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MSmix is a recently developed R package implementing maximum likelihood estimation of finite mixtures of Mallows models with Spearman distance for full and partial rankings. The package is designed to implement computationally tractable estimation routines of the model parameters, with the ability to handle arbitrary forms of partial rankings and sequences of a large number of items. The frequentist estimation task is accomplished via EM algorithms, integrating data augmentation strategies to recover the unobserved heterogeneity and the missing ranks. The package also provides functionalities for uncertainty quantification of the estimated parameters, via diverse bootstrap methods and asymptotic confidence intervals. Generic methods for S3 class objects are constructed for more effectively managing the output of the main routines. The usefulness of the package and its computational performance compared with competing software is illustrated via applications to both simulated and original real ranking datasets., Comment: 29 pages, 7 figures, 3 tables

We present an approach to compute the Floquet quasienergy spectrum of time-periodic systems. The method allows to characterize the light-matter interaction in finite and extended structures by carefully addressing the resolution of the position operator. In periodic systems we discuss the role of the quantum-geometric gauge freedom of Bloch states and employ a Wannier-based scheme to compute the required matrix elements. As a consequence, the method is accurate and applicable to a broad range of systems, from atoms and molecules to cold atomic gases and materials described by density functional theory, as well as model systems. We demonstrate the applicability of the approach by studying two cases: a particle trapped in a one-dimensional box and the semiconducting material BC$_2$N. We employ the first example to provide a numerical proof of the invariance of the Floquet quasienergy spectrum with respect to the choice of electromagnetic gauge. The analysis of BC$_2$N then serves to illustrate the physical effects described by the quasienergies, such as multiphoton resonances, and their expected range of occurrence in real materials in terms of external electric field and frequency of the drive pulse., Comment: 16 pages, 6 figures

We analyze the pinning of vortices for a stationary rotating dipolar supersolid along the low-density paths between droplets as a function of the rotation frequency. We restrict ourselves to the stationary configurations of vortices with the same symmetry as that of the array of droplets. Our approach exploits the fact that the wave function of each droplet acquires a linear phase on the coordinates, and hence the relative phases between neighboring droplets allows us to predict the position of the vortices. For a confined system, the estimate accurately reproduces the Gross-Pitaevskii results in the spatial regions where the neighboring droplets are well defined.

Short-wavelength repulsive potentials for quantum gases allow to realize new systems and to study new phenomena. Here we report the realization of repulsive optical potentials for dysprosium atoms in the blue region of the spectrum, at wavelengths close to 400 nm. We employ a spectrallyfiltered diode laser system to measure both scalar and tensorial components of the polarizability of dysprosium, which we find in good agreement with the theoretical predictions. We demonstrate the implementation of potential strengths appropriate to manipulate Bose-Einstein condensates, with scattering-limited lifetimes exceeding one second. This type of optical potentials opens interesting directions for the study of dipolar superfluids and supersolids., Comment: 7 pages, 8 figures

Recent research on Simultaneous Localization and Mapping (SLAM) based on implicit representation has shown promising results in indoor environments. However, there are still some challenges: the limited scene representation capability of implicit encodings, the uncertainty in the rendering process from implicit representations, and the disruption of consistency by dynamic objects. To address these challenges, we propose a real-time dynamic visual SLAM system based on local-global fusion neural implicit representation, named DVN-SLAM. To improve the scene representation capability, we introduce a local-global fusion neural implicit representation that enables the construction of an implicit map while considering both global structure and local details. To tackle uncertainties arising from the rendering process, we design an information concentration loss for optimization, aiming to concentrate scene information on object surfaces. The proposed DVN-SLAM achieves competitive performance in localization and mapping across multiple datasets. More importantly, DVN-SLAM demonstrates robustness in dynamic scenes, a trait that sets it apart from other NeRF-based methods.

