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arXiv:2603.01760

Experimental engineering of Floquet topological phases in a one-dimensional optical lattice

Pengju Zhao, 魏豫东, Zhongshu Hu, Shengjie Jin, Xuzong Chen Xuzong Chen, Xiong-Jun Liu

Published Mar 2, 2026• 0 citations
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Abstract

Periodic driving enables realization of topological phases without static counterparts. We experimentally realize and detect a one-dimensional anomalous Floquet topological phase in an optical lattice, using multi-frequency control to manipulate the relative sign structure of the gap windings $(W_0,W_π)$ associated with the $0$ and $π$ quasienergy gaps. We develop a lattice-depth modulation scheme that induces staggered nearest-neighbor $s$-$p$ orbital couplings and realize a minimal nontrivial Floquet topology under single-tone driving. Introducing a second tone, its relative phase controls the effective coupling signs in the $0$ and $π$ gaps, thereby tuning the corresponding windings to add and produce a high-winding phase or to cancel while retaining nontrivial gap indices. We read out $(W_0,W_π)$ with a band-inversion-surface (BIS)-resolved Ramsey protocol assisted by lattice-position shaking, which measures relative Floquet phases on the BISs. Controlled quenches further confirm phase-dependent band modifications even at quasimomenta far from resonance. These results establish multi-frequency control with a tunable relative phase as a quantitative route to engineering anomalous Floquet topology, and demonstrate phase-coherent coexistence of distinct drive modalities.

DOI
10.48550/arxiv.2603.01760

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Periodic driving enables realization of topological phases without static counterparts. We experimentally realize and detect a one-dimensional anomalous Floquet topological phase in an optical lattice, using multi-frequency control to manipulate the relative sign structure of the gap windings (W0,Wπ)(W_0,W_π)(W0​,Wπ​) associated with the 000 and πππ quasienergy gaps. We develop a lattice-depth modulation scheme that induces staggered nearest-neighbor sss-ppp orbital couplings and realize a minimal nontrivial Floquet topology under single-tone driving. Introducing a second tone, its relative phase controls the effective coupling signs in the 000 and πππ gaps, thereby tuning the corresponding windings to add and produce a high-winding phase or to cancel while retaining nontrivial gap indices. We read out (W0,Wπ)(W_0,W_π)(W0​,Wπ​) with a band-inversion-surface (BIS)-resolved Ramsey protocol assisted by lattice-position shaking, which measures relative Floquet phases on the BISs. Controlled quenches further confirm phase-dependent band modifications even at quasimomenta far from resonance. These results establish multi-frequency control with a tunable relative phase as a quantitative route to engineering anomalous Floquet topology, and demonstrate phase-coherent coexistence of distinct drive modalities.
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This thesis reports on the realization of Floquet topological systems with ultracold atoms in an optical honeycomb lattice. Using periodically driven quantum systems, topological phases of matter can be simulated by an effective, static Hamiltonian related to the time-evolution at integer multiples of the driving period, which is known as Floquet engineering. However, periodic driving can also give rise to genuinely time-dependent settings without static counterparts. One example is the anomalous Floquet phase in two dimensions, in which all bulk bands have a Chern number of zero but nevertheless robust chiral edge modes appear, which would be precluded by the bulk-edge correspondence in a static system. In an optical honeycomb lattice, anomalous Floquet systems can be created by continuous, periodic modulation of the laser intensities. This driving scheme results in different topological regimes, three of which are investigated, including the anomalous Floquet phase and a Haldane-like phase. Periodically driven systems feature periodic quasienergies and can be characterized in terms of winding numbers, which count the number of chiral edge modes in each quasienergy gap. By interferometric measurements of the quasienergy gaps between the first two Floquet bands, the topological phase transitions, emerging as gap closings, are located. For periodically driven systems, a modified bulk-edge correspondence can be formulated. In particular, the change of the winding number at a phase transition is related to the sign change of the local Berry curvature. The Berry curvature at the gap closing points is probed by Hall deflection measurements to obtain the winding numbers in each of the topological regimes, revealing the existence of chiral edge modes also in a setting with smooth boundaries as used in the experiments. The measured quasienergy gaps and transverse deflections are quantitatively well described by a numerical calculation of the Floquet bandstructure that includes coupling to higher bands during the driving period. To derive the spectrum of the modulated lattice in a geometry with edges, a tight-binding description of the system is discussed. Circular phase modulation of the honeycomb lattice can also give rise to an anomalous Floquet system when inversion symmetry is broken. The topological phase diagrams and the experimental feasibility are compared for both modulation schemes. Due to the vanishing Chern numbers, the bulk states in the anomalous Floquet regime can be fully localized by a disorder potential. This could prevent heating in interacting, periodically driven systems, resulting in a many-body localized bulk coexisting with thermalizing edge states. The experimental realization of disorder and strong interactions, as well as independent probes of the edge states are investigated. Bloch band geometry can be extended to multiband systems, using Wilson lines. The possible symmetry protection of their eigenvalues is discussed, along with measurements in the optical honeycomb lattice. Moreover, the onset of heating in weakly-interacting, periodically driven systems, triggered by parametric instabilities, is studied experimentally in a one-dimensional lattice.
Time-periodic modulation of a static system is a powerful method for realizing robust unidirectional topological states. So far, all such realizations have been based on interactions among sss orbitals, without incorporating inter-orbital couplings. Here, we demonstrate higher-orbital Floquet topological insulators by introducing periodically modulated couplings between the optical sss and ppp orbitals in a square lattice. The staggered phase of the sss-ppp couplings gives rise to a synthetic uniform πππ magnetic flux per plaquette of the lattice, and periodic driving of the couplings opens a topological bandgap, characterized by the Floquet winding number. We image topological edge modes of sss-ppp orbitals traveling unidirectionally around a corner. Here, the topological phases are realized by a combined effect of the periodic driving and synthetic magnetic flux. Consequently, when the synthetic flux is turned off, the system becomes trivial over a range of driving parameters. Our results open a promising pathway for exploring topological phenomena by introducing the orbital degree of freedom.
The dynamic engineering of band structures for ultracold atoms in optical lattices represents an innovative approach to understand and explore the fundamental principles of topological matter. In particular, the folded Floquet spectrum determines the associated band topology via band inversion. We experimentally and theoretically study two-frequency phase modulation to asymmetrically hybridize the lowest two bands of a one-dimensional lattice. Using quasi-degenerate perturbation theory in the extended Floquet space we derive an effective two-band model that quantitatively describes our setting. The energy gaps are experimentally probed via Landau-Zener transitions between Floquet-Bloch bands using an accelerated Bose-Einstein condensate. Separate and simultaneous control over the closing and reopening of these band gaps is demonstrated. We find good agreement between experiment and theory, establishing an analytic description for resonant Floquet-Bloch engineering that includes single- and multi-photon couplings, as well as interference effects between several commensurate drives.