arXiv subjects

F. Nur Ünal

Publications and source records attributed to F. Nur Ünal.

At least 19 recordsLinked to original sources

arXiv2026

Localization and topological signatures under periodic twisting

We theoretically explore a dynamical generalization of the Aubry-André model in two dimensions formed by superimposing two square-lattice potentials. Motivated by the rich physics emerging at different twist angles between the two lattices at equilibrium, we introduce periodic twisting by continuously rotating one of the lattices with respect to the other in the plane. We demonstrate that the distinct time-dependent twisting in this system gives rise to an intricate form of periodic multi-frequency driving that changes with the distance from the rotation axis. We find that the incommensurate nature of the potential no longer plays the pivotal role as it does in the static case. Rather, the tunneling can be understood in terms of a local, spatially varying dynamical localization effect, which we show to yield ring-shaped states localized within the bulk that have interesting transport signatures. Quantifying the eigenstates with the Bott index and local Chern marker, we find that there is a zoo of states with non-trivial topological signatures, the most ubiquitous of which result in relatively uniform ring-shaped regions of the Chern marker. We investigate the origin of these effects from various angles and identify that hybridization between different delocalized ring states plays a vital role. Lastly, we discuss possible experimental realizations in quantum simulation settings. Our results open a new avenue of investigation with periodic twisting inducing a spatially varying multi-frequency drive.

cond-mat.quant-gas↗

arXiv2026

Measuring non-Abelian quantum geometry and topology in a multi-gap photonic lattice

Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of topological phases necessitates novel approaches to probe them in laboratories, a pursuit that intricately relates to evaluating non-Abelian generalizations of the Abelian quantum geometric tensor (QGT) that characterizes geometric responses. Here, we pioneer the direct measurement of the non-Abelian QGT. We achieve this by implementing a novel orbital-resolved polarimetry technique to probe the full Bloch Hamiltonian of a six-band two-dimensional (2D) synthetic lattice, which grants direct experimental access to non-Abelian quaternion charges, the Euler curvature, and the non-Abelian quantum metric associated with all bands. Quantum geometry has been highlighted to play a key role on macroscopic phenomena ranging from superconductivity in flat-bands, to optical responses, transport, metrology, and quantum Hall physics. Therefore, our work unlocks the experimental probing of a wide phenomenology of multi-gap systems, at the confluence of topology, geometry and non-Abelian physics.

cond-mat.mes-hall↗

arXiv2026

Realizing anomalous Floquet non-Abelian band topology in photonic scattering networks

The concept of multi-gap topology has recently been shown to give rise to uncharted phases beyond conventional single-gap classifications. These phases relate to band nodes with non-Abelian quaternion charges and momentum-space braiding processes characterized by new invariants such as paradigmatic Euler class, phenomena that intrinsically require at least two spatial dimensions. Extending such phases into the non-equilibrium regime is predicted to unlock even richer multi-gap topologies beyond static settings, yet their experimental realization has remained elusive due to the stringent requirements on dimensionality, symmetry, and dynamical control. Here, we theoretically demonstrate and, for the first time, experimentally realize two-dimensional (2D) Floquet non-Abelian band topology in photonic scattering networks. Within this platform, we uncover a sequence of topological phenomena unique to 2D multi-gap systems far from equilibrium, including anomalous multi-gap phases interconnected by band nodes, Floquet Euler transfer, gapped phases with anomalous Dirac string configurations, and Floquet-induced non-Abelian braiding of band nodes. In addition, we observe Floquet-periodic anomalous edge states across multiple gaps, providing experimental signatures of these sought-after 2D multi-gap Floquet topological phases. Our results establish photonic scattering networks as a practical and versatile route to non-Abelian Floquet systems, opening avenues for dynamical topological physics with braiding capability and robust photonic functionalities.

physics.optics↗

arXiv2025

Circular Dichroism on the Edge of Quantum Hall Systems: From Many-Body Chern Number to Anisotropy Measurements