Quadrupedal robots excel in mobility, navigating complex terrains with agility. However, their complex control systems present challenges that are still far from being fully addressed. In this paper, we introduce the use of Sample-Based Stochastic control strategies for quadrupedal robots, as an alternative to traditional optimal control laws. We show that Sample-Based Stochastic methods, supported by GPU acceleration, can be effectively applied to real quadruped robots. In particular, in this work, we focus on achieving gait frequency adaptation, a notable challenge in quadrupedal locomotion for gradient-based methods. To validate the effectiveness of Sample-Based Stochastic controllers we test two distinct approaches for quadrupedal robots and compare them against a conventional gradient-based Model Predictive Control system. Our findings, validated both in simulation and on a real 21Kg Aliengo quadruped, demonstrate that our method is on par with a traditional Model Predictive Control strategy when the robot is subject to zero or moderate disturbance, while it surpasses gradient-based methods in handling sustained external disturbances, thanks to the straightforward gait adaptation strategy that is possible to achieve within their formulation., Comment: Accepted for publication at the 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

Disorder or quasi-disorder is known to favor the localization in many-body Bose systems. Here in contrast, we demonstrate an anomalous delocalization effect induced by incommensurability in quasiperiodic lattices. Loading ultracold atoms in two shallow periodic lattices with equal amplitude and either equal or incommensurate spatial periods, we show the onset of a Mott transition not only in the periodic case but also in the quasiperiodic case. Upon increase of the incommensurate component of the potential we find that the Mott insulator turns into a delocalized superfluid. Our experimental results agree with quantum Monte Carlo calculations, showing anomalous delocalization induced by the interplay between the commensuration and interaction.

We present a direct comparison between the stroboscopic and non-stroboscopic effective approaches for ultracold atoms in shaken honeycomb lattices, focusing specifically on the optimal driving introduced by A. Verdeny and F. Mintert [Phys. Rev. A 92, 063615 (2015)]. In the fast-driving regime, we compare the effective non-stroboscopic Hamiltonian derived through a perturbative expansion with a non-perturbative calculation of the stroboscopic Floquet Hamiltonian, obtained through a simple non-perturbative numerical approach. We show that while some of the tunneling parameters are inherently model-dependent, the topological properties of the system remains robust, as expected. Using the same numerical approach we compute the topological phase diagram, arguing that it is most effectively represented in terms of the physical parameters characterizing the driving and the bare Hamiltonian -- parameters directly accessible in experiments -- rather than the emergent tunneling parameters, that depend on the model representation., Comment: 11 pages, 7 figures

Recently, a new category of superfluids and superconductors has been discovered in various systems. These could be linked to the idea of a supersolid phase, featuring a macroscopic wavefunction with spatial modulation resulting from simultaneous, spontaneous breaking of gauge and translational symmetries. However, this relation has only been recognized in some cases and there is the need for universal properties quantifying the differences between supersolids and ordinary superfluids/superconductors or crystals. A key property is the superfluid fraction, which measures the reduction in superfluid stiffness due to spatial modulation, leading to the non-standard superfluid dynamics of supersolids. Here we employ the Josephson effect, common in superfluids and superconductors, to measure the superfluid fraction in a supersolid. Even without a physical barrier, the Josephson effect arises spontaneously in a supersolid due to spatial modulation. Individual lattice cells act as self-induced Josephson junctions, allowing the direct determination of the local superfluid fraction. We studied a cold-atom dipolar supersolid, revealing a significant sub-unity superfluid fraction. Our results open new research directions, enabling the exploration of novel phenomena like partially quantized vortices and supercurrents, potentially unifying the understanding of supersolid-like systems, and introducing a new type of Josephson junction., Comment: 15 pages, 10 figures

Legged robots, particularly quadrupeds, offer promising navigation capabilities, especially in scenarios requiring traversal over diverse terrains and obstacle avoidance. This paper addresses the challenge of enabling legged robots to navigate complex environments effectively through the integration of data-driven path-planning methods. We propose an approach that utilizes differentiable planners, allowing the learning of end-to-end global plans via a neural network for commanding quadruped robots. The approach leverages 2D maps and obstacle specifications as inputs to generate a global path. To enhance the functionality of the developed neural network-based path planner, we use Vision Transformers (ViT) for map pre-processing, to enable the effective handling of larger maps. Experimental evaluations on two real robotic quadrupeds (Boston Dynamics Spot and Unitree Go1) demonstrate the effectiveness and versatility of the proposed approach in generating reliable path plans., Comment: 6 pages, 6 figures, conference

