09:00  10:00

Monika Aidelsburger
(LudwigMaximiliansUniversität München)
Static and dynamical gauge fields with ultracold atoms in periodicallydriven lattices
Ultracold atoms in optical lattices are powerful experimental platforms to study a variety of phenomena ranging from condensedmatter to statistical physics. Recently, a promising new direction was opened by the successful realization of two paradigmatic topological condensed matter models, i.e. the Hofstadter and the Haldane model. Topological states of matter exhibit unique conductivity properties, which are particularly robust against perturbations. One of the most prominent examples is the integer quantum Hall effect, where a twodimensional electron gas under extreme conditions exhibits a quantized conductivity.
Investigating related phenomena with chargeneutral atoms required the development of novel experimental techniques to mimic the behavior of charged particles in magnetic fields. I will introduce some of the most common methods using Floquet engineering, i.e. periodic driving of the system's parameters to emulate the properties of a system that is otherwise not available in static settings. These methods led to the successful generation of artificial magnetic fields in optical lattices and direct observations of the associated nontrivial topological properties in the topological condensed matter models mentioned above.
The simulation of complete gauge theories requires additional key ingredients that allow for an interaction between matter and gauge fields. One of the main challenges consists in engineering synthetic gauge fields with internal degrees of freedom that interact with the matter fields in a suitable manner that respects the symmetry of the gauge theory. Here, I will present recent results, where we have used a twocomponent mixture of ultracold bosonic atoms and resonant periodic driving at the value of the interspecies Hubbard interactions. Choosing particular modulation parameters enables the implementation of a $Z_2$ symmetric model, which we study in an optical doublewell potential  the basic building block of the $Z_2$ lattice gauge theory.

10:00  10:30

Christof Weitenberg
(Universität Hamburg)
New approaches to topological states with ultracold atoms
Ultracold atoms in optical lattices are a versatile platform to study the fascinating phenomena of gauge fields and topological matter. Periodic driving can induce topological band structures with nontrivial Chern number of the effective Floquet Hamiltonian and paradigmatic models, such as the Haldane model on the honeycomb latticce, can be directly engineered.
Here, I will present recent experiments, in which we realized three new approaches for measuring the Chern number in this system. First, we use a new topological effect  the quantization of the circular dichroism with the Chern number  which appears as the integrated difference of the depletion rates in chiral spectroscopy of both chiralities. Our experiments confirm this quantization and establish depletionrate measurements as a versatile probe. Second, we study the dynamics of the system after a quench into the topological regime using timeresolved Blochstate tomography and employ the mapping of the Chern number to the linking number manifesting in the emerging dynamical vortices. In these experiments, we obtain the Chern number directly from a topological object instead of infering it from a quantized response. Third, we apply stateoftheart deep learning techniques to our momentumspace images and train a network to recognize the Chern number from single images. This allows mapping out the full twodimensional Haldane phase diagram, which was unfeasible with conventional analysis. These new approaches to topology also define a promising starting point for probing topological order of interacting systems such as fractional Chern insulators.

10:30  11:00

coffee break

11:00  12:00

Eddy Ardonne
(Stockholm University)
Screening properties of quasielectrons
In the quantum Hall effect, determining the statistic properties of quasielectrons has remained more problematic in comparison to quasiholes. In this talk, I will quickly review the properties of the various proposals for quasielectrons, and their shortcomings. By using the MPS approach, we study the CFT formulation quasielectrons. This reveals on the one hand that the shortcoming of this proposal is rooted in the screening properties, but also how to screen the quasielectrons, so that they behave in the proper way.

