Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session E13: Exploring Topological Physics with Cold AtomsInvited
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Sponsoring Units: DAMOP Room: 309 |
Tuesday, March 15, 2016 8:00AM - 8:36AM |
E13.00001: From Berry's Phase to Wilson Lines in a Honeycomb Optical Lattice Invited Speaker: Monika Schleier-Smith I will report on methods for fully characterizing the topology and geometry of Bloch bands in optical lattices. Using a Bose-Einstein condensate as a momentum-resolved probe, we study a paradigmatic model system, the honeycomb lattice. Its salient features are two Dirac points, each producing a half-quantum of Berry flux similar to the magnetic flux of an infinitesimally narrow solenoid. We have detected this singular Berry flux by forming an Aharonov-Bohm-type interferometer in momentum space.\footnote{L. Duca, T. Li, M. Reitter, I. Bloch, M. Schleier-Smith, and U. Schneider. \textit{Science} {\bf 347}, 288 (2015).} Our technique is broadly applicable to mapping out the Berry curvature or directly measuring the Chern number of a single band. I will furthermore show how interband dynamics can reveal the matrix-valued Wilson line, the generalization of Berry's phase to the multi-band setting.\footnote{T. Li, L. Duca, M. Reitter, F. Grusdt, E. Demler, M. Endres, M. Schleier-Smith, I. Bloch, and U. Schneider. \textit{arXiv}:1509.02185[cond-mat/quant-gas] (2015).} In the simple case where the Wilson line is path-independent and Abelian, it serves as a powerful tool for tomographic reconstruction of the band eigenstates. [Preview Abstract] |
Tuesday, March 15, 2016 8:36AM - 9:12AM |
E13.00002: Geometric ``charge'' pumping with a Bose-Einstein condensate Invited Speaker: Ian Spielman We realized a quantum "charge" pump for a Bose-Einstein condensate (BEC) in a novel bipartite magnetic lattice, whose bands are characterized by non-trivial topological invariants: the Zak phases. For each band, the Zak phase is determined by that band's integrated Berry curvature, a geometric quantity defined at each crystal momentum. We probed this Berry curvature in a charge pump experiment, by periodically and adiabatically driving the system. Unlike topological charge pumps in filled bands that yield quantized pumping, our BEC occupied just a single crystal momentum state allowing us to access its band's local geometry. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wavepacket's position in each unit cell, i.e., the polarization. Our magnetic lattice enabled us to observe this modulation by measuring the BEC's magnetization. While our periodic drive shifted the lattice potential by one unit cell per cycle, the displacement of the BEC, solely determined by the underlying Berry curvature, was always less than the lattice's displacement. [Preview Abstract] |
Tuesday, March 15, 2016 9:12AM - 9:48AM |
E13.00003: Measuring Chern numbers in Atomic Gases: 2D and 4D Quantum Hall Physics in the Lab Invited Speaker: Nathan Goldman Optical-lattice experiments have recently succeeded in probing the geometry of 2D Bloch bands with cold neutral atoms. Beyond these local geometrical effects, which are captured by the Berry curvature, 2D Bloch bands may also display non-trivial topology, a global property captured by a topological invariant (e.g. the first Chern number). Such topological properties have dramatic consequences on the transport of non-interacting atoms, such as quantized responses whenever the bands are uniformly populated. In this talk, I will start with the first experimental demonstration of topological transport in a gas of neutral particles, which revealed the Chern number through a cold-atom analogue of quantum-Hall measurements\footnote{\emph{Measuring the Chern Number of Hofstadter Bands with Ultracold Bosonic Atoms},\\ M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbene, N. R. Cooper, I. Bloch and N. Goldman,\\ Nature Physics {\bf 11}, 162 (2015).}. I will then describe how this Chern-number measurement could be extended in order to probe the topology of higher-dimensional systems. In particular, I will show how the \emph{second Chern number} -- an emblematic topological invariant associated with 4D Bloch bands -- could be extracted from an atomic gas, using a 3D optical lattice extended by a synthetic dimension\footnote{\emph{Four-Dimensional Quantum Hall Effect with Ultracold Atoms},\\ H. M. Price, O. Zilberberg, T. Ozawa, I. Carusotto and N. Goldman, \\ Phys. Rev. Lett. {\bf 115}, 195303 (2015).}. Finally, I will describe a general scheme by which optical lattices of subwavelength spacing could be realized\footnote{\emph{Dynamic Optical Lattices of Subwavelength Spacing for Ultracold Atoms},\\ S. Nascimbene, N. Goldman, N. R. Cooper and J. Dalibard,\\ Phys. Rev. Lett. {\bf 115}, 140401 (2015).}. This method leads to topological band structures with significantly enhanced energy scales, offering an interesting route towards the experimental realization of strongly-correlated topological states with cold atoms. [Preview Abstract] |
Tuesday, March 15, 2016 9:48AM - 10:24AM |
E13.00004: Experimental Realization of the Harper-Hofstadter Model Invited Speaker: Colin Kennedy Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new states of matter with topological properties. Traditionally, this has been achieved using magnetic fields or spin--orbit interactions, which couple only to charged particles. For neutral ultracold atoms, synthetic magnetic fields have been created that are strong enough to realize the Harper--Hofstadter model. In this talk, I report on work studying Bose--Einstein condensation in the Harper--Hofstadter Hamiltonian with one-half flux quantum per lattice unit cell. The diffraction pattern of the superfluid state directly shows the momentum distribution of the wavefunction, which is gauge-dependent, and it reveals both the reduced symmetry of the vector potential and the degeneracy of the ground state. I present an adiabatic, many-body state preparation protocol via the Mott insulating phase and show the superfluid ground state in a three-dimensional lattice with moderate interactions. I will discuss progress towards a triple-superlattice implementation as well as prospects for exploring exotic states close to the Mott transition. [Preview Abstract] |
Tuesday, March 15, 2016 10:24AM - 11:00AM |
E13.00005: Topological Charge Pumping with Cold Atoms Invited Speaker: Yoshiro Takahashi More than 30 years ago, Thouless considered an interesting phenomenon of quantum transport of an electron gas in an infinite one-dimensional periodic potential, driven in a periodic cycle. The charge pumped by this Thouless pump is a topological quantum number and does not depend on a smooth change of parameters. Importantly, this charge pumping shares the same topological origin as the integer quantum Hall effect. In spite of the importance in a topological quantum physics, this Thouless pump has never been realized in any system. In this study, we successfully realize the Thouless topological pump by exploiting the controllability of ultracold atoms in an optical superlattice. The charge pumping is detected as a shift of the center of mass of an atomic cloud measured with in situ absorption imaging. We extract the Chern number of the system from the average shift of the center of mass per pumping cycle. The topological nature of the pump is revealed by the clear dependence on the topology of the pumping trajectories in parameter space of our superlattice. We will describe the detail of our experiments using fermionic ytterbium atoms and also discuss the prospects of our research. [Preview Abstract] |
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