Hall viscosity characterizes the geometric response of a quantum Hall droplet to deformations of the underlying metric, yet it has remained difficult to measure directly. We propose a spectroscopic probe based on circular dichroism, using chiral metric-sensitive drives – implemented as rotating quadrupolar ("saddle") perturbations – that effectively modulate the metric and couple to the generators of area-preserving deformations. The resulting dichroic signal directly measures the Hall viscosity, while frequency-resolved spectroscopy disentangles it from other excitations. A local formulation further enables spatially resolved markers of Hall viscosity applicable to both continuum and lattice systems. Our results open a direct route to measuring Hall viscosity in quantum-engineered platforms such as cold atoms in optical lattices.

Periodically driven quantum systems offer remarkable flexibility in tailoring effective Hamiltonians and synthetic band structures. However, such driving also induces heating and dynamical instabilities that limit the coherence and lifetime of many-body states. Here, we demonstrate that these instabilities can be suppressed by employing multi-tone driving schemes. Using a Bose-Einstein condensate of cesium atoms in an optical lattice, we experimentally explore two approaches: pulsed driving composed of odd harmonics and two-tone driving with tunable amplitude and relative phase. We show that both methods allow independent control of the effective tunneling amplitude and Peierls phase factor, while significantly reducing phonon excitation and the resulting rapid decay of the condensate. Numerical simulations and theoretical modeling based on Bogoliubov-de Gennes equations confirm the suppression of unstable modes under optimized driving conditions. Our results establish multifrequency drives as powerful tools for stabilizing driven many-body systems and pave the way toward robust Floquet engineering with interactions.

The interplay between interactions and quantum geometry can drive weakly dispersive bosons into different exotic many-body phases. In this work we study a quasi flat-band model in one dimension that exhibits an extended pair-superfluid phase in the all-flat-band limit. Introducing single-particle hopping leads to an intriguing competition with a more conventional single-particle superfluid: we find that the pair superfluid remains stable for a finite range of the hopping strength until the system eventually transitions into the conventional superfluid phase. In our study, we make use of a variational Gaussian state approach that provides a unified description of the single-particle and pair superfluid phases, regarding both the ground state wavefunction and the collective excitation spectrum. In particular, we derive a general relation between the speed of sound and a “quantum geometric kernel”, thereby extending earlier connections to the quantum metric, which relied on single-particle mean-field theory. This approach is combined with insights from the two-boson problem and exact diagonalization to map out the full phase diagram of the model. Our results show that the Gaussian approach is a versatile tool for studying a broad range of superfluid phases of interacting bosons in multi-orbital lattices.

At high frequency, a periodically driven quantum spin-1/2 system can emulate a chiral spin liquid (CSL) described by an effective static local chiral Hamiltonian. In contrast, at low frequency these settings realize "Swap" models exhibiting anomalous CSL phases, in which one-way spin transport occurs at the edge although the bulk time-evolution operator over one period is trivial. In this work, we explicitly construct a family of Floquet quantum spin-1/2 models on the square lattice implementing Swap models to investigate the stability of the anomalous CSL under frequency detuning and the transition to the high-frequency regime. We used the average-energy spectrum on finite-size tori and cylinders to unfold the Floquet quasienergy spectrum over the whole frequency range and obtain the geometrical Berry phases. This enabled us to identify three regimes upon increasing detuning: (i) a finite-size regime (with no folding of the Floquet spectrum), (ii) an intermediate (narrow) regime with folding and very few resonances, and (iii) a regime with an increased density of resonances suggesting heating. At small detuning, edge modes are revealed by spectroscopic tools and from the Streda response of the system, giving access to the anomalous winding number. The analysis of all the data suggests that the anomalous CSL is not continuously connected to the high-frequency CSL. We also discuss the possible occurrence of a long-lived prethermal anomalous CSL.

Mobile impurities provide a powerful means of probing correlated and topological quantum matter, through their dressing by the surrounding medium and the practical probes granting access to the resulting composite object. Motivated by the recent observation of anyon-impurity composites in the solid state, as well as recent realizations of Laughlin-type states in engineered lattice systems, we investigate the formation of a bound state between a mobile impurity and a single pinned quasihole in the interacting Harper-Hofstadter model deep in the fractional Chern insulator regime. Combining analytical arguments with large-scale numerical simulations, we characterize the structure, energetics, and stability of hybrid anyon-impurity bound states, and show that their binding energy provides direct access to the fractional charge of the quasihole under conditions that we identify. We further demonstrate that the composite object can be coherently transported by externally steering the quasihole pinning potential. Our results establish a realistic pathway for controlled anyon-impurity manipulation in quantum-engineered platforms, enabling experimentally feasible protocols for braiding.

