Strongly dipolar gases, such as dysprosium, erbium and thulium, exhibit dense Feshbach spectra whose level statistics have been associated with quantum chaos arising from couplings among many molecular channels. Here, we combine a precise calibration of the Feshbach spectrum of ^162Dy with spectroscopic measurements of the differential magnetic moments of bound states associated with more than 80 resonances between 0 and 30 G. These magnetic moments provide an eigenstate-sensitive probe of the molecular states underlying the resonance spectrum. We find that the level statistics are not uniform: resonances associated with states near the center of the magnetic-moment distribution display enhanced level repulsion, whereas those near the lower edge remain close to Poisson statistics. Our results reveal hidden structure within the chaotic dysprosium Feshbach spectrum and identify molecular-state composition as a key ingredient in the emergence of quantum chaos in strongly dipolar scattering.

Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which enforces a half-quantized Hall response. Anomaly inflow mechanism allows this effect to be observed at the surfaces of three-dimensional topological insulators, however, its realization in a genuinely two-dimensional system has remained elusive. Here we report the observation of a parity-anomalous Hall response at the critical point of a quantum Hall topological phase transition in a synthetic two-dimensional system of ultracold dysprosium atoms. By coupling a continuous spatial dimension to a finite synthetic dimension encoded in atomic spin states, we engineer tunable Chern bands with C = 0 and 1. At the transition, the bulk gap closes at a single Dirac point, where we observe a robust half-quantized Hall drift despite strong non-adiabatic excitations. We show that this response originates from the global structure of the band topology, is protected by an emergent parity symmetry at criticality, and disappears when parity is explicitly broken. Our work establishes synthetic quantum systems as a powerful platform to probe quantum anomalies and their interplay with topology and non-equilibrium dynamics.

We investigate the real-time buildup of short-range correlations in a nondegenerate ultracold Bose gas near a narrow Fano-Feshbach resonance. Using rapid optical control, we quench the closed-channel molecular energy to resonance on sub-microsecond timescales and track the evolution of the two-body contact through photo-dissociation losses. Repeated pulse sequences enhance sensitivity to early-time two-body losses and reveal long-lived coherence between atom pairs and molecular states. The observed dynamics are accurately reproduced by our dynamical two-channel zero-range theory, which explicitly accounts for the resonance's narrow width and finite closed-channel decay, establishing a predictive framework for correlation dynamics in quantum gases near Fano-Feshbach resonances.

Open-shell lanthanide atoms, and dysprosium in particular, combine a large ground-state angular momentum with dense electronic spectra, making their dynamical polarizability strongly dependent on wavelength and internal state and therefore particularly challenging to characterize accurately. This issue has become especially relevant with the recent development of single-atom trapping of dysprosium in optical-tweezer arrays, where precise knowledge of the polarizability is needed to design optimized trapping architectures. Here, we exploit the strong spin-dependent light shift near the J'=J-1 intercombination line at 530.306 nm to determine the background scalar and vector polarizabilities of ^162Dy in its ground state near this wavelength. Our measurements quantitatively agree with atomic-structure calculations and provide new insight into the contributions of nearby transitions in a spectral region relevant to emerging dysprosium tweezer platforms.

Mixtures of ultracold gases with long-range interactions are expected to open new avenues in the study of quantum matter. Natural candidates for this research are spin mixtures of atomic species with large magnetic moments. However, the lifetime of such assemblies can be strongly affected by the dipolar relaxation that occurs in spin-flip collisions. Here we present experimental results for a mixture composed of the two lowest Zeeman states of ^162Dy atoms, that act as dark states with respect to a light-induced quadratic Zeeman effect. We show that, due to an interference phenomenon, the rate for such inelastic processes is dramatically reduced with respect to the Wigner threshold law. Additionally, we determine the scattering lengths characterizing the s-wave interaction between these states, providing all necessary data to predict the miscibility range of the mixture, depending on its dimensionality.