Quantum Hall states are characterized by a topological invariant, the many-body Chern number, which determines their quantized Hall conductivity. This invariant also emerges in circular dichroic responses, namely, by applying a circular drive and comparing excitation rates for opposite orientations. This work explores the dichroic response of confined, isolated quantum Hall systems, where bulk and edge contributions cancel exactly:~When the edge response is properly isolated, the circular dichroic signal becomes quantized, serving as a direct and elegant probe of the many-body Chern number encoded in the edge physics. We demonstrate that this quantized edge response is entirely captured by low-energy chiral edge modes, allowing for a universal description of this effect based on Wen's edge theory. Its low-energy nature implies that the quantized edge response can be distinguished from the bulk response in the frequency domain. The edge response is also shown to be a sensitive diagnostic of geometric features. This opens the possibility of characterizing the shape of quantum Hall droplets through edge spectroscopic measurements, without requiring knowledge of the system's boundary profile. We illustrate our findings using realistic models of integer and fractional Chern insulators, with different edge geometries, and propose detection schemes suitable for ultracold atoms.

cond-mat.quant-gas↗

arXiv2025

Non-periodic Boundary Conditions for Euler Class and Dynamical Signatures of Obstruction

While the landscape of free-fermion phases has drastically been expanded in the last decades, recently novel multi-gap topological phases were proposed where groups of bands can acquire new invariants such as Euler class. As in conventional single-gap topologies, obstruction plays an inherent role that so far has only been incidentally addressed. We here systematically investigate the nuances of the relation between the non-Bravais lattice configurations and the Brillouin zone boundary conditions (BZBCs) for any number of dimensions. Clarifying the nomenclature, we provide a general periodictization recipe to obtain a gauge with an almost Brillouin-zone-periodic Bloch Hamiltonian both generally and upon imposing a reality condition on Hamiltonians for Euler class. Focusing on three-band $\mathcal{C}_2$ symmetric Euler systems in two dimensions as a guiding example, we present a procedure to enumerate the possible lattice configurations, and thus the unique BZBCs possibilities. We establish a comprehensive classification for the identified BZBC patterns according to the parity constraints they impose on the Euler invariant, highlighting how it extends to more bands and higher dimensions. Moreover, by building upon previous work utilizing Hopf maps, we illustrate physical consequences of non-trivial BZBCs in the quench dynamics of non-Bravais lattice Euler systems, reflecting the parity of the Euler invariant. We numerically confirm our results and corresponding observable signatures, and discuss possible experimental implementations. Our work presents a general framework to study the role of non-trivial boundary conditions and obstructions on multi-gap topology that can be employed for arbitrary number bands or in higher dimensions.

cond-mat.quant-gas↗

arXiv2025

Optical manifestations and bounds of topological Euler class

We analyze quantum-geometric bounds on optical weights in topological phases with pairs of bands hosting nontrivial Euler class, a multigap invariant characterizing non-Abelian band topology. We show how the bounds constrain the combined optical weights of the Euler bands at different dopings and further restrict the size of the adjacent band gaps. In this process, we also consider the associated interband contributions to dc conductivities in the flat-band limit. We physically validate these results by recasting the bound in terms of transition rates associated with the optical absorption of light, and demonstrate how the Euler connections and curvatures can be determined through the use of momentum and frequency-resolved optical measurements, allowing for a direct measurement of this multiband invariant. Additionally, we prove that the bound holds beyond the degenerate limit of Euler bands, resulting in nodal topology captured by the patch Euler class. In this context, we deduce optical manifestations of Euler topology within $\vec{k} \cdot \vec{p}$ models, which include quantized optical conductivity, and third-order jerk photoconductivities. We showcase our findings with numerical validation in lattice-regularized models that benchmark effective theories for real materials and are realizable in metamaterials and optical lattices.

