How much knowledge can we obtain about a physical system and to what degree can we control it? At the microscopic level, the answer to this question is dictated by the laws of quantum mechanics. For example, few-particle quantum-optics systems, such as trapped ions or atoms in cavities, are now controlled and probed at the fundamental level of individual quanta.

In contrast, large collections of entangled quantum particles pose entirely new challenges due to the enormous number of microscopic parameters and the resulting difficulties in describing and detecting their quantum state. At the same time, they also provide new resources for applications in quantum science: Our goal is to harness such entangled quantum quantum many-body systems for quantum simulation, quantum computing and quantum metrology beyond capabilities of classical systems.

More generally, we believe in a highly collaborative approach to research that crosses boundaries between AMO physics, quantum information, and quantum many-body physics while integrating experiments and theoretical investigations.

In contrast, large collections of entangled quantum particles pose entirely new challenges due to the enormous number of microscopic parameters and the resulting difficulties in describing and detecting their quantum state. At the same time, they also provide new resources for applications in quantum science: Our goal is to harness such entangled quantum quantum many-body systems for quantum simulation, quantum computing and quantum metrology beyond capabilities of classical systems.

More generally, we believe in a highly collaborative approach to research that crosses boundaries between AMO physics, quantum information, and quantum many-body physics while integrating experiments and theoretical investigations.

## Current research directions:

**Entanglement control in alkaline-earth Rydberg arrays :**

Our major experimental goal is to generate strongly entangled states of 20-150 individually controlled qubits for applications in quantum simulation, quantum information, and quantum metrology beyond classical capabilities, currently one of the major outstanding challenges in quantum science. To this end, we are trapping individually controlled alkaline-earth atoms (Strontium-88) in large scale tweezer arrays. We plan on generating entanglement with a unique Rydberg excitation scheme that promises a dramatic increase in coherence time, enabling coherent entanglement spreading over very large system volumes. Our platform further opens up a range of interesting directions in basic AMO physics concerning novel laser cooling schemes, molecular control, etc through precision control of individual alkaline-earth atoms.

**Theory for quantum behavior and control of Rydberg arrays:**

In collaboration with Caltech theorists, we are exploring various new ideas for employing Rydberg arrays in quantum simulation, quantum information, entangled state engineering, and quantum metrology. Projects range from more abstract questions to realistic modeling of experimental scenarios, including open system dynamics. We are further investigating the use of machine-learning techniques applied to questions in quantum many body theory and experiments.

**Towards assembly of electronic matter:**

In a collaboration with Chris Green's group at Purdue, we are theoretically exploring a new idea for coherent charge hopping between alkaline-earth ion cores trapped in optical tweezers. This could one day enable the assembly and dynamical control of electronic matter with optically trapped ionic cores that are individually controlled.

**Effects of dynamically changing Berry phases:**

In a theory collaboration with Gil Refael, we are exploring effects of dynamically changing Berry phases in optical lattices.

**Rydberg array quantum simulation with alkali atoms:**

In collaboration with Misha Lukin's group at Harvard, we have been developing new techniques for quantum simulations based on Rydberg atom arrays. These experiments are based on atom-by-atom assembly of defect-free atomic arrays with optical tweezer.

## Examples of previous research topics:

**Detection of dynamical correlation functions:**

In collaboration with Michael Knap's group at TU Munich, we are exploring new techniques for measuring dynamical correlation functions, including out-of-time ordered functions.

Entanglement detection: In collaboration with the Rosario Fazio's group, we theoretically proposed a method for spin-entanglement detection in optical lattices that was subsequently experimentally realized in a collaboration with the Bloch group. |

Optical lattice version of strained graphene: In collaboration with David Pekker's group, we proposed a method to generate relativistic Landau levels by straining an optical lattice |

**Coupling of atoms to nanophotonic structures:**

In collaboration with Misha Lukin's group, we are coupling individual Rubidium atoms to one-dimensional photonic crystal structures enabling interactions between the atoms and single photons. Our main goal is to extend the scheme to multiple atoms for entanglement generation and photon-induced atom-atom interactions.

Wilson loops as probes for Bloch band topology: In collaboration with the Bloch group, we are working on novel ways to probe the geometry of Bloch bands using Wilson loops and lines. |

Development of a quantum microscope for optical lattices: Development of a novel method for imaging and manipulating individual atoms in optical lattices. |

Detection of a Higgs mode close to a 2d quantum phase transition: We observed an amplitude ‘Higgs’ modes close to the 2d superfluid-Mott insulator transition by measuring the dynamical response to lattice modulation with single-atom-sensitivity. The observability of ‘Higgs’ modes close to 2d quantum phase transitions has been debated and our measurements helped to resolve the discussion. |

Two-site and non-local correlation functions: Using the quantum microscope, we detected correlation functions at the single particle level including a proof-of-principle that nonlocal observables are experimentally accessible. Such nonlocal quantities, taking into account detailed information of extended regions, are necessary for describing order in quantum phases that are beyond the standard Landau description (e.g., topological phases). |

Out-of-equilibrium dynamics of correlations: Experimental observation of light-cone spreading of two-site correlations after a quantum quench of 1d Mott insulators. |

**Quantum dynamics of individual spins and magnon bound states:**

We prepared individual spin impurities using single atom addressing and watched their dynamics.

**Theory for nonlocal correlations:**

We worked out a theoretical extension of nonlocal order to 2d systems showing that area correlations correspond to spatial Wilson loops in a dual description. Further, we theoretically investigated the out-of-equilibrium dynamics of non-local correlations.