A Continuously Tunable Topological Quantum Pump in a High-dimensional Cold Atomic Gas

Yan-Bin Yang, Yong Xu

Published Jan 25, 2018• 0 citations

Abstract

Over thirty years ago, Thouless introduced the quantized particle transport that can occur in a one-dimensional quantum system under a cyclic adiabatic variation of periodic potentials without a bias voltage. This phenomenon is attributed to the formation of a dynamical Chern insulator on a parameter surface formed by quasimomentum and time. Recently, three-dimensional topological gapless phenomena have sparked tremendous attention in various fields. Here, we demonstrate that dynamical Weyl points and dynamical 4D Weyl nodal rings protected by the first Chern number emerge in a two-dimensional and three-dimensional system, respectively. We find that the topological quantum pump occurs in these systems but the amount of pumped particles is not quantized and can be tuned continuously by controlling experimental parameters. Finally, we propose an experimental scheme to realize the dynamical Weyl points and 4D Weyl nodal rings and their corresponding topological pump in cold atomic gases.

Related papers

Dynamical Weyl Points and 4D Nodal Rings in Cold Atomic Gases

Yan-Bin Yang, Luming Duan, Yong Xu

Controllability of ultracold atomic gases has reached an unprecedented level, allowing for experimental realization of the long-sought-after Thouless pump, which can be interpreted as a dynamical quantum Hall effect. On the other hand, Weyl semimetals and Weyl nodal line semimetals with touching points and rings in band structures have sparked tremendous interest in various fields in the past few years. Here, we show that dynamical Weyl points and dynamical 4D Weyl nodal rings, which are protected by the first Chern number on a parameter surface formed by quasi-momentum and time, emerge in a two-dimensional and three-dimensional system, respectively. We find that the topological pump occurs in these systems but the amount of pumped particles is not quantized and can be continuously tuned by controlling experimental parameters over a wide range. We also propose an experimental scheme to realize the dynamical Weyl points and 4D Weyl nodal rings and to observe their corresponding topological pump in cold atomic gases.

arXiv:1801.08255Jan 25, 201813 citations

Topological gapless matters in three-dimensional ultracold atomic gases

Yong Xu

Three-dimensional topological gapless matters with gapless degeneracies protected by a topological invariant defined over a closed manifold in momentum space have attracted considerable interest in various fields ranging from condensed matter materials to ultracold atomic gases. As a highly controllable and disorder free system, ultracold atomic gases provide a versatile platform to simulate topological gapless matters. Here, the current progress in studies of topological gapless phenomena in three-dimensional cold atom systems is summarized in the review. It is mainly focused on Weyl points, structured (type-II) Weyl points, Dirac points, nodal rings and Weyl exceptional rings in cold atoms. Since interactions in cold atoms can be controlled via Feshbach resonances, the progress in both superfluids for attractive interactions and non-interacting cold atom gases is reviewed.

arXiv:1812.03756Frontiers of PhysicsApr 23, 201935 citations

Dirac and Weyl rings in three-dimensional cold-atom optical lattices

Yong Xu, Chuanwei Zhang

Recently three-dimensional topological quantum materials with gapless energy spectra have attracted considerable interest in many branches of physics. Besides the celebrated example, Dirac and Weyl points which possess gapless point structures in the underlying energy dispersion, the topologically protected gapless spectrum, can also occur along a ring, named Dirac and Weyl nodal rings. Ultracold atomic gases provide an ideal platform for exploring new topological materials with designed symmetries and dispersion. However, whether Dirac and Weyl rings can exist in the single-particle spectrum of cold atoms remains elusive. Here we propose a realistic model for realizing Dirac and Weyl rings in the single-particle band dispersion of a cold-atom optical lattice. Our scheme is based on a previously experimentally implemented Raman coupling setup for realizing spin-orbit coupling. Without the Zeeman field, the model preserves both pseudo-time-reversal and inversion symmetries, allowing Dirac rings. The Dirac rings split into Weyl rings with a Zeeman field that breaks the pseudo-time-reversal symmetry. We examine the superfluidity of attractive Fermi gases in this model and also find Dirac and Weyl rings in the quasiparticle spectrum.

