We report on a universal topological dichroism of chiral three-dimensional systems in response to the chirality of light. We show that chiral topological invariants result in integer-quantized dichroic excitation rate differences. Moreover, we demonstrate that such topological effects arise more generally from coupling optical chirality to higher tensor Berry curvatures and Dixmier-Douady invariants of quantum states, including Hopf indices. We finally propose an experimental setup that leverages superchiral light as a smoking-gun probe of chiral band topologies in three-dimensional materials. Our findings establish an optical route for probing to date unobserved chiral electronic band topologies.
We report on a universal topological dichroism of chiral three-dimensional systems in response to the chirality of light. We show that chiral topological invariants result in integer-quantized dichroic excitation rate differences. Moreover, we demonstrate that such topological effects arise more generally from coupling optical chirality to higher tensor Berry curvatures and Dixmier-Douady invariants of quantum states, including Hopf indices. We finally propose an experimental setup that leverages superchiral light as a smoking-gun probe of chiral band topologies in three-dimensional materials. Our findings establish an optical route for probing to date unobserved chiral electronic band topologies.
We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional Z(2) topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states--the Dirac cones--can be probed through time-of-flight imaging or Bragg spectroscopy and the flat band can be detected via measurement of the atomic density profile in a weak global trap. The realization of this novel topological phase with a flat band in an optical lattice will provide a unique experimental platform to study the interplay between interaction and topology and open new avenues for application of topological states.
The detection of topological phases of matter has become a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or quantum transport signature of a real material, which may be imperfect or even absent. On the other hand, quantum simulation offers an alternative approach to directly measure the topological invariant on a universal quantum computer. However, experimentally demonstrating high-dimensional topological phases remains a challenge due to the technical limitations of current experimental platforms. Here, we investigate the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class, which yet lack experimental realization. Using the nuclear magnetic resonance system, we experimentally demonstrate their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed. As a result, the topological invariants are measured with high precision on the band-inversion surface, exhibiting robustness to the decoherence effect. Our Letter paves the way toward the quantum simulation of topological phases of matter in higher dimensions and more complex systems through controllable quantum phases transitions.
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete classification of topological phases remains elusive. In this context, experimental studies are key, both for studying the interplay between topology and complex effects and for identifying new forms of topological order. It is therefore crucial to find complementary means to measure topological properties in order to reach a fundamental understanding of topological phases. In one dimensional chiral systems, we suggest a new way to construct and identify topologically protected bound states, which are the smoking gun of these materials. In two dimensional Hofstadter strips (i.e: systems which are very short along one dimension), we suggest a new way to measure the topological invariant directly from the atomic dynamics.
Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this universal concept to non-Hermitian systems by defining topological chirality, an invariant that emerges whenever an exceptional-points (EP) pair is present. Built from the non-commutative fundamental group and its braid representation, topological chirality acts as a singularity selector: clockwise EP loops occupy a homotopy class that avoids EPs, whereas counter-clockwise mirrors are equivalent only if they cross the EPs themselves. We confirm this binary rule in an optical microcavity and a non-Hermitian topological band. The same two-sheeted topology governs EP pairs in spin systems, photonic crystals and hybrid light-matter structures, where EP encirclements have already been demonstrated, so the framework transfers without alteration and confirms its experimental viability. Our findings lay the cornerstone for interpreting loop-sensitive observables such as spectral vorticity, the complex Berry phase and the non-Abelian holonomy. Finally, a gluing-of-planes construction extends the invariant to an n-sheeted surface hosting 2m EPs, unifying higher-order EP pairs.
The topology of two-dimensional materials traditionally manifests itself through the quantization of the Hall conductance, which is revealed in transport measurements1,2,3. Recently, it was predicted that topology can also give rise to a characteristic spectroscopic response on subjecting a Chern insulator to a circular drive: comparing the frequency-integrated depletion rates associated with drives of opposite orientation leads to a quantized response dictated by the topological Chern number of the populated Bloch band4,5. Here we experimentally demonstrate this intriguing topological effect using ultracold fermionic atoms in topological Floquet bands. In addition, our depletion-rate measurements also provide an experimental estimation of the Wannier-spread functional, a fundamental geometric property of Bloch bands related to the quantum metric6,7. Our results establish topological spectroscopic responses as a versatile probe, which could be applied to access the geometry and topology of many-body quantum systems, such as fractional Chern insulators
Understanding the geometry of quantum Hall systems is a central challenge in modern condensed matter physics. We introduce a framework for probing the geometric structure of quantum Hall droplets by engineering the geometry of a dichroic probe and identifying the onset of "perfect elliptic dichroism", a regime in which the system responds exclusively to an elliptically polarized drive of a given chirality. This phenomenon provides a direct diagnostic of the droplet's intrinsic metric, and we show that it extends naturally to ideal Chern bands, where holomorphicity of the occupied states guarantees the vanishing of one chiral absorption rate with a quantized response for the other. In lattice realizations, such as the Harper-Hofstadter model, finite lattice-spacing corrections break the exact continuum metric description and give rise to a renormalized, emergent Landau-orbit metric; the probe ellipticity at which perfect dichroism is achieved then shifts accordingly, offering a direct spectroscopic window onto this lattice-induced geometric renormalization. Our results illuminate the rich geometric structure of quantum Hall phases and offer concrete pathways for observing these effects in quantum-engineered platforms.