Using ultracold atoms to study microscopic behavior of topologically non-trivial systems.

Topologically non-trivial materials are of great interest for their robustness, with existing applications in metrology and potential applications in quantum computing. Quantum Hall systems provide one of the simplest examples of topologically non-trivial materials, exhibiting transverse conductance, quantized to a very precise degree in accordance with their topology. More generally, the topology of 2D lattices can be characterized in terms of a Chern number, that also defines the number of conducting edge channels at the boundary of finite systems. We experimentally explore how small a finite size system can be while still exhibiting bulk topological properties. We use the control and precise measurement ability afforded by cold atoms to observe the microscopic motion in the bulk without relying on collective conduction measurements, and extract a Chern number for our system. Our experiments were performed in a synthetic-dimension lattice with of Bose-condensed 87 Rb [1,2,3] with about 1/3 flux quanta per unit cell, in thin strips only 3 and 5 sites wide. We applied a force along lattice's long dimension to sample the entire Brillouin zone, and demonstrated that for both a 3-site wide strip and a 5-site wide strip the bands still manifested non-trivial bulk topology [4,5].\\ \\ [1] A. Celi, P. Massignan, J. Ruseckas, N. Goldman, I.B. Spielman, G. Juzeliūnas, M. Lewenstein ,Synthetic gauge fields in synthetic dimensions. Phys. Rev. Lett. 112, 043001 (2014) [2] B. K. Stuhl, H.-I Lu, L. M. Aycock, D. Genkina, I. B. Spielman, Visualizing edge states with an atomic Bose gas in the quantum Hall regime. Science 349, 1514–1518 (2015). [3] M. Mancini 1 , G. Pagano, G. Cappellini, L. Livi, M. Rider, J. Catani, C. Sias, P. Zoller, M. Inguscio, M. Dalmonte, L. Fallani. Observation of chiral edge states with neutral fermions in synthetic hall ribbons. Science 349, 1510– (2015). [4] Wang C, Gao C, Jian C M and Zhai H, Direct measurement of topological invariants in optical lattices. 2010 Phys. Rev. Lett. 105 160403 [5] S. Mugel, A. Dauphin, P Massignan, L. Tarruell, M. Lewenstein, C Lobo, A. Celi, Measuring Chern numbers in Hofstadter strips. Scipost Physics. 3. 10.21468/SciPostPhys.3.2.012.