arXiv subjects

Nigel R. Cooper

Publications and source records attributed to Nigel R. Cooper.

At least 19 recordsLinked to original sources

arXiv2026

Unravelling the Li-Haldane Conjecture with the Projected Ensemble

The entanglement spectra of fractional quantum Hall states contain universal fingerprints of their underlying topological order, as posited by the Li-Haldane conjecture. In this work, we uncover a finer universal structure within the entanglement spectra unravelled by projective measurements. Concretely, we study the projected ensemble of fractional quantum Hall states, defined as the collection of quantum states on a subsystem conditioned on measurement outcomes of its complement. We find that this ensemble exhibits a hidden hierarchy inside the Li-Haldane edge manifold: by conditioning on measurement outcomes, the entanglement spectrum's support is split into measurement-dependent sectors whose ranks we demonstrate are fixed by conformal field theory counting, an observation we dub the measurement-resolved Li-Haldane conjecture. For the non-Abelian Moore-Read state, this hierarchy is particularly rich: each parity-resolved edge manifold contains internal subspaces whose dimensions reproduce the conformal field theory counting of the opposite-parity sector. This structure persists even in realistic Coulomb-interacting ground states, establishing the projected ensemble as a sharp new probe of topological order beyond what the entanglement spectrum alone can detect.

cond-mat.mes-hall↗

arXiv2026

Local spectroscopy of anyons bound to charge traps

Fractional quantum Hall states host anyons, emergent quasiparticles with fractional charge and nontrivial exchange statistics. Controlling, trapping, and braiding anyons are central goals for both fundamental physics and topological quantum computation. A key step toward such control is understanding how anyons behave when confined in local potentials, where their internal structure can become relevant. Here, we use the scanning tunneling microscopy/spectroscopy (STM/STS) to study the excitation spectrum in integer and fractional quantum Hall states of monolayer graphene near individual charged impurities. In the integer quantum Hall states, the STS spectra show lifting of orbital degeneracy near defects, appearing as a band of discrete energy levels. In fractional states, (v=1/3 and 2/5), however, we observe an additional energy splitting of the lowest-energy spectral feature that occurs only when the chemical potential lies within a fractional gap and is absent in compressible or integer regimes. We attribute this to many-body configurations of anyons trapped by an impurity potential. Strikingly, numerical calculations show that the splitting requires an anisotropic confining potential, vanishing for a rotationally symmetric trap. The competing multi-anyon states carry nearly identical charge within the core of the potential but differ in how that charge is redistributed at larger radius. Our results establish local tunneling spectroscopy as a direct probe of anyon bound states, providing a key step toward understanding and controlling their behavior in confined geometries relevant for braiding and fusion.

cond-mat.mes-hall↗

arXiv2026

Observation of Vinen turbulence during far-from-equilibrium Bose-Einstein condensation

Relaxation of far-from-equilibrium quantum fluids, intimately related to the emergence of long-range order, is theoretically associated with the decay of a turbulent isotropic tangle of vortex lines. We observe and study such decaying quantum turbulence in a homogeneous 3D atomic Bose gas. Using matter-wave techniques to magnify the gas density distribution, and then imaging a thin slice of the magnified cloud, we observe imprints of randomly oriented vortex lines and measure the vortex line-length density $\mathcal{L}$. The observed decay of $\mathcal{L}$ agrees with the prediction for Vinen `ultraquantum' turbulence. Although our weakly interacting gases are highly compressible, their large-scale dynamics are consistent with the behavior of an incompressible hydrodynamic fluid, with the decay of $\mathcal{L}$ not depending on the strength of the interatomic interactions and being similar to that in the strongly interacting superfluid helium.

cond-mat.quant-gas↗

arXiv2026

Luttinger's Theorem Violation and Green's Function Topological Invariants in a Fractional Chern Insulator