arXiv:1510.03355Physical Review AJun 7, 201637 citations

Topological insulator and particle pumping in a one-dimensional shaken optical lattice

Feng Mei, Jia-Bin You, Dan-Wei Zhang +4 more

We propose a simple method to simulate and detect topological insulators with cold atoms trapped in a one-dimensional bichromatic optical lattice subjected to a time-periodic modulation. The tight-binding form of this shaken system is equivalent to the periodically driven Aubry-Andre model. We demonstrate that this model can be mapped into a two-dimensional Chern insulator model, whose energy spectrum hosts a topological phase within an experimentally accessible parameter regime. By tuning the laser phase adiabatically, such one-dimensional system constitutes a natural platform to realize topological particle pumping. We show that the Chern number characterizing the topological features of this system can be measured by detecting the density shift after one cycle of pumping.

arXiv:1902.08338Physical Review ADec 29, 201473 citations

Topological charge pumping in ultracold quantum gases

Eric Bertok

A topological charge pump is a one-dimensional, dynamical analogue of a quantum Hall system that is particularly well suited for studying topology, both theoretically and experimentally, since no synthetic gauge fields are required and efficient numerical algorithms exist to treat one-dimensional interacting systems in the form of matrix-product state methods. Instead of a robustly quantized Hall conductivity, a topological charge pump pumps a quantized amount of charge in each cycle of a parameter modulation that is given by the same topological invariant as in the quantum Hall effect. The goal of this thesis is to understand the stability of quantized transport in various contexts that are relevant in ultracold quantum gases, such as disordered systems, quantum systems where energy can be exchanged with a bath and in the presence of genuine many-body interactions. The results are presented as part of four scientific papers. In the first paper, we characterize the breakdown of quantized pumping as a function of disorder strength by employing various instantaneous and time-dependent measures. We argue that in disorder averages, the full energy gap distributions should be considered. In the second paper, we study the breakdown of quantized pumping due to electron-phonon coupling and find a resonant breakdown when the pump frequency equals the phonon frequency. The third paper introduces the possibility of a splitting of critical points in a Rice-Mele Hubbard model, which allows for interaction-induced pumping. The final paper presents experimental data of an ultracold-atom setup studying this interaction-induced pumping, as well as numerical calculations detailing the breakdown due to the crossing of a spin-gapless line.

Jan 1, 20230 citations

Non-equilibrium aspects of topological Floquet quantum systems

Lorenzo Privitera

The manifestations of topology are ubiquitous in condensed matter physics. One of the most striking examples is the integer quantum Hall effect, which served as a theoretical basis for developing many classes of new materials in the last years such as topological insulators. It has been realized that topology can manifest itself also in time-dependent quantum systems. The question that we try to address in this thesis is how much of these topological structures can be harnessed in the realistic dynamics of a periodically driven closed quantum system. We investigate two kinds of topological periodically driven systems Thouless pumping and Floquet Chern insulators. Our analysis shows that the nonequilibrium occupations of the eigenvalues of the Floquet Hamiltonian, the so called quasienergies, play a crucial role. In the case of Thouless pumping we analysed the pumped charge averaged over many cycles and discovered that the corrections to perfect quantization of the pumped charge are actually quadratic in the frequency of the driving for a suddenly switched-on driving. In the case of Floquet Chern insulators, we studied fermions on the honeycomb lattice subjected to a circularly polarised field. We found that while the quasienergy bulk states can be populated in a controlled way, edge states get unavoidable excitations due to exponentially small gaps preventing adiabaticity. These defects reflect in nonequilibrium currents flowing at the edges, that can be manipulated by tailoring the parameters of the periodic driving. Nevertheless, the nonequilibrium state undergoes a generalized form of topological transition, thanks to the controlled population of bulk states. We describe it with a generalized version of the Chern marker of Bianco and Resta

Oct 16, 20171 citation