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arXiv:1112.3157 · Physical Review A

Simulating Z2 topological insulators with cold atoms in a one-dimensional optical lattice

Feng Mei, Shi-Liang Zhu, Zhi‐Ming Zhang, C. H. Oh, Nathan Goldman

Published Jan 27, 2012• 112 citations
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Abstract

We propose an experimental scheme to simulate and detect the properties of time-reversal invariant topological insulators, using cold atoms trapped in one-dimensional bichromatic optical lattices. This system is described by a one-dimensional Aubry-Andre model with an additional SU(2) gauge structure, which captures the essential properties of a two-dimensional ${Z}_{2}$ topological insulator. We demonstrate that topologically protected edge states, with opposite spin orientations, can be pumped across the lattice by sweeping a laser phase adiabatically. This process is an elegant way to transfer topologically protected quantum states in a highly controllable environment. We discuss how density measurements could provide clear signatures of the topological phases emanating from our one-dimensional system.

DOI
10.1103/physreva.85.013638

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We propose an experimental scheme to simulate and detect the properties of time-reversal invariant topological insulators, using cold atoms trapped in one-dimensional bichromatic optical lattices. This system is described by a one-dimensional Aubry-Andre model with an additional SU(2) gauge structure, which captures the essential properties of a two-dimensional Z2{Z}_{2}Z2​ topological insulator. We demonstrate that topologically protected edge states, with opposite spin orientations, can be pumped across the lattice by sweeping a laser phase adiabatically. This process is an elegant way to transfer topologically protected quantum states in a highly controllable environment. We discuss how density measurements could provide clear signatures of the topological phases emanating from our one-dimensional system.
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.
We propose a one-dimensional optical lattice model to simulate and explore two-dimensional topological phases with ultracold atoms, considering the phases of the hopping strengths as an extra dimension. It is shown that the model exhibits nontrivial phases, and corresponding two chiral-edge states. Moreover, we demonstrate the connections between changes in the topological invariants and the Dirac points. Furthermore, the topological order detected by the particle pumping approach in cold atoms is also investigated. The results obtained here provide a feasible and flexible method of simulating and exploring high-dimensional topological phases in low-dimension systems via the controllable phase of the hopping strength.
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.
We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional Z(2) topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states--the Dirac cones--can be probed through time-of-flight imaging or Bragg spectroscopy and the flat band can be detected via measurement of the atomic density profile in a weak global trap. The realization of this novel topological phase with a flat band in an optical lattice will provide a unique experimental platform to study the interplay between interaction and topology and open new avenues for application of topological states.
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We show that one-dimensional quasiperiodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on the optical superlattice is a topological insulator characterized by a nonzero topological invariant. The topological nature can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions uniquely determined by the ration of wavelengths of the bichromatic optical lattice. The butterflylike spectrum of the superlattice system can be also determined from the finite-temperature density profiles of the trapped fermion system. This finding opens an alternative avenue to study the topological phases and Hofstadter-like spectrum in one-dimensional optical lattices.