cond-mat.mes-hall↗

arXiv2024

Anomalous wave-packet transport on boundaries of Floquet topological systems

A two-dimensional periodically driven (Floquet) system with zero winding number in the absence of time-reversal symmetry is usually considered topologically trivial. Here, we study the dynamics of a Gaussian wave packet placed at the boundary of a two-dimensional driven system with zero winding numbers but multiple valley-protected edge states that can be realized in a square Raman lattice, and investigate the unidirectionally propagating topological edge currents. By carefully tuning the initial parameters of the wave packet including its spin polarization as well as the initial time of the periodic driving, we control the population of different edge states, where the speed of the resulting propagation establishes a direct correspondence with the target dispersions across different gaps and valleys. Interestingly, we find that the edge states at different valleys in the $π$ gap can hybridize and form bowtie-shaped edge bands fully detached from the bulk. This phase, not only presents a favorable regime with narrower bulk bands, but also exhibits distinct edge dynamics where the majority of particles bounce back-and-forth confined to a boundary while a small portion can follow a chiral transport around the sample.

cond-mat.quant-gas↗

arXiv2024

Anomalous multi-gap topological phases in periodically driven quantum rotors

We demonstrate that periodically driven quantum rotors provide a promising and broadly applicable platform to implement multi-gap topological phases, where groups of bands can acquire topological invariants due to non-Abelian braiding of band degeneracies. By adiabatically varying the periodic kicks to the rotor we find nodal-line braiding, which causes sign flips of topological charges of band nodes and can prevent them from annihilating, indicated by non-zero values of the %non-Abelian patch Euler class. In particular, we report on the emergence of an anomalous Dirac string phase arising in the strongly driven regime, a truly out-of-equilibrium phase of the quantum rotor. This phase emanates from braiding processes involving all (quasienergy) gaps and manifests itself with edge states at zero angular momentum. Our results reveal direct applications in state-of-the-art experiments of quantum rotors, such as linear molecules driven by periodic far-off-resonant laser pulses or artificial quantum rotors in optical lattices, whose extensive versatility offers precise modification and observation of novel non-Abelian topological properties.

quant-ph↗

arXiv2024

Non-Abelian Hopf-Euler insulators

We discuss a class of three-band non-Abelian topological insulators in three dimensions that carry a single bulk Hopf index protected by spatiotemporal ($\mathcal{PT}$) inversion symmetry. These phases may also host subdimensional topological invariants given by the Euler characteristic class, resulting in real Hopf-Euler insulators. Such systems naturally realize helical nodal structures in the three-dimensional Brillouin zone, providing a physical manifestation of the linking number described by the Hopf invariant. We show that, by opening a gap between the valence bands of these systems, one finds a fully-gapped ``flag'' phase, which displays a three-band multi-gap Pontryagin invariant. Unlike the previously reported $\mathcal{PT}$-symmetric four-band real Hopf insulator, which hosts a $\mathbb{Z} \oplus \mathbb{Z}$ invariant, these phases are not unitarily equivalent to two copies of a complex two-band Hopf insulator. We show that such uncharted phases can be obtained through dimensional extension of two-dimensional Euler insulators, and that they support (i) an optical bulk integrated circular shift effect quantized by the Hopf invariant, (ii) quantum-geometric breathing in the real space Wannier functions, and (iii) surface Euler topology on boundaries. Consequently, our findings pave the way for novel experimental realizations of real-space quantum-geometry, as these systems may be directly simulated by utilizing synthetic dimensions in metamaterials or ultracold atoms.

cond-mat.mes-hall↗

arXiv2024

Interferometry of non-Abelian band singularities and Euler class topology

In systems with a real Bloch Hamiltonian band nodes can be characterised by a non-Abelian frame-rotation charge. The ability of these band nodes to annihilate pairwise is path dependent, since by braiding nodes in adjacent gaps the sign of their charges can be changed. Here, we theoretically construct and numerically confirm two concrete methods to experimentally probe these non-Abelian braiding processes and charges in ultracold atomic systems. We consider a coherent superposition of two bands that can be created by moving atoms through the band singularities at some angle in momentum space. Analyzing the dependency of excitations on the frame charges, we demonstrate an interferometry scheme passing through two band nodes, which reveals the relative frame charges and allows for measuring the multi-gap topological invariant. The second method relies on a single wavepacket probing two nodes sequentially, where the frame charges can be determined from the band populations. Our results present a feasible avenue for measuring non-Abelian charges of band nodes and the direct experimental verification of braiding procedures, which can be applied in a variety of settings including the recently discovered anomalous non-Abelian phases arising under periodic driving.