We characterize the role of the roton instability in the formation of a supersolid state of an elongated dipolar condensate, following a quench of the contact interactions across the superfluid-supersolid transition, as observed in recent experiments. We perform dynamical simulations by means of the extended Gross-Pitaevskii equation including quantum corrections, for different final values of the $s-$wave scattering length. The corresponding excitation spectrum is computed using an effective one-dimensional description, revealing that the calculated growth rates of the unstable roton mode accurately reproduce the observed behavior. Our results provide valuable insights regarding the formation time of the supersolid and its scaling behavior with respect to the $s$-wave scattering length.

State-of-the-art sensorimotor learning algorithms offer policies that can often produce unstable behaviors, damaging the robot and/or the environment. Traditional robot learning, on the contrary, relies on dynamical system-based policies that can be analyzed for stability/safety. Such policies, however, are neither flexible nor generic and usually work only with proprioceptive sensor states. In this work, we bridge the gap between generic neural network policies and dynamical system-based policies, and we introduce Autonomous Neural Dynamic Policies (ANDPs) that: (a) are based on autonomous dynamical systems, (b) always produce asymptotically stable behaviors, and (c) are more flexible than traditional stable dynamical system-based policies. ANDPs are fully differentiable, flexible generic-policies that can be used in imitation learning setups while ensuring asymptotic stability. In this paper, we explore the flexibility and capacity of ANDPs in several imitation learning tasks including experiments with image observations. The results show that ANDPs combine the benefits of both neural network-based and dynamical system-based methods., Comment: 6 pages, 7 figures, Accepted at the Life-Long Learning with Human Help(L3H2) ICRA 2023 Workshop

At the interface between two fluid layers in relative motion, infinitesimal fluctuations can be exponentially amplified, inducing vorticity and the breakdown of the laminar flow. This process, known as the Kelvin-Helmholtz instability, is responsible for many familiar phenomena observed in the atmosphere and in the oceans, as well as in astrophysical objects, being known as one of the paradigmatic routes to turbulence in fluid mechanics. While shear-flow instabilities in classical fluids have been extensively observed in various contexts, controlled experiments in the presence of quantized circulation are comparatively very few. Here, we engineer two counter-rotating atomic superflows, a configuration that in classical inviscid fluids is unstable via the Kelvin-Helmholtz instability. We observe how the contact interface, i.e. the shear layer, develops into an ordered circular array of quantized vortices, which loses stability and rolls up into vortex clusters. We extract the instability growth rates and find that they obey the same scaling relations across different superfluid regimes, ranging from weakly-interacting bosonic to strongly-correlated fermionic pair condensates. The measured scalings, reproduced by numerical simulations and well described by a microscopic point-vortex model, are consistent with the classical hydrodynamic Kelvin-Helmholtz instability of a finite-width shear layer. Our results establish interesting connections between vortex arrays and shear-flow instabilities, suggesting a possible interpretation of the observed quantized vortex dynamics as a manifestation of the underlying unstable flow. Moreover, they open the way for exploring a wealth of out-of-equilibrium phenomena, from vortex-matter phase transitions to the spontaneous emergence and decay of two-dimensional quantum turbulence.

