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arXiv:2111.12378

Zak phase reconstruction enabled by thermal motion of atoms

Ruosong Mao, Xingqi Xu, Jiefei Wang, Chenran Xu, Gewei Qian, Han Cai, Shi‐Yao Zhu, Dawei Wang

Published Nov 24, 2021• 0 citations
arXivHTMLPDF

Abstract

Ultracold atoms provide a flexible platform for simulating topological phases. However, they are intrinsically prone to thermal noise, which can overwhelm topological response and hamper promised applications. On the other hand, topological invariants can be reconstructed from the energy spectra of particles subjected to a static force, based on the polarization relation between Wannier-Stark ladders and Zak phases. Such spectroscopic methods circumvent the obstacle to measuring topological invariants in thermal atoms. Here we reconstruct Zak phases from the anti-crossing between Wannier-Stark ladders in room-temperature superradiance lattices. Without dynamical manipulation routinely needed in ultracold atoms, we evaluate Zak phases directly from the absorption spectra. The thermal atomic motion, an essential source of noise in cold atoms, plays a key role in extracting Zak phases. Our approach paves the way of measuring topological invariants and developing their applications in room-temperature atoms.

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Ultracold atoms provide a flexible platform for simulating topological phases. However, they are intrinsically prone to thermal noise, which can overwhelm topological response and hamper promised applications. On the other hand, topological invariants can be reconstructed from the energy spectra of particles subjected to a static force, based on the polarization relation between Wannier-Stark ladders and Zak phases. Such spectroscopic methods circumvent the obstacle to measuring topological invariants in thermal atoms. Here we reconstruct Zak phases from the anti-crossing between Wannier-Stark ladders in room-temperature superradiance lattices. Without dynamical manipulation routinely needed in ultracold atoms, we evaluate Zak phases directly from the absorption spectra. The thermal atomic motion, an essential source of noise in cold atoms, plays a key role in extracting Zak phases. Our approach paves the way of measuring topological invariants and developing their applications in room-temperature atoms.
Floquet modulation has been widely used in optical lattices for coherent control of quantum gases, in particular for synthesizing artificial gauge fields and simulating topological matters. However, such modulation induces heating which can overwhelm the signal of quantum dynamics in ultracold atoms. Here we report that the thermal motion, instead of being a noise source, provides a new control knob in Floquet-modulated superradiance lattices, which are momentum-space tight-binding lattices of collectively excited states of atoms. The Doppler shifts combined with Floquet modulation provide effective forces along arbitrary directions in a lattice in frequency and momentum dimensions. Dynamic localization, dynamic delocalization, and chiral edge currents can be simultaneously observed from a single transport spectrum of superradiance lattices in thermal atoms. Our Letter paves a way for simulating Floquet topological matters in room-temperature atoms and facilitates their applications in photonic devices.
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems, which produced both fascinating physics findings and exciting opportunities for applications. Among the physical systems that have been considered to realize and probe these intriguing phases, ultracold atoms become promising platforms due to their high flexibility and controllability. Quantum simulation of topological phases with cold atomic gases is a rapidly evolving field, and recent theoretical and experimental developments reveal that some toy models originally proposed in condensed matter physics have been realized with this artificial quantum system. The purpose of this article is to introduce these developments. The article begins with a tutorial review of topological invariants and the methods to control parameters in the Hamiltonians of neutral atoms. Next, topological quantum phases in optical lattices are introduced in some detail, especially several celebrated models, such as the Su–Schrieffer–Heeger model, the Hofstadter–Harper model, the Haldane model and the Kane–Mele model. The theoretical proposals and experimental implementations of these models are discussed. Notably, many of these models cannot be directly realized in conventional solid-state experiments. The newly developed methods for probing the intrinsic properties of the topological phases in cold-atom systems are also reviewed. Finally, some topological phases with cold atoms in the continuum and in the presence of interactions are discussed, and an outlook on future work is given.
Chiral edge currents play an important role in characterizing topological matter. In atoms, they have been observed at such a low temperature that the atomic motion can be measured. Here we report the first experimental observation of chiral edge currents in atoms at room temperature. Staggered magnetic fluxes are induced by the spatial phase difference between two standing-wave light fields, which couple atoms to form a momentum-space zigzag superradiance lattice. The chiral edge currents are measured by comparing the directional superradiant emissions of two timed Dicke states in the lattice. Our results pave the way for simulating topological physics in hot atoms.
Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.
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.
In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological Zak phase is directly related to the Zak phase of an elementary quasiparticle excitation in the system. By considering various systems, we establish this connection for a number of different interacting phases including the Su-Schrieffer-Heeger model, ppp-wave topological superconductors, and the Haldane chain. Crucially, in contrast to the bulk many-body Zak phase associated with the ground state of such systems, the topological invariant associated with quasiparticle excitations (above this ground state) exhibits a more natural route for direct experimental detection. To this end, we build upon recent work [F. Grusdt, et al., Nat. Commun. 7, 11994 (2016)] and demonstrate that mobile quantum impurities can be used, in combination with Ramsey interferometry and Bloch oscillations, to directly measure these quasiparticle topological invariants. Finally, a concrete experimental realization of our protocol for dimerized Mott insulators in ultracold atomic systems is discussed and analyzed.