Luttinger's theorem constrains the particle density of interacting fermions through global properties of the single-particle Green's function, and its violation signals a breakdown of the identification between the quantized Hall response and the Green-function-based Ishikawa-Matsuyama invariant. This phenomenon becomes especially compelling in strongly correlated topological phases, such as fractional Chern insulators, where fractionalized quasiparticles lack an adiabatic connection to electrons, raising the question of how Green's-function-based topological invariants manifest in such phases. Using exact diagonalization of the fermionic Harper-Hofstadter-Hubbard model, we compute bulk single-particle Green's functions deep inside a fractional Chern insulating phase and directly evaluate the Luttinger count, its possible correction (the Luttinger integral), and the Ishikawa-Matsuyama invariant $N_3[\mathrm{G}]$. We demonstrate a clear violation of Luttinger's theorem and show that the fractional nature of the many-body Chern number is encoded in the St\v{r}eda response of the Luttinger integral, while the integer invariant $N_3[\mathrm{G}]$ arises from the St\v{r}eda response of the Luttinger count. We also analytically prove that $N_3[\mathrm{G}]$ is fully determined by the Luttinger count together with the Chern number of the occupied Bloch band, upon neglecting Bloch-band mixing. Finally, we propose an experimental protocol to extract all Green-function-based topological invariants from local density-of-states measurements, experimentally accessible in fractional quantum Hall systems.

cond-mat.str-el↗

arXiv2026

Strong Correlations in the Dynamical Evolution of Lowest Landau Level Bosons

Recent experiments with rotating Bose gases have demonstrated the interaction-driven hydrodynamic instability of an initial extended strip-like state in the lowest Landau level. We investigate this phenomenon in the low density limit, where the mean-field Gross--Pitaevskii theory becomes inadequate, using exact diagonalisation studies and analytic arguments. We show that the behaviour can be understood in terms of weakly-interacting repulsively-bound few-body clusters. Signatures of cluster behaviour are observed in the expectation values of observables which oscillate at frequencies characterised by the energies of few-body boundstates. Using a semiclassical theory for interacting clusters, we predict the long-time growth of the cloud width to be a power law in the logarithm of time. This slow thermalisation of bound clusters represents a form of quantum many-body scars.

cond-mat.quant-gas↗

arXiv2025

Characterizing topology at nonzero temperature: Topological invariants and indicators in the extended SSH model

We compare three complementary diagnostics for mixed Gaussian states at nonzero temperature, focusing on the Su-Schrieffer-Heeger (SSH) chain and its inversion-symmetric extension. Whilst the ensemble geometric phase, a mixed-state generalization of the Zak phase, remains well defined at nonzero temperature, the modulus of the corresponding expectation value vanishes in the thermodynamic limit, limiting its practical use. To develop diagnostics suitable for large systems, we introduce local twist operators acting on neighboring sites, whose expectation values provide local indicators of the underlying topological phase. The topological phase is identified from the relative magnitude of these expectation values, which only requires measuring two local expectation values at nonzero temperature, together with one additional nonlocal expectation value when next-nearest-neighbor hopping is included. In addition, we generalize the local chiral marker to mixed Gaussian states, fully determined by its single-particle correlation matrix, with a nonzero purity gap in their effective single-particle Hamiltonian. The presence of a purity gap ensures that the correlation matrix can be flattened to an effective projector. Evaluating the chiral marker with respect to the band-flattened correlation matrix yields a real-space topological invariant that coincides with the winding number in the zero-temperature limit. The ensemble geometric phase, the local twist operators, and the local chiral marker provide complementary methods to characterize topology in the SSH chain beyond pure states.

cond-mat.mes-hall↗

arXiv2025

Ideal Optical Flux Lattices

The realization of fractional quantum Hall (FQH) states in cold atomic gases is a long-standing goal in quantum simulation. Established approaches, including rapidly rotating gases and tight-binding lattices, are often hampered by low interaction energies and small many-body energy gaps. While optical flux lattices (OFLs) can achieve higher effective magnetic flux densities, standard two-state configurations generate highly non-uniform fields, and extensions to multi-state systems introduce significant experimental complexity. Here, we present a new paradigm for engineering robust FQH phases in OFLs using only two internal atomic states. We show that the introduction of an additional scalar potential provides a generic mechanism for creating Chern bands that are simultaneously essentially flat and "ideal". These desirable properties arise by tuning lattice parameters to certain $N$-flat manifolds $(N=1,2,\dots)$, where the $1$-flat manifold shares its origin with certain "magic-angle" conditions familiar from moir\'e materials. A central result is the design of a dark-state OFL whose adiabatic Hamiltonian is exactly of Aharonov-Casher (AC) form. This exact AC equivalence guarantees perfectly flat, exactly vortexable Chern bands in the adiabatic limit. This method allows for precise tuning of band flatness and stabilizes both Abelian and non-Abelian FQH phases. Our scheme is compatible with existing experimental capabilities using vector polarizability, opening practical routes to exploring strongly correlated topological physics with cold atoms.