cond-mat.quant-gas↗

arXiv2024

Comment on "Floquet non-Abelian topological insulator and multifold bulk-edge correspondence"

We comment on the recent paper ``Floquet non-Abelian topological insulator and multifold bulk-edge correspondence" by Tianyu Li and Haiping Hu, Nat. Comm. {\bf 14}, 6418 (2023). Apart from the fact that the authors unjustly imply to study multi-gap topology in Floquet systems for the first time, only known homotopic relations are presented. While such insights are used to present interesting Floquet phenomena and phases, which is an attractive result in itself, they cannot be used to deduce the total bulk characterization in the dynamical context without further proof. In fact, the authors essentially rephrase a Zak phase description. These results should in particular be contrasted to earlier results, arXiv:2208.12824, in which static-compatible Zak phases {\it and} dynamical Dirac strings were shown to be able to {\it distinguish} rather similar non-Abelian Floquet phases in $2+1$ dimensional systems. As a result, the claim of a sharp multifold bulk-edge correspondence cannot be concluded from the given arguments.

cond-mat.mes-hall↗

arXiv2023

Wave packet dynamics and edge transport in anomalous Floquet topological phases

The possibility of attaining chiral edge modes under periodic driving has spurred tremendous attention, both theoretically and experimentally, especially in light of anomalous Floquet topological phases that feature vanishing Chern numbers unlike any static counterpart. We here consider a periodically modulated honeycomb lattice and experimentally relevant driving protocols, which allows us to obtain edge modes of various character in a simple model. We calculate the phase diagram over a wide range of parameters and recover an anomalous topological phase with quasienergy gaps harbouring edge states with opposite chirality. Motivated by the advances in single-site control in optical lattices, we investigate wave packet dynamics localized at the edges in distinct Floquet topological regimes that cannot be achieved in equilibrium. We analyse transport properties in edge modes originating from the same bands, but with support at different quasienergies and sublattices as well as possessing different chiralities. We find that an anomalous Floquet topological phase can in general generate more robust chiral edge motion than a Haldane phase. Our results demonstrate that the rich interplay of wave packet dynamics and topological edge states can serve as a versatile tool in ultracold quantum gases in optical lattices.

cond-mat.quant-gas↗

arXiv2022

Experimental demonstration of topological bounds in quantum metrology

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of band structures can dictate strict lower bounds on metrological properties, hence establishing a strong connection between topology and quantum metrology. In this work, we provide a first experimental verification of such topological bounds, by performing optimal quantum multi-parameter estimation and achieving the best possible measurement precision. By emulating the band structure of a Chern insulator, we experimentally determine the metrological potential across a topological phase transition, and demonstrate strong enhancement in the topologically non-trivial regime. Our work opens the door to metrological applications empowered by topology, with potential implications for quantum many-body systems.

quant-ph↗

arXiv2022

Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase

Topological phases of matter span a wide area of research shaping fundamental pursuits and offering promise for future applications. While a significant fraction of topological materials has been characterized using symmetry requirements of wave functions, the past two years have witnessed the rise of novel multi-gap dependent topological states, the properties of which go beyond these approaches and are yet to be fully explored. Thriving upon these insights, we report on uncharted anomalous phases and properties that can only arise in out-of-equilibrium Floquet settings. In particular, we identify Floquet-induced non-Abelian braiding mechanisms, which in turn lead to a phase characterized by an anomalous Euler class, the prime example of a multi-gap topological invariant. Most strikingly, we also retrieve the first example of an `anomalous Dirac string phase'. This gapped out-of-equilibrium phase features an unconventional Dirac string configuration that physically manifests itself via anomalous edge states on the boundary. Our results therefore not only provide a stepping stone for the exploration of intrinsically dynamical and experimentally viable multi-gap topological phases, but also demonstrate a powerful way to observe these non-Abelian processes notably in quantum simulators.

