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arXiv:2601.08914

Observation of Unidirectional s-p Orbital Topological Edge States in Driven Photonic Lattices

Gayathry Rajeevan, Sebabrata Mukherjee

physics.opticscond-mat.mes-hallquant-phSubmitted Jan 13, 2026• Announced Jan 15, 2026
arXivHTMLPDF

Abstract

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 $s$ orbitals, without incorporating inter-orbital couplings. Here, we demonstrate higher-orbital Floquet topological insulators by introducing periodically modulated couplings between the optical $s$ and $p$ orbitals in a square lattice. The staggered phase of the $s$-$p$ couplings gives rise to a synthetic uniform $π$ 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 $s$-$p$ 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.

Journal reference
Communications Physics (2026)
DOI
10.1038/s42005-026-02756-8
Comments
Comments are welcome

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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.
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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.
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.
Topological phases with a widely tunable number of edge modes have been extensively studied as a typical class of exotic states of matter with potentially important applications. Although several models have been shown to support such phases, they are not easy to realize in solid-state systems due to the complexity of various intervening factors. Inspired by the realization of synthetic spin-orbit coupling in a cold-atom system [Z. Wu et al., Science 354, 83 (2016)], we propose a periodic quenching scheme to realize large-topological-number phases with multiple edge modes in optical lattices. Via introducing the periodic quenching to the Raman lattice, it is found that a large number of edge modes can be induced in a controllable manner from the static topologically trivial system. Our result provides an experimentally accessible method to artificially synthesize and manipulate exotic topological phases with large topological numbers and multiple edge modes.
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Periodic driving has a longstanding reputation for generating exotic phases of matter with no static counterparts. This work explores the interplay between periodic driving, interaction effects, and Z2{\mathbb{Z}}_{2}Z2​ symmetry that leads to the emergence of Floquet symmetry protected second-order topological phases in a simple but insightful two-dimensional spin-1/2 lattice. Through a combination of analytical and numerical treatments, we verify the formation of corner-localized 0 and $\ensuremath{\pi}$ modes, i.e., Z2{\mathbb{Z}}_{2}Z2​ symmetry broken operators that commute and anticommute, respectively, with the one-period time evolution operator, as well as establish the topological nature of these modes by demonstrating their presence over a wide range of parameter values and explicitly deriving their associated topological invariants under special conditions. Finally, we propose a means to detect the signature of such modes in experiments, and we discuss the effect of imperfections.