryusev, S. Helmrich, C. S. Hofmann, S. Whitlock and **M. Weidemüller**. Observing the Dynamics of Dipole-Mediated Energy Transport by Interaction-Enhanced Imaging. *Science 342, 954, (2013)*.

11. H. Weimer, R. Löw, **T. Pfau**, and H. P. Büchler. Quantum critical behavior in strongly interacting Rydberg gases. *Phys. Rev. Lett. 101, 250601 (2008)*.

12. T. Pohl, E. Demler, and M. D. Lukin. Dynamical crystallization in the dipole blockade of ultracold atoms. *Phys. Rev. Lett. 104, 043002 (2010)*.

13. P. Schauß, M. Cheneau, M. Endres, T. Fukuhara, S. Hild, A. Omran, T. Pohl, C. Gross, S. Kuhr, I. Bloch. Observation of spatially ordered structures in a two-dimensional Rydberg gas. *Nature 491, 87 (2012)*.

14. N. Henkel, R. Nath, and T. Pohl. Three-dimensional roton excitations and supersolid formation in Rydberg-excited Bose-Einstein condensates. *Phys. Rev. Lett. 104, 195302 (2010)*.

15. N. Henkel, F. Cinti, P. Jain, G. Pupillo, and T. Pohl. Supersolid vortex crystals in Rydberg-dressed Bose-Einstein condensates. *Phys. Rev. Lett. 108, 265301 (2012)*.

15. F. Cinti, T. Macrì, W. Lechner, G. Pupillo, and T. Pohl. Defect-induced supersolidity with soft-core bosons. *Nature Commun. 5, 3235 (2014)*.