In this paper, we introduce a method to deal with the problem of robot local path planning among pushable objects -- an open problem in robotics. In particular, we achieve that by training multiple agents simultaneously in a physics-based simulation environment, utilizing an Advantage Actor-Critic algorithm coupled with a deep neural network. The developed online policy enables these agents to push obstacles in ways that are not limited to axial alignments, adapt to unforeseen changes in obstacle dynamics instantaneously, and effectively tackle local path planning in confined areas. We tested the method in various simulated environments to prove the adaptation effectiveness to various unseen scenarios in unfamiliar settings. Moreover, we have successfully applied this policy on an actual quadruped robot, confirming its capability to handle the unpredictability and noise associated with real-world sensors and the inherent uncertainties present in unexplored object pushing tasks., Comment: 7 pages, 7 figures, 4 tables

We present a general discussion of the dipole modes of a heteronuclear bosonic mixture in a harmonic trap by comparing the prediction of the sum-rule approach with full Gross-Pitaevskii (GP) calculations. Yet in the range of interaction in which the mixture is miscible and stable at the mean field level, $g_{12}^2

We unravel the coupled dipole dynamics of a two-species Bose-Einstein condensate with tunable interspecies interaction. We produce a degenerate mixture of $^{41}$K-$^{87}$Rb in an optical trap and we study the dipole oscillations of both atomic species in the linear response regime. Varying the interspecies interaction from the weakly to the strongly attractive side, we measure the frequencies and the composition of the two dipole eigenmodes. For enough strong interactions, even beyond the mean-field collapse, we find that the frequency of the low-energy eigenmode is determined only by the bare trap frequencies and the species population imbalance. The experimental results are well reproduced by numerical simulations based on two coupled Gross-Pitaevskii equations. Our findings provide a detailed picture of the dipole excitations in asymmetric bosonic mixtures., Comment: 8 pages, 4 figures

We provide a theoretical characterization of the dynamical crossing of the superfluid-supersolid phase transition for a dipolar condensate confined in an elongated trap, as observed in the recent experiment by G. Biagioni et al. [Phys. Rev. X 12, 021019 (2022)]. By means of the extended Gross-Pitaevskii theory, which includes the Lee-Huang-Yang quantum fluctuation correction, we first analyze the ground state configurations of the system as a function of the interparticle scattering length, for both trap configurations employed in the experiment. Then, we discuss the effects of the ramp velocity, by which the scattering length is tuned across the transition, on the collective excitations of the system in both the superfluid and supersolid phases. We find that, when the transverse confinement is sufficiently strong and the transition has a smooth (continuous) character, the system essentially displays a (quasi) 1D behavior, its excitation dynamics being dominated by the axial breathing modes. Instead, for shallower transverse trapping, when the transition becomes discontinuous, the collective excitations of the supersolid display a coupling with the transverse modes, signalling the onset of a dimensional crossover., Comment: 9 pages, 8 figures

We assess experimentally and theoretically the character of the superfluid-supersolid quantum phase transition recently discovered in trapped dipolar quantum gases. We find that one-row supersolids can have already two types of phase transitions, discontinuous and continuous, that are reminiscent of the first- and second-order transitions predicted in the thermodynamic limit in 2D and 1D, respectively. The smooth crossover between the two regimes is peculiar to supersolids and can be controlled via the transverse confinement and the atom number. We justify our observations on the general ground of the Landau theory of phase transitions. The quasi-adiabatic crossing of a continuous phase transition opens new directions of investigation for supersolids., Comment: 15 pages, 15 figures

We address the existence and stability of one-dimensional (1D) holes and kinks and two-dimensional (2D) vortex-holes nested in extended binary Bose mixtures, which emerge in the presence of Lee-Huang-Yang (LHY) quantum corrections to the mean-field energy, along with self-bound quantum droplets. We consider both the symmetric system with equal intra-species scattering lengths and atomic masses, modeled by a single (scalar) LHY-corrected Gross-Pitaevskii equation (GPE), and the general asymmetric case with different intra-species scattering lengths, described by two coupled (spinor) GPEs. We found that in the symmetric setting, 1D and 2D holes can exist in a stable form within a range of chemical potentials that overlaps with that of self-bound quantum droplets, but that extends far beyond it. In this case, holes are found to be stable in 1D and they transform into pairs of stable out-of-phase kinks at the critical chemical potential at which localized droplets turn into flat-top states, thereby revealing the connection between localized and extended nonlinear states. In contrast, spinor nature of the asymmetric systems may lead to instability of 1D holes, which tend to break into two gray states moving in the opposite directions. Such instability arises due to spinor nature of the system and it affects only holes nested in extended modulationally-stable backgrounds, while localized quantum droplet families remain completely stable, even in the asymmetric case, while 1D holes remain stable only close to the point where they transform into pairs of kinks. We also found that symmetric systems allow fully stable 2D vortex-carrying single-charge states at moderate amplitudes, while unconventional instabilities appear also at high amplitudes. Symmetry also strongly inhibits instabilities for double-charge vortex-holes, which thus exhibit unexpectedly robust evolutions at low amplitudes., Comment: 9 pages, 7 figures, to appear in New Journal of Physics