cond-mat.mes-hall↗

arXiv2022

Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere

The geometric interpretation of (pseudo)spin 1/2 systems on the Bloch sphere has been appreciated across different areas ranging from condensed matter to quantum information and high energy physics. Although similar notions for larger Hilbert spaces are established in mathematics, they have been so far less explored beyond the two-level case for practical usage in condensed matter settings, or have involved restrictions to sub manifolds within the full Hilbert space. We here employ a coherence vector description to theoretically characterize a general N-level system on the higher dimensional generalized Bloch (hyper)sphere by respecting the structure of the underlying SU(N) algebra and construct physically intuitive geometric pictures for topological concepts. Focusing on two spatial dimensions, we reveal a geometric interpretation for the Chern number in larger Hilbert spaces in terms of a nested structure comprising N-1 two-spheres. We demonstrate that for the N-level case, there is an exterior two-sphere that provides a useful characterization of the system, notably by playing a primary role in determining the Chern number. The external sphere can be directly measured in ultracold atoms via well-established band mapping techniques, thereby imparting knowledge of the topological nature of state. We also investigate how the time evolution of the coherence vector defined on the generalized Bloch hypersphere can be utilized to extract the full state vector in experiments, allowing us to develop a tomography scheme involving quenches for three-level systems. Our geometric description opens up a new avenue for the interpretation of the topological classification and the dynamical illustration of multi-level systems, which in turn is anticipated to help in the design of new experimental probes.

cond-mat.quant-gas↗

arXiv2021

Robust and Ultrafast State Preparation by Ramping Artificial Gauge Potentials

The implementation of static artificial magnetic fields in ultracold atomic systems has become a powerful tool, e.g. for simulating quantum-Hall physics with charge-neutral atoms. Taking an interacting bosonic flux ladder as a minimal model, we investigate protocols for adiabatic state preparation via magnetic flux ramps. Considering the fact that it is actually the artificial vector potential (in the form of Peierls phases) that can be experimentally engineered in optical lattices, rather than the magnetic field, we find that the time required for adiabatic state preparation dramatically depends on which pattern of Peierls phases is used. This can be understood intuitively by noting that different patterns of time-dependent Peierls phases that all give rise to the same magnetic field ramp, generally lead to different artificial electric fields during the ramp. Remarkably, we find that an optimal choice allows for preparing the ground state almost instantaneously. We relate this observation to shortcuts to adiabaticity via counterdiabatic driving. Our findings open new possibilities for robust state preparation in atomic quantum simulators.

cond-mat.quant-gas↗

arXiv2020

Realization of an anomalous Floquet topological system with ultracold atoms

Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems. However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties of these driven settings. Most prominently, there exist two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers are equal to zero. Here, we realize such a system with bosonic atoms in a periodically-driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections.

cond-mat.quant-gas↗

arXiv2020

Topological Euler class as a dynamical observable in optical lattices

The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic invariant $(ξ)$ falls outside conventional symmetry-eigenvalue indicated phases and, in simplest incarnation, is described by triples of bands that comprise a gapless pair, featuring $2ξ$ stable band nodes, and a gapped band. These nodes host non-Abelian charges and can be further undone by converting their charge upon intricate braiding mechanisms, revealing that Euler class is a fragile topology. We theoretically demonstrate that quenching with non-trivial Euler Hamiltonian results in stable monopole-antimonopole pairs, which in turn induce a linking of momentum-time trajectories under the first Hopf map, making the invariant experimentally observable. Detailing explicit tomography protocols in a variety of cold-atom setups, our results provide a basis for exploring new topologies and their interplay with crystalline symmetries in optical lattices beyond paradigmatic Chern insulators.

cond-mat.quant-gas↗