We investigate the emergence of many-body dynamical localization (MBDL) in the Fock space of an interacting two-mode bosonic system subject to periodic driving. Using a mapping to the paradigmatic kicked-top model, we analyze the interplay between classical chaotic diffusion and quantum interference effects. While the mean-field (classical) dynamics exhibits bounded ergodic diffusion along the population imbalance axis, the quantum dynamics reveals strong suppression of transport in Fock space, in close analogy with Anderson localization in disordered lattices. We characterize the localization length, its scaling with particle number and driving parameters, and reveal the spectral crossover from random-matrix to Poisson statistics as the many-body ensemble localizes. We highlight the connection between MBDL and discrete time crystals. Our findings offer a promising avenue to study the Anderson transition in Fock space.

This work investigates the coexistence of distinct topologically ordered phases within a single setup. We demonstrate this concept through tensor network simulations of the Hofstadter-Bose-Hubbard model under a spatially modulated chemical potential. Focusing on cylindrical geometries, we realize regions exhibiting the Laughlin-1/2 phase and its particle-hole conjugate, and confirm their topological character via the local Streda's response and Laughlin's flux insertion protocol. Our approach offers a pathway for experimentally and numerically charting entire phase diagrams within a single system, possibly eliminating the need for independent parameter scans.

The exponential growth of many-body Hilbert space presents a fundamental barrier to quantum technology, obscuring the search for physically significant states within an astronomically vast landscape. Consequently, resources for quantum-enhanced metrology have been largely confined to the symmetric subspace whose dimensionality scales only polynomially with the particle number-leaving the vast majority of the Hilbert space largely unexplored and poorly understood. Here we challenge this paradigm by demonstrating that metrological advantage can arise as a ubiquitous feature across exponential-dimensional manifolds. By tailoring the first-moment structure of random unitaries, we uncover dense manifolds of engineered random states (ERSs) where Heisenberg-limited scaling emerges as a statistically generic property. This ubiquity endows these resource states with inherent resilience against parameter disorder. We experimentally validate this framework on a trapped-ion processor, achieving a metrological enhancement of 6.98 ± 0.38 dB beyond the standard quantum limit. Potential applications extend to diverse platforms, ranging from superconducting circuits and waveguide QED to solid-state spins and polar molecules. Our results establish a powerful paradigm where quantum-enhanced precision can be harvested from the exponential vastness of the Hilbert space.

We study thermal transport along the edge of a small chiral spin liquid device coupled to two Ising-chain reservoirs, a platform suitable for quantum-engineered systems. Adiabatically switching on the tunnel couplings to the reservoirs generates a thermal current that dynamically builds up and reaches a quasi-steady-state regime. In this experimentally critical time window, the two-terminal thermal conductance can approach half-quantized values—a hallmark of Majorana-mediated transport—under finely tuned conditions. The results agree with an effective Landauer-Büttiker description in the large-reservoir limit, where energy-resolved transmission rates help identify the optimal parameters to achieve the half-quantized conductance. This work provides a controllable platform to investigate topological thermal transport in engineered spin systems, such as realized in cold-atom and Rydberg-atom settings.

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.

Quantum many-body scars are rare nonthermal states embedded within otherwise thermalizing spectra, making them promising candidates for storing and manipulating quantum information. However, a general framework that can both identify such states without prior knowledge of their microscopic scarring mechanism and determine when they enable a quantum error correcting code has remained elusive. Here, we develop an end-to-end framework connecting nonthermal-state discovery to certifiable quantum error correction using a many-body spectral localizer. By searching for states jointly localized in energy and a diagnostic observable in systems with a many-body grading symmetry, the spectral localizer identifies candidate scars within dense many-body spectra in tandem with a topological index whose shifts determine their graded subspace. For suitable pairs of same-graded scars, the grading renders grading-odd errors exactly detectable, while their localization can suppress the logical action of sufficiently local grading-even error products, yielding an approximate Knill–Laflamme condition and an operator-algebra quantum error-correction structure. We demonstrate the scar-identification framework in one- and two-dimensional density-difference-dependent bosonic models and in the PXP model, and explicitly construct the resulting approximate quantum code in the one-dimensional bosonic system. Our results establish a systematic route from identifying nonthermal many-body states to exploiting them for protecting quantum information, and position pseudospectral methods as a broadly applicable tool for discovering useful behaviors in interacting quantum systems.

