In our research we aim to combine *ultracold atomic quantum gases* and *Rydberg
atoms*, to explore new types of quantum many-body systems. These systems will
feature long-range interactions which are tunable not only in their strength
but also in their shape.

Existing experiments on ultracold Rydberg systems use one of the two mainly as a “tool” to explore the physics of the other. Examples include the preparation of dense samples or even atomic Mott insulators of ultracold gases as initial states to explore Rydberg many-body physics on very short (microseconds) timescales [1-3]. The roles can also be exchanged, as demonstrated recently when Rydberg molecules were used to implement novel, minimal destructive detection schemes for ultracold atom systems [4].

However, the greatest potential of Rydberg atoms for quantum many-body physics
lies in the combination of Rydberg induced interactions and atomic motion in
the quantum regime. This requires the long-range interaction between Rydberg
atoms to be coherent on the timescale set by the atomic motion. Off-resonant
laser coupling to Rydberg states, also called *Rydberg dressing*, has been
proposed as a technique exactly for this purpose. By the choice of the laser
parameters the extremely strong dipolar interactions can be balanced with the
rate of dissipative light scattering. For strong laser coupling and small
system sizes of up to approximately hundred atoms, the realization of tunable
long-range interacting quantum many-body systems is experimentally feasible [5, 6].

Within this project we explore *several aspects of these fundamentally new
many-body systems*. To this end, we designed a novel experimental apparatus
tailored for high power laser coupling to Rydberg states as well as for the
precise local detection of systems with small atom number by quantum gas
microscopy [7, 8].

We choose potassium as our atomic species, of which the bosonic as well as the fermionic isotope is routinely cooled to quantum degeneracy and for which high power Rydberg coupling is technologically possible. We will then use this apparatus to study Rydberg dressing in two-dimensional continuous systems which are a promising candidate for the realization of supersolid quantum states [9, 10]. Furthermore, we will load the two-dimensional Rydberg dressed system into an optical lattice to explore Hubbard models beyond onsite interactions [11, 12] and to realize quantum magnets with engineered inter-spin interactions [13, 14].

Our experimental setup is designed to be very flexible and it allows us to trap atoms in optical tweezers in alternative to, or additionally to the trapping in optical lattices. In combination with Raman sideband cooling this will enable us to realize very fast experimental cycle times, similar to what has recently been demonstrated with the optical tweezer platform [15, 16] or by direct sideband cooling in an optical lattice [17]. Such a high repetition rate is key to realize many precision experiments requiring high staistics. Examples include the dynamics of single excitations in two-dimensional quantum magnets, the measurement of entanglement entropy or variational quantum simulation.

### Selected References

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).G. Günter, H. Schempp, M. Robert-de-Saint-Vincent, V. Gavryusev, S. Helmrich, C. S. Hofmann, S. Whitlock & M. Weidemüller.

*Observing the Dynamics of Dipole-Mediated Energy Transport by Interaction-Enhanced Imaging*. Science**342**, 954–956 (2013).P. Schauß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macrì, T. Pohl, I. Bloch & C. Gross.

*Crystallization in Ising Quantum Magnets*. Science**347**, 1455–1458 (2015).T. Manthey, T. Niederprüm, O. Thomas & H. Ott.

*Dynamically Probing Ultracold Lattice Gases via Rydberg Molecules*. New Journal of Physics**17**, 103024 (2015).J. Zeiher, R. van Bijnen, P. Schauß, S. Hild, J. -y. Choi, T. Pohl, I. Bloch & C. Gross.

*Many-Body Interferometry of a Rydberg-Dressed Spin Lattice*. Nature Physics**12**, 1095–1099 (2016).J. Zeiher, J. -y. Choi, A. Rubio-Abadal, T. Pohl, R. van Bijnen, I. Bloch & C. Gross.

*Coherent Many-Body Spin Dynamics in a Long-Range Interacting Ising Chain*. Physical Review X**7**, 041063 (2017).W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling & M. Greiner.

*A Quantum Gas Microscope for Detecting Single Atoms in a Hubbard-Regime Optical Lattice*. Nature**462**, 74–77 (2009).J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch & S. Kuhr.

*Single-Atom-Resolved Fluorescence Imaging of an Atomic Mott Insulator*. Nature**467**, 68–72 (2010).N. Henkel, R. Nath & T. Pohl.

*Three-Dimensional Roton Excitations and Supersolid Formation in Rydberg-Excited Bose-Einstein Condensates*. Physical Review Letters**104**, 195302 (2010).G. Pupillo, A. Micheli, M. Boninsegni, I. Lesanovsky & P. Zoller.

*Strongly Correlated Gases of Rydberg-Dressed Atoms: Quantum and Classical Dynamics*. Physical Review Letters**104**, 223002 (2010).E. G. Dalla Torre, E. Berg & E. Altman.

*Hidden Order in 1D Bose Insulators*. Physical Review Letters**97**, 260401 (2006).M. Mattioli, M. Dalmonte, W. Lechner & G. Pupillo.

*Cluster Luttinger Liquids of Rydberg-Dressed Atoms in Optical Lattices*. Physical Review Letters**111**, 165302 (2013).A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch & P. Zoller.

*Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms*. Physical Review Letters**114**, 173002 (2015).R. M. W. van Bijnen & T. Pohl.

*Quantum Magnetism and Topological Ordering via Rydberg Dressing near Förster Resonances*. Physical Review Letters**114**, 243002 (2015).H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić & M. D. Lukin.

*Probing many-body dynamics on a 51-atom quantum simulator*. Nature**551**, 579–584 (2017).V. Lienhard, S. de Léséleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L.-P. Henry & A. M. Läuchli.

*Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions*. Phys. Rev. X**8**, 021070 (2018).J. Hu, A. Urvoy, Z. Vendeiro, V. Crépel, W. Chen & V. Vuletić.

*Creation of a Bose-condensed gas of*. Science^{87}Rb by laser cooling**358**, 1078–1080 (2017).