Department of Physics • University of Cologne

I will discuss recent developments in quantum simulation of quantum many-body systems with atomic platforms from a theory perspective. Systems of interests include atoms in optical lattices, Rydberg atoms in optical tweezer arrays, and trapped ions. Quantum simulation has so far been discussed as analog simulation, where we physically build a system with the desired Hamiltonian; or as digital quantum simulation, where time evolution of a many-body system is represented as a sequence of quantum gates on a quantum computer. I will add to this variation quantum simulation, where a quantum feedback loop between a classical computer and an analog quantum simulator, which acts as a quantum co-processor. As an example I will present results from an ongoing theory - experiment collaboration in Innsbruck: here our quantum resource is a trapped-ion 20-qubit analog quantum simulator, representing a transverse Ising model, and we compute on the quantum device the ground and excited states of the Lattice Schwinger Model as 1D Quantum Electrodynamics. Remarkably, variational quantum simulation allows "self-verification" of quantum results on the quantum machine, as assessment of the error. As a second topic we will discuss novel measurement protocols for Rényi entropies, and for out-of-time-ordered correlation functions (OTOCs), which can be extracted from on statistical correlations between randomized measurements. I will show a recent experiment with an ion chain, demonstrating experimental observation of entanglement entropies in quench dynamics in 10 and 20 qubit devices. I will conclude my talk with a brief outlook on possible future directions, including sub-wavelength optical lattices for atomic Hubbard models, and quantum chemistry.

The intimate connection between topology and quantum physics has been widely explored in solid-state physics, revealing a plethora of remarkable physical phenomena over the years. Building on their universal nature, topological properties are currently studied in an even broader context, ranging from ultracold atomic gases to photonics, where distinct observables and probes offer a novel view on topological quantum matter. In this talk, I will discuss how the geometry of quantum states can be revealed using a universal scheme based on excitation-rate measurements upon periodic driving [1,2,3]. When applied to Chern insulators or Landau levels, this approach leads to a quantized circular dichroism phenomenon [1,2], which can be interpreted as the dissipative counterpart of the quantum Hall effect. Besides, we will present protocols allowing for the experimental detection of the quantum metric tensor [3], which could be applied to detect new forms of monopoles in higher dimensions [4]. Finally, I will report on the first experimental observation of quantized circular dichroism in an ultracold Fermi gas [5]. [1] D. T. Tran, A. Dauphin, A. G. Grushin, P. Zoller and N. Goldman, Science Advances 3, e1701207 (2017). [2] D. T. Tran, N. R. Cooper, and N. Goldman, Phys. Rev. A 97, 061602(R) (2018). [3] T. Ozawa and N. Goldman, Phys. Rev. B 97, 201117(R) (2018). [4] G. Palumbo and N. Goldman, arXiv:1805.01247(2018). [5] L. Asteria, D. T. Tran, T. Ozawa, M. Tarnowski, B. S. Rem, N. Fläschner, K. Sengstock, N. Goldman and C. Weitenberg, arXiv:1805.11077 (2018).