Fluxonium superconducting circuits were originally proposed to realize highly coherent qubits. In this work, we explore how these circuits can be used to implement and harness qutrits, by tuning their energy levels and matrix elements via an external flux bias. In particular, we investigate the distinctive features of arrays of fluxonium qutrits, and their potential for the quantum simulation of exotic quantum matter. We identify four different operational regimes, classified according to the plasmon-like versus fluxon-like nature of the qutrit excitations. Highly tunable on-site interactions are complemented by correlated single-particle hopping, pair hopping and non-local interactions, which naturally emerge and have different weights in the four regimes. Dispersive corrections and decoherence are also analyzed. We investigate the rich ground-state phase diagram of qutrit arrays and propose practical dynamical experiments to probe the different regimes. Altogether, fluxonium qutrit arrays emerge as a versatile and experimentally accessible platform to explore strongly correlated bosonic matter beyond the Bose-Hubbard paradigm, and with a potential toward simulating lattice gauge theories and non-Abelian topological states.

Topologically ordered quantum systems give rise to anyonic quasiparticles, whose controlled braiding operations form the foundation of topological quantum computation. Traditionally, studies of anyons have relied on edge-state interferometry, leaving the direct detection and manipulation of anyons in the bulk a major experimental challenge. Here, we propose and theoretically investigate a pathway toward this goal by demonstrating that a long-lived, optically generated interlayer exciton can bind to a quasihole in a fractional quantum Hall state, forming a novel composite excitation: the anyon-trion. Using exact diagonalization techniques, we reveal that anyon-trions exhibit millielectronvolt-scale binding energies and a linear dependence on the fractional charge of the quasihole. This scaling offers a powerful means to optically extract the quasihole’s fractional charge through measurable shifts in exciton resonances. We outline a feasible experimental implementation via photoluminescence spectroscopy in a quantum twisting microscope setup, providing a promising route for the direct optical observation of anyon-trions within the bulk.

We introduce a unified framework that relates orbital and heat magnetizations to experimentally accessible excitation spectra, through thermoelectric probes and generalized sum rules. By analyzing zero-temperature transport coefficients and applying Kramers-Kronig relations, we derive spectral representations of magnetization densities from thermoelectric correlation functions. Excitation rates under chiral thermoelectric drives then naturally emerge as direct probes of these Kubo-type correlators, placing orbital and heat magnetizations on equal footing with the topological Chern number. As a direct consequence of our formalism, we introduce a hierarchical construction that organizes orbital and heat magnetizations into distinct physical contributions accessible through sum rules, and also naturally obtain real-space markers of these magnetizations. Besides, nonchiral thermal probes identify a heat quantum metric, which is defined over the space of gravitomagnetic deformations. From an experimental standpoint, we propose concrete implementations of thermoelectric dichroic measurements in quantum-engineered platforms based on modulated strain fields. These results establish thermoelectric dichroic measurements as a versatile route to access and disentangle fundamental ground-state properties.

One-dimensional strongly repulsive quantum mixtures exhibit non-trivial exchange statistics arising from the interplay between orbital and spin degrees of freedom. Using an exact solution, we demonstrate that in the single-impurity limit the wavefunction of Fermi-Fermi and Bose-Bose mixtures on a ring threaded by an artificial gauge field display exact anyonic statistics under exchange of the impurity with the majority particles. The resulting fractional exchange phase is fixed by the angular momentum sector selected through the applied flux. We find that the impurity momentum distribution coincide exactly with the anyonic one, independently of the bosonic or fermionic nature of the mixture, with the large-momentum tails encoding a direct signature of the anyonic statistical angle. Finally, we devise a quench protocol for reversible dynamical anyonization. Our results provide a path for realizing and manipulating anyonized states with ultracold atoms.

