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arXiv:2001.11471 · Physical Review Letters

Realization and Detection of Nonergodic Critical Phases in an Optical Raman Lattice

Yucheng Wang, Long Zhang, Sen Niu, Dapeng Yu, Xiong-Jun Liu

Published Aug 12, 2020• 72 citations
arXivHTMLPDF

Abstract

The critical phases, being delocalized but nonergodic, are fundamental phases different from both the many-body localization and ergodic extended quantum phases, and have so far not been realized in experiment. Here we propose an incommensurate topological insulating model of AIII symmetry class to realize such critical phases through an optical Raman lattice scheme, which possesses a one-dimensional (1D) spin-orbit coupling and an incommensurate Zeeman potential. We show the existence of both noninteracting and many-body critical phases, which can coexist with the topological phase, and show that the critical-localization transition coincides with the topological phase boundary in noninteracting regime. The dynamical detection of the critical phases is proposed and studied in detail based on the available experimental techniques. Finally, we demonstrate how the proposed critical phases can be achieved within the current ultracold atom experiments. This work paves the way to observe the novel critical phases.

DOI
10.1103/physrevlett.125.073204

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The critical phases, being delocalized but nonergodic, are fundamental phases different from both the many-body localization and ergodic extended quantum phases, and have so far not been realized in experiment. Here we propose an incommensurate topological insulating model of AIII symmetry class to realize such critical phases through an optical Raman lattice scheme, which possesses a one-dimensional (1D) spin-orbit coupling and an incommensurate Zeeman potential. We show the existence of both noninteracting and many-body critical phases, which can coexist with the topological phase, and show that the critical-localization transition coincides with the topological phase boundary in noninteracting regime. The dynamical detection of the critical phases is proposed and studied in detail based on the available experimental techniques. Finally, we demonstrate how the proposed critical phases can be achieved within the current ultracold atom experiments. This work paves the way to observe the novel critical phases.
Cold atoms with laser-induced spin-orbit (SO) interactions provide promising platforms to explore novel quantum physics, in particular the exotic topological phases, beyond natural conditions of solids. The past several years have witnessed important progresses in both theory and experiment in the study of SO coupling and novel quantum states for ultracold atoms. Here we review the physics of the SO coupled quantum gases, focusing on the latest theoretical and experimental progresses of realizing SO couplings beyond one-dimension (1D), and the further investigation of novel topological quantum phases in such systems, including the topological insulating phases and topological superfluids. A pedagogical introduction to the SO coupling for ultracold atoms and topological quantum phases is presented. We show that the so-called optical Raman lattice schemes, which combine the creation of the conventional optical lattice and Raman lattice with topological stability, can provide minimal methods with high experimental feasibility to realize 1D to 3D SO couplings. The optical Raman lattices exhibit novel intrinsic symmetries, which enable the natural realization of topological phases belonging to different symmetry classes, with the topology being detectable through minimal measurement strategies. We introduce how the non-Abelian Majorana modes emerge in the SO coupled superfluid phases which can be topologically nontrivial or trivial, for which a few fundamental theorems are presented and discussed. The experimental schemes for achieving non-Abelian superfluid phases are given. Finally, we point out the future important issues in this rapidly growing research field.
Ultracold atoms provide a controllable platform to explore topological matter induced by spin-orbit (SO) coupling. This thesis reports an experimental realization of topological matter with Ytterbium atoms implemented by a Raman (or SO coupling) lattice - an optical lattice dressed by SO coupling, where internal atomic states are coupled by Raman beams. Remarkably, the lattice simultaneously serves as one of the Raman beams. As the building block of the Raman lattice, SO coupling is first studied in a one-dimensional (1D) bulk system and manifested by two hallmarks, the locking between the atomic spin and momentum and the dephasing in the Rabi oscillation. SO coupling in a periodic lattice renders topological matter. 1D Raman lattice show-cases a novel symmetry-protected topological (SPT) phase beyond the tenfold Altland-Zirnbauer classification. SPT phases distinguished by the Z2 invariant are determined from spin-textures. We highlight textures not only in equilibrium, but also of far-from-equilibrium dynamics after a quench between distinct phases, reflecting the band topology. Higher dimensional Raman lattices are richer. A three-dimensional (3D) topological nodal line semimetal structure has been observed for the first time with ultracold atoms, and reconstructed by a well-designed (pseudo-)tomography - extraction of Dirac points on different momentum layers, owing to the emergence of a crystalline symmetry. Similarly, topological features, such as band inversion lines that are bulk counterparts of Fermi arc states and connect Dirac points, are also uncovered from quench dynamics. "More is different." The SU(N) symmetric spin-independent interaction is investigated by Tan's contact and collective modes. Enhanced by the (orbital) Feshbach resonance, the Raman lattice with tunable interactions can be applied to engineer elusive topological many-body phases, which is envisaged for unveiling the attractive topological superfuilds.
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.
Abstract The disordered quantum world hosts three fundamental types of states, being extended, localized, and critical. Among various quantum phases formed by their interplay, the most nontrivial is the tripartite phase, wherein all three types of states coexist in the spectrum and are separated by anomalous mobility edges. Here, we report the realization of this exotic phase in a quasi-periodically driven orbital optical lattice with ultracold atoms. The optical lattice with a quasiperiodic Floquet modulation which couples the sss and ppp orbitals is realized in experiment and shown to host the tripartite phase based on exact theory. We establish a novel two-stage protocol to achieve a controlled preparation and detection of the tripartite phase, with all three types of quantum states being observed. The characteristic exponents of these states are determined from expansion dynamics, showing their distinct universal transport properties. Our study paves the way for a comprehensive exploration of the unconventional critical phenomena and localization physics with ultracold atoms.
Abstract We propose a novel scheme to realize non-Abelian dynamical gauge field for ultracold fermions, and uncover a new pairing mechanism for topological superfluidity. The dynamical gauge fields arise from a nontrivial compensation effect between the large Zeeman detuning and strong Hubbard interaction in a two-dimensional (2D) optical Raman lattice. The spin-flip transitions are forbidden by the large Zeeman detuning, but restored when the Zeeman splitting is compensated by Hubbard interaction, generating a dynamical non-Abelian gauge field that leads to a correlated 2D spin-orbit interaction depending on local state configurations. The topological superfluid from a novel pairing driven by 2D dynamical gauge fields is reached with high feasibility, showing a broad phase region without competing orders at relevant fillings, and can be easily prepared in experiment. Our work can open up an avenue to emulate non-Abelian dynamical gauge fields and exotic correlated topological phases with feasibility and particularly, paves the way for realizing the non-Abelian topological superfluids.
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.