We experimentally and theoretically investigate the influence of the dipole-dipole interactions (DDIs) on the total inter-species interaction in an erbium-dysprosium mixture. By rotating the dipole orientation we are able to tune the effect of the long-range and anisotropic DDI, and therefore the in-trap clouds displacement. We present a theoretical description for our binary system based on an extended Gross-Pitaevskii (eGP) theory, including the single-species beyond mean-field terms, and we predict a lower and an upper bound for the inter-species scattering length $a_{12}$. Our work is a first step towards the investigation of the experimentally unexplored dipolar miscibility-immiscibility phase diagram and the realization of quantum droplets and supersolid states with heteronuclear dipolar mixtures., Comment: 10 pages, 6+2 figures

We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped in a harmonic trap. The effective scaling approach produces an auxiliary equation for the scaling parameter interpolating between the noninteracting and the Thomas-Fermi limits. This allows us to implement a frictionless quench by engineering inversely the smooth trap frequency, as compared to the two-jump trajectory. Our result is beneficial to design the shortcut-to-adiabaticity expansion of trapped Bose gases for arbitrary values of interaction, and can be directly extended to the three-dimensional case., Comment: 6 pages, 4 figures

We theoretically investigate the one-dimensional dynamics of a dark soliton in a two-component immiscible mixture of Bose-Einstein condensates with repulsive interactions. We analyze the reflection and transmission of a soliton when it propagates through the domain wall, and we show that a dark-bright soliton can be dynamically generated by the interaction of the dark soliton with the domain wall, outside the regime of parameters where stationary solutions are known to exist. The dynamics of this dark-bright soliton is harmonic like, with a numerical frequency that is in good agreement with the predictions of a semi-analytical model., Comment: 7 pages, 5 figures

We experimentally demonstrate a multi-mode interferometer comprising a Bose-Einstein condensate of $^{39}$K atoms trapped in a harmonic potential, where the interatomic interaction can be cancelled exploiting Feshbach resonances. Kapitza-Dirac diffraction from an optical lattice coherently splits the BEC in multiple momentum components equally spaced that form different interferometric paths, closed by the trapping harmonic potential. We investigate two different interferometric schemes, where the recombination pulse is applied after a full or half oscillation in the confining potential. We find that the relative amplitudes of the momentum components at the interferometer output are sensitive to external forces, through the induced displacement of the harmonic potential with respect to the optical lattice. We show how to calibrate the interferometer, fully characterize its output and discuss perspective improvements., Comment: 7 pages, 6 figures

We report the experimental realization of a new kind of optical lattice for ultra-cold atoms where arbitrarily large separation between the sites can be achieved without renouncing to the stability of ordinary lattices. Two collinear lasers, with slightly different commensurate wavelengths and retroreflected on a mirror, generate a superlattice potential with a periodic "beat-note" profile where the regions with large amplitude modulation provide the effective potential minima for the atoms. To prove the analogy with a standard large spacing optical lattice we study Bloch oscillations of a Bose Einstein condensate with negligible interactions in the presence of a small force. The observed dynamics between sites separated by ten microns for times exceeding one second proves the high stability of the potential. This novel lattice is the ideal candidate for the coherent manipulation of atomic samples at large spatial separations and might find direct application in atom-based technologies like trapped atom interferometers and quantum simulators., Comment: 5 pages, 4 figures