cond-mat.quant-gas↗

arXiv2025

Gapless Edge Gravitons and Quasiparticles in Fractional Quantum Hall Systems with Non-Local Confinement

One of the central tenets of the theory of the fractional quantum Hall effect is that the bulk quantized Hall response requires the existence of a gapless chiral edge mode. The field theoretical arguments for this rely on locality. While locality is typically met in standard experimental settings, it need not always apply. Motivated by experimental capabilities of photonic platforms, we study confining potentials that are step-like in angular momentum, and thus non-local in position. We show that this non-local potential does not host conventional chiral edge modes. These are replaced by gapless spin-2 edge states, which we show are connected to the collective 'graviton' excitations that are gapped in the bulk. Furthermore, we show that FQH states host gapless (charged) quasiparticles on their edges, even in the absence of conventional edge modes. The edge state energies vanish as a power-law in system size, with an exponent that characterises the bulk topological order.

cond-mat.mes-hall↗

arXiv2025

Perfect State Transfer of Mixed States and Purification in Central Spin Systems

We show how two many-body, generally mixed, quantum states can be swapped via collective, all-to-all interactions. Specifically, we present an experimentally relevant implementation for quantum dots that enables coherent exchange of quantum information between different species of nuclear spins, effectively achieving a perfect swap gate for qudits formed from these different species. This process also serves as a tool for nuclear spin purification. The results are obtained by mapping the problem onto perfect state transfer on a 1D chain. In the partially polarized limit, we demonstrate that the states can be exchanged independently of the initial state. We also assess the robustness of the procedure to decoherence and errors.

quant-ph↗

arXiv2024

Absorbing state phase transitions beyond directed percolation in dissipative quantum state preparation

We show that absorbing state phase transitions where the absorbing state itself exhibits long-range phase coherence can lead to critical behavior distinct from directed percolation. To do this, we investigate a simple, purely dissipative quantum reaction-diffusion model, which may also be viewed as a dissipative quantum state preparation procedure for the (generalized) W state with errors. The "error" Lindblad jump operators preserve the W state as a dark state, but nonetheless act to decohere the system and induce the phase transition. We find cases where the preparation protocol is either fragile or robust against weak error quantum jump rates and show that local remnants of the coherence persist in the decohering phase. The distinct critical behavior stems from the spreading of coherence throughout the system at the critical point.

quant-ph↗

arXiv2024

Correlations of the Current Density in Many-Body Landau Level States

Motivated by recent advances in quantum gas microscopy, we investigate correlation functions of the current density in many-body Landau Level states, such as the Laughlin state of the fractional quantum Hall effect. For states fully in the lowest Landau level, we present an exact relationship which shows that all correlation functions involving the current density are directly related to correlation functions of the number density. We calculate perturbative corrections to this relationship arising from inter-particle interactions, and show that this provides a method by which to extract the system's interaction energy. Finally, we demonstrate the applicability of our results also to lattice systems.

cond-mat.mes-hall↗

arXiv2024

How Subradiance Enables Nonlinearity in Weakly Driven Quantum Arrays

Harnessing the nonlinear response of a medium is essential for applications including frequency conversion and light amplification, as well as for the generation of quantum many-body correlations of light or matter. However, achieving these effects typically requires high drive intensities and thick samples, which induce undesired heating effects that typically suppress quantum correlations. In this work, we demonstrate that atom-thin arrays of quantum emitters exhibit a robust nonlinear response even at arbitrarily weak drive intensities. This discovery challenges the long-held assumption that weakly driven ensembles behave classically; instead, we reveal that subradiant states provide a dominant nonlinear contribution that persists in the low-intensity limit. Using a Dynamical Mean-Field Theory (DMFT) approach, we predict that these nonlinearities generate a quantum-correlated steady state composed of interacting pairs of subradiant excitations, characterized by long-range correlations and multi-mode squeezing. Our findings establish a new frontier for nonlinear quantum optics at minimal power, and provide a scalable protocol for preparing multimode squeezing, offering potential for applications in quantum metrology.