Dipolar gases like erbium and dysprosium have a dense spectrum of resonant loss features associated with their strong anisotropic interaction potential. These resonances display various behaviours with density and temperature, implying diverse microscopic properties. Here, we quantitatively investigate the low-field ($B < 6\,\text{G}$) loss features in ultracold thermal samples of $^{162}$Dy, revealing two- and three-body dominated loss processes. We investigate their temperature dependence and detect a feature compatible with a $d$-wave Fano-Feshbach resonance, which has not been observed before. We also analyse the expansion of the dipolar Bose-Einstein condensate as a function of the magnetic field and interpret the changes in size close to the resonances with a variation in the scattering length.

Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted in dimensions D > 3. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms. We measure the nontrivial topological index of the ground band through a full characterization of the nonlinear electromagnetic response and observe the associated anisotropic hyperedge modes. We also excite nonplanar cyclotron motion, in contrast to the planar orbits in D ≤ 3. Our work may enable the investigation of strongly correlated topological liquids in 4D, generalizing fractional quantum Hall states.

Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally quantifies entanglement, has been proposed as a first signature of topological order. Conversely, the full description of entanglement relies on the entanglement Hamiltonian, a more complex object originally introduced to formulate quantum entanglement in curved spacetime. As conjectured by Li and Haldane, the entanglement Hamiltonian of a many-body system appears to be directly linked to its boundary properties, making it particularly useful for characterizing topological systems. While the entanglement spectrum is commonly used to identify complex phases arising in numerical simulations, its measurement remains an outstanding challenge. Here, we perform a variational approach to realize experimentally, as a genuine Hamiltonian, the entanglement Hamiltonian of a synthetic quantum Hall system. We use a synthetic dimension, encoded in the electronic spin of dysprosium atoms, to implement spatially deformed Hall systems, as suggested by the Bisognano-Wichmann prediction. The spectrum of the optimal variational Hamiltonian exhibits a chiral dispersion akin to a topological edge mode, revealing the fundamental link between entanglement and boundary physics. Our variational procedure can be easily generalized to interacting many-body systems on various platforms, marking an important step towards the exploration of exotic quantum systems with long-range correlations, such as fractional Hall states, chiral spin liquids and critical systems.

We investigate the loss of spatial coherence of one-dimensional bosonic gases in optical lattices illuminated by a near-resonant excitation laser. Because the atoms recoil in a random direction after each spontaneous emission, the atomic momentum distribution progressively broadens. Equivalently, the spatial correlation function (the Fourier-conjugate quantity of the momentum distribution) progressively narrows down as more photons are scattered. Here we measure the correlation function of the matter field for fixed distances corresponding to nearest-neighbor (n-n) and next-nearest-neighbor (n-n-n) sites of the optical lattice as a function of time, hereafter called n-n and n-n-n correlators. For strongly interacting lattice gases, we find that the n-n correlator C 1 decays as a power-law at long times, C 1 a 1/ t alpha , in stark contrast with the exponential decay expected for independent particles. The power-law decay reflects a non-trivial dissipative many-body dynamics, where interactions change drastically the interplay between fluorescence destroying spatial coherence, and coherent tunnelling between neighboring sites restoring spatial coherence at short distances. The observed decay exponent alpha approximate to 0.54(6) is in good agreement with the prediction alpha = 1/2 from a dissipative Bose-Hubbard model accounting for the fluorescence-induced decoherence. Furthermore, we find that the n-n correlator C 1 controls the n-n-n correlator C 2 through the relation C 2 approximate to C 1 2 , also in accordance with the dissipative Bose-Hubbard model.