Topological states of matter, such as quantum Hall states, are characterized by the absence of local order parameters. In the continuum, their topological order has been reinterpreted as the condensation of nonlocal composite bosons, but this condensation and the resulting long-range correlations have so far eluded direct confirmation beyond the simplest trial states. Here, we apply tensor-network methods to lattice Hamiltonians hosting quantum Hall states, revealing this exotic order directly in interacting ground states and demonstrating both the long-range correlations and the condensation of composite bosons. These correlations define a nonlocal order parameter that identifies phase transitions between trivial and topological phases, for both bosonic and fermionic models. The corresponding operators are accessible through site-resolved, local measurements on an extensive number of particles, making them directly probable in quantum simulators. Our work opens new avenues for microscopic studies of topological quantum matter beyond the reach of traditional solid-state approaches.

The coherent control and braiding of anyons remain central challenges in realizing topologically protected quantum operations. We propose a Ramsey interferometry protocol to directly access the geometric phases associated with anyons in fractional Chern insulators. Our approach employs impurities with individually addressable internal states that bind to the anyons, allowing their adiabatic motion and exchange under full spatial control. By combining Ramsey and spin-echo sequences using one and two impurities, the protocol gives independent access to the Aharonov-Bohm and exchange contributions to the total geometric phase, thereby providing an unambiguous probe of anyonic statistics. Our scheme can potentially be implemented in cold-atom quantum simulators as well as in van der Waals heterostructures. Complementary finite-size simulations in noninteracting Chern insulators quantify the system sizes required to faithfully extract geometric phases, highlighting the role of edge effects. Our results establish impurity-based interferometry as a feasible route toward direct anyon braiding experiments in quantum simulators and lay the groundwork for future explorations of non-Abelian braiding and topological quantum control.

The Středa formula links the Hall conductivity of an insulator to the magnetic-field response of its particle density, providing a local and universal probe of the topological Chern number. Beyond this quantized response, an energy-resolved Středa marker can be defined from the magnetic response of the density of states, revealing detailed features of the quantum geometry of Bloch bands. We show that driven-dissipative bosonic lattices provide direct access to both the integrated and energy-resolved Středa responses. Our scheme uses controlled pumping with uniform strength and random phases across the lattice, together with uniform loss, to yield a Lorentzian filter of eigenmode occupations. For generic dispersive bands, this enables reconstruction of a coarse-grained energy-resolved Středa response, establishing these platforms as versatile probes of anomalous spectral flow and energy-resolved quantum geometry. As a striking application, we show that this marker elucidates the fate of topological bands under strong disorder, capturing the quantum-geometric structure underlying topological Anderson insulators.

Quantized bulk response functions are hallmark signatures of topological phases, but their manifestation in periodically driven (Floquet) systems is not yet fully established. Here, we show that two-dimensional anomalous Floquet systems exhibit a quantized bulk response encoded in a Chern-Simons axion (CSA) coupling angle θ_{CS}^{F}∈2πZ, reflecting a topological magnetoelectric effect analogous to that in three-dimensional insulators. The periodic drive introduces an emergent "photon" dimension, allowing the system to be viewed as a three-dimensional Sambe lattice. Within this framework, quantized cross-correlated responses-namely, photon-space polarization and magnetization density-emerge as physical signatures of the CSA coupling. The CSA angle, constructed from the non-Abelian Berry connection of Floquet states, admits a natural interpretation in terms of the geometry of hybrid Wannier states. These results provide a unified framework linking Floquet band topology to quantized bulk observables, demystifying the topology of gapped 2D anomalous Floquet systems by establishing their connection to static 3D topological systems.

Synthetic dimensions are a powerful tool for engineering desired quantum systems, based on coupling together sets of states and reinterpreting these as lattice sites along an artificial dimension. Recently, a synthetic dimension of harmonic trap states has been successfully implemented in an ultracold atom experiment, opening the way for future realizations in this platform of topological lattice models, such as hybrid Harper-Hofstadter (HH) systems, which have one real and one synthetic dimension. However, unlike conventional systems, inter-particle interactions along a synthetic dimension of harmonic trap states are inhomogeneous, long-ranged and non-state-preserving. Therefore, this setup provides a natural platform for the exploration of the interplay between long range interactions (including correlated pair tunneling) and magnetic effects. In this paper, we set out to numerically study the effect of such interactions on both a hybrid two-legged HH ladder and a 2D HH model. In the former, we find variants of vortex and Meissner phases familiar from conventional models, while in the latter, we observe the emergence, in small finite systems, of unusual ground states, including a “Meissner stripe" state, which combines counter-propagating Meissner-like currents with strong density variations. This opens up interesting questions, including about the nature of strongly-correlated states that would emerge in such a platform.