cond-mat.quant-gas↗

arXiv2024

Fate of the Mollow triplet in strongly-coupled atomic arrays

Subwavelength arrays of quantum two-level emitters have emerged as an interesting platform displaying prominent collective effects that can be harnessed for applications. Here we study such arrays under strong coherent driving, realizing an open quantum many-body problem in a strongly non-linear regime. For this we introduce a novel approach to this problem in terms of a Dynamical Mean Field Theory (DMFT), paving the way for further studies. We show that the spectrum of scattered light, characterized by the famous Mollow triplet for a single atom, develops a characteristic lineshape with flat sidebands determined by dipolar interactions and relevant for experiments. Remarkably, this is to some extent independent of the specific geometry, but is sensitive to the ordered arrangement of the atoms. This lineshape therefore characterizes atomic arrays and distinguishes them from disordered ensembles and non-interacting emitters.

cond-mat.quant-gas↗

arXiv2023

Fluctuation-dominated quantum oscillations in excitonic insulators

The realization of excitonic insulators in transition metal dichalcogenide systems has opened the door to explorations of the exotic properties such a state exhibits. We study theoretically the potential for excitonic insulators to show an anomalous form of quantum oscillations: the de Haas-van Alphen effect in an insulating system. We focus on the role of the interactions that generate the energy gap and show that it is crucial to consider quantum fluctuations that go beyond the mean field treatment. Remarkably, quantum fluctuations can be dominant, and lead to quantum oscillations than are significantly larger than those predicted using mean field theory. Indeed, in experimentally accessible parameter regimes these fluctuation-generated quantum oscillations can even be larger than what would be found for the corresponding gapless system.

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↗

arXiv2022

Leaky exciton condensates in transition metal dichalcogenide moiré bilayers

We show that the "dark condensates" that arise when excitons form a Bose-Einstein condensate in a material with an indirect bandgap are not completely dark to optical emission. Rather, such states are "leaky condensates" in which optical emission is facilitated by many-body interactions. We analyze the properties of these leaky condensates in the context of twisted bilayers of transition metal dichalcogenides, which host strongly interacting excitons and an indirect bandgap. We show that this interaction-driven "leaky" emission dominates photoluminescence at low temperatures, with distinctive qualitative features. Finally, we propose that in these materials, unique intervalley physics can lead to crystal symmetry-breaking excitonic ordering, with implications for optical processes.

cond-mat.mes-hall↗

arXiv2022

Kramers' degeneracy for open systems in thermal equilibrium

Kramers' degeneracy theorem underpins many interesting effects in quantum systems with time-reversal symmetry. We show that the generator of dynamics for Markovian open fermionic systems can exhibit an analogous degeneracy, protected by a combination of time-reversal symmetry and the microreversibility (detailed balance) property of systems at thermal equilibrium -- the degeneracy is lifted if either condition is not met. We provide simple examples of this phenomenon and show that the degeneracy is reflected in the single-particle Green's functions. Furthermore, we show that certain experimental signatures of topological edge modes in open many-body systems can be protected by microreversibility in the same way. Our results highlight the importance of detailed balance in characterizing open topological matter.

cond-mat.mes-hall↗

arXiv2022

Experimental realization of a fermionic spin-momentum lattice

We experimentally realize a spin-momentum lattice with a homogeneously trapped Fermi gas. The lattice is created via cyclically-rotated atom-laser couplings between three bare atomic spin states, and are such that they form a triangular lattice in a synthetic spin-momentum space. We demonstrate the lattice and explore its dynamics with spin- and momentum-resolved absorption imaging. This platform will provide new opportunities for synthetic spin systems and the engineering of topological bands. In particular, the use of three spin states in two spatial dimensions would allow the simulation of synthetic magnetic fields of high spatial uniformity, which would lead to ultra-narrow Chern bands that support robust fractional quantum Hall states.

cond-mat.quant-gas↗