Topological states of matter lie at the heart of our modern understanding of condensed matter systems. In two-dimensional (2D) quantum Hall insulators, the non-trivial topology, defined by the first Chern number, manifests as a quantized Hall conductance and protected ballistic edge modes. Besides topological insulators and Weyl semi-metals experimentally realized in 3D materials, a large variety of topological systems, theoretically predicted in dimensions $D > 3$, remains unexplored - among them a generalization of the quantum Hall effect in 4D. So far, topological properties linked with the 4D Hall effect have been revealed via geometrical charge pump experiments in 2D systems. A truly 4D Hall system has also been realized using electronic circuits - however, no direct evidence of topological quantization has been reported. Here, we engineer an atomic quantum Hall system evolving in 4D, by coupling with light fields two spatial dimensions and two synthetic ones encoded in the electronic spin $J = 8$ of dysprosium atoms. We measure the characteristic properties of a 4D quantum Hall system, namely the quantization of its electromagnetic non-linear response by a second Chern number, and the special nature of its 3D hyperedge modes, which combine ballistic motion along one orientation and insulating behaviour in the two remaining directions. We also probe low-lying excitations, revealing non-planar cyclotron orbits in contrast with their circular equivalents in $D\leq3$. Our findings pave the way to the exploration of interacting quantum Hall systems in 4D, from the investigation of strongly-correlated liquids to the simulation of high-energy models in link with quantum gravity and Yang-Mills field theory.

Encoding a dimension in the internal degree of freedom of an atom provides an interesting tool for quantum simulation, facilitating the realization of artificial gauge fields. We propose an extension of the synthetic dimension toolbox, making it possible to encode two dimensions within a large atomic spin. The protocol combines first- and second-order spin couplings such that the spin projection $m$ and the remainder $r=m$ (mod 3) of its Euclidian division by 3 act as orthogonal coordinates on a synthetic cylinder. It is suited for an implementation with lanthanide atoms, which feature a large electronic spin and narrow optical transitions for applying the required spin couplings. This method is useful for simulating geometries with periodic boundary conditions and engineering various types of topological systems evolving in high dimensions.

The quantum Hall effect occurring in two-dimensional electron gases was first explained by Laughlin, who developed a thought experiment that laid the groundwork for our understanding of topological quantum matter. His proposal is based on a quantum Hall cylinder periodically driven by an axial magnetic field, resulting in the quantized motion of electrons. We realize this milestone experiment with an ultracold gas of dysprosium atoms, the cyclic dimension being encoded in the electronic spin and the axial field controlled by the phases of laser-induced spin-orbit couplings. Our experiment provides a straightforward manifestation of the nontrivial topology of quantum Hall insulators, and could be generalized to strongly correlated topological systems.

Superfluidity in its various forms has been of interest since the observation of frictionless flow in liquid helium II1,2. In three spatial dimensions it is conceptually associated with the emergence of long-range order at a critical temperature. One of the hallmarks of superfluidity, as predicted by the two-fluid model3,4 and observed in both liquid helium5 and in ultracold atomic gases6,7, is the existence of two kinds of sound excitation—the first and second sound. In two-dimensional systems, thermal fluctuations preclude long-range order8,9; however, superfluidity nevertheless emerges at a non-zero critical temperature through the infinite-order Berezinskii–Kosterlitz–Thouless (BKT) transition10,11, which is associated with a universal jump12 in the superfluid density without any discontinuities in the thermodynamic properties of the fluid. BKT superfluids are also predicted to support two sounds, but so far this has not been observed experimentally. Here we observe first and second sound in a homogeneous two-dimensional atomic Bose gas, and use the two temperature-dependent sound speeds to determine the superfluid density of the gas13–16. Our results agree with the predictions of BKT theory, including the prediction of a universal jump in the superfluid density at the critical temperature. First and second sound are experimentally observed in a two-dimensional superfluid, and the temperature-dependent sound speeds reveal the predicted jump in the superfluid density at the infinite-order Berezinskii–Kosterlitz–Thouless transition.

We experimentally and theoretically investigate the lowest-lying axial excitation of an atomic Bose-Einstein condensate in a cylindrical box trap. By tuning the atomic density, we observe how the nature of the mode changes from a single-particle excitation (in the low-density limit) to a sound wave (in the high-density limit). Throughout this crossover the measured mode frequency agrees with Bogoliubov theory. Using approximate low-energy models we show that the evolution of the mode frequency is directly related to the interaction-induced shape changes of the condensate and the excitation. Finally, if we create a large-amplitude excitation, and then let the system evolve freely, we observe that the mode amplitude decays nonexponentially in time; this nonlinear behavior is indicative of interactions between the elementary excitations, but remains to be quantitatively understood.