12:00  12:30

discussion

12:30  13:30

lunch

13:30  15:00

discussion

15:00  16:00

Charles Kane
(University of Pennsylvania)
Fractional excitonic insulator
We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling 1/m. We introduce a variant of the Laughlin wavefunction for electrons and holes and show that for m=1 it describes a Chern insulator that is the exact ground state of a free fermion model with p_x + i p_y excitonic pairing. For m>1 we develop a composite fermion mean field theory, and we will give several pieces of evidence that our wavefunction correctly describes this phase. We will present physical arguments that the m=3 state can be realized in a system with C_6 rotational symmetry in which energy bands with angular momentum that differ by 3 cross at the Fermi energy. This leads to a gapless state with (p_x + i p_y)^3 excitonic pairing, which we argue is conducive to forming the fractional excitonic insulator in the presence of interactions. Prospects for numerics on model systems and band structure engineering to realize this phase in real materials will be discussed.

16:00  16:30

coffee break

16:30  17:00

Guy Le Lay
(AixMarseille University)
Exotic forms of lowdimensional artificial Xenes
Silicene, the silicon counterpart of graphene, possibly hosting a remarkable Quantum Spin Hall effect [1], has become a “Hot Research Front” [2], since its initial synthesis by epitaxy on Ag(111) in 2012 [3]. It has further given a quick to research on related elemental lowdimensional materials called Xenes. Typically, Kagome silicene [4], nearly planar twodimensional (2D) germanene [5] and stanene [6], as well as 1D Si nanoribbons solely composed of pentagonal moieties [7] and 0D nanodots [7,8], with unique characteristics, have been artificially created on different substrates.
The electronic properties of silicene have been rapidly exploited to fabricate ultrathin planar devices, typically fieldeffect transistors with a monolayer silicene channel have been already fabricated in 2015 [9].
In my talk, I will present the realization and properties of these new exotic lowdimensional materials and draw perspectives for future research, e.g., the quest for Majoranas.
References:
[1] C.C. Liu, W. Feng, Y. Yao, Phys. Rev. Lett. 107 076802 (2011).
[2] C. Day, Physics Today, September 25, 2015
[3] P. Vogt et al., Phys. Rev. Lett. 108 155501 (2012).
[4] Y. Sassa et al., to be submitted.
[5] M. E. Dávila et al., New Journal of Physics 16 095002 (2014).
[6] J. Yuhara et al., 2D Materials 5 025002 (2018).
[7] J. Cerdá et al., Nature Comm. 7 13076 (2016).
[8] S. Sheng et al., Nano Lett. 18 2937 (2018).
[9] L. Tao et al., Nature Nanotechnol. 10 227 (2015).
Guy Le Lay
PIIM  CNRS, AixMarseille University, France
Email: guy.lelay@univamu.fr

17:00  17:30

Onur Umucalilar
(Mimar Sinan Fine Arts University)
Timeofflight measurements as a possible method to observe anyonic statistics
We propose a standard timeofflight experiment as a method for observing the anyonic statistics of quasiholes in a fractional quantum Hall state of ultracold atoms. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. Our proposed method is validated by Monte Carlo calculations for $\nu = 1/2$ and 1/3 fractional quantum Hall liquids containing a realistic number of particles.

17:30  18:00

Frederic Mila
(École Polytechnique Fédérale de Lausanne)
Chiral phases of ultra cold fermions in optical lattices
We discuss the stabilization of chiral phases in realistic models of ultra cold fermions with SU(N) symmetry in optical lattices. Concentrating on the triangular lattice with one particle per site, we show that a chiral phase is stabilized by a complex ring exchange term for N from 3 to 9. Such a term, which breaks timereversal symmetry, is expected to be the leading correction to the Heisenberg model in a strong coupling expansion of the Hubbard model with an artificial gauge field. In addition, we provide numerical evidence suggesting that, even in the absence of an artificial gauge field, a chiral phase that spontaneously breaks timereversal symmetry is stabilized for the SU(3) Hubbard model between the threesublattice ordered phase at very strong coupling and the weakcoupling metallic phase.

19:00  22:00

workshop dinner at the restaurant Hierschönessen, Görlitzer Str. 20, phone: +4935125652898