We present an evaporative cooling technique for atoms trapped in an optical dipole trap that benefits from narrow optical transitions. For an appropriate choice of wavelength and polarization, a single laser beam leads to opposite light-shifts in two internal states of the lowest energy manifold. Radio-frequency coupling between these two states results in evaporative cooling at a constant trap stiffness. The evaporation protocol is well adapted to several atomic species, in particular to the case of Lanthanides such as Er, Dy, and fermionic Yb, but also to alkali-earth metals such as fermionic Sr. We derive the dimensionless expressions that allow us to estimate the evaporation efficiency. As a concrete example, we consider the case of Dy and present a numerical analysis of the evaporation in a dipole trap near the J ′ = J optical transition at 832 nm. We show that this technique can lead to runaway evaporation in a minimalist experimental setup.

Received 15 July 2021DOI:https://doi.org/10.1103/PhysRevA.104.049903©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose gasesBose-Einstein condensatesBosonsInterparticle interactionsNonlinear acousticsPhononsSuperfluid densitySuperfluidityTransport phenomenaUltracold collisionsAtomic, Molecular & OpticalFluid DynamicsStatistical PhysicsGeneral PhysicsCondensed Matter, Materials & Applied PhysicsNonlinear Dynamics

We study the decay mechanism of the gapped lowest-lying axial excitation of a quasipure atomic Bose-Einstein condensate confined in a cylindrical box trap. Owing to the absence of accessible lower-energy modes, or direct coupling to an external bath, this excitation is protected against one-body (linear) decay, and the damping mechanism is exclusively nonlinear. We develop a universal theoretical model that explains this fundamentally nonlinear damping as a process whereby two quanta of the gapped lowest excitation mode couple to a higher-energy mode, which subsequently decays into a continuum. We find quantitative agreement between our experiments and the predictions of this model. Finally, by strongly driving the system below its (lowest) resonant frequency, we observe third-harmonic generation, a hallmark of nonlinear behavior.

Quantum spins of mesoscopic size are a well-studied playground for engineering nonclassical states. If the spin represents the collective state of an ensemble of qubits, its nonclassical behavior is linked to entanglement between the qubits. In this paper, we report on an experimental study of entanglement between two subsystems of dysprosium’s electronic spin. Its ground state, of angular momentum J = 8, can formally be viewed as a set of 2 J qubits symmetric upon exchange. To access entanglement properties, we partition the spin by optically coupling it to an excited state J (cid:2) = J − 1, which removes a pair of qubits in a state defined by the light polarization. Starting with the well-known W and squeezed states, we extract the concurrence of qubit pairs, which quantifies their nonclassical character. We also directly demonstrate entanglement between the 14- and 2-qubit subsystems via an increase in entropy upon partition. In a complementary set of experiments, we probe decoherence of a state prepared in the excited level J (cid:2) = J + 1 and interpret spontaneous emission as a loss of a qubit pair in a random state. This allows us to contrast the robustness of nonclassical pairwise correlations of the W state with the fragility of the coherence involved in a Schrödinger cat state. Our findings open up the possibility to engineer novel types of entangled atomic ensembles, in which entanglement occurs within each atom’s electronic spin as well as between different atoms. Qubit ensembles with large entanglement depth could then be realized with a few atoms only, facilitating the scaling up of quantum-enhanced sensors. An off-resonant optical cavity in the strong-coupling regime couples an ensemble of N atoms together. For σ + polarized cavity light, the total spin projection along z is conserved, and the cavity mediates the coherent exchange of ↑ qubit excitations between atoms. Such couplings can be used to stabilize a W state, with a single ↑ excitation symmetrically shared between the N × (2 J ) qubits.