We theoretically investigate the self-evaporation dynamics of quantum droplets in a 41K-87Rb mixture, in free-space. The dynamical formation of the droplet and the effects related to the presence of three-body losses are analyzed by means of numerical simulations. We identify a regime of parameters allowing for the observation of the droplet self-evaporation in a feasible experimental setup., Comment: 11 pages, 3 figures; submitted to the Special Issue "Quantum Degenerate Atomic Mixtures"

Understanding the effect of interactions in the phase evolution of expanding atomic Bose Einstein condensates is fundamental to describe the basic phenomenon of matter wave interference. Many theoretical and experimental works tackled this problem, always with the implicit assumption that the mutual interaction between two expanding condensates rigidly modifies the phase evolution through an effective force. In this paper, we present a combined experimental and theoretical investigation of the interference profile of expanding $^{87}$Rb condensates, with a specific focus on the effect of interactions. We come to the different conclusion that the mutual interaction produces local modifications of the condensate phase only in the region where the wavepackets overlap., Comment: 10 pages, 14 figures; published version

We compare the exact evolution of an expanding three-dimensional Bose-Einstein condensate with that obtained from the effective scaling approach introduced in D. Gu\'ery-Odelin [Phys. Rev. A 66, 033613 (2002)]. This approach, which consists in looking for self-similar solutions to be satisfied on average, is tested here in different geometries and configurations. We find that, in case of almost isotropic traps, the effective scaling reproduces with high accuracy the exact evolution dictated by the Gross-Pitaevskii equation for arbitrary values of the interactions, in agreement with the proof-of-concept of M. Modugno, G. Pagnini, and M. A. Valle-Basagoiti [Phys. Rev. A 97, 043604 (2018)]. Conversely, it is shown that the hypothesis of universal self-similarity breaks down in case of strong anisotropies and trapped geometries., Comment: Shortened version to appear on Physical Review Research (9 pages, 10 figures)

We report on the production of a $^{41}$K-$^{87}$Rb dual-species Bose-Einstein condensate with tunable interspecies interaction and we study the mixture in the attractive regime, i.e. for negative values of the interspecies scattering length $a_{12}$. The binary condensate is prepared in the ground state and confined in a pure optical trap. We exploit Feshbach resonances for tuning the value of $a_{12}$. After compensating the gravitational sag between the two species with a magnetic field gradient, we drive the mixture into the attractive regime. We let the system to evolve both in free space and in an optical waveguide. In both geometries, for strong attractive interactions, we observe the formation of self-bound states, recognizable as quantum droplets. Our findings prove that robust, long-lived droplet states can be realized in attractive two-species mixtures, despite the two atomic components may experience different potentials., Comment: 9 figures, accepted by Condensed Matter as Special issue 'Proceedings of the conference SuperFluctuations 2019'

We review the geometric theory of \emp{smooth systems of smooth maps}, of \emp{smooth systems of smooth sections} of a smooth double fibred manifold and of \emp{smooth systems of smooth connections} of a smooth fibred manifold. Moreover, after reviewing the concept of \emp{F-smooth space} due to A. Fr\"olicher, we discuss the \emp{F-smooth systems of smooth maps}, the \emp{F-smooth systems of fibrewisely smooth sections} of a smooth double fibred manifold, the \emp{F-smooth systems of fibrewisely smooth connections} of a smooth fibred manifold and of \emp{F-smooth connections} of an F-smooth system of fibrewisely smooth sections., Comment: 103 pages, minor typographic corrections, comments welcome

We report on the dynamical formation of self-bound quantum droplets in attractive mixtures of $^{39}$K atoms. Considering the experimental observations of Semeghini et al., Phys. Rev. Lett. 120, 235301 (2018), we perform numerical simulations to understand the relevant processes involved in the formation of a metastable droplet from an out-of-equilibrium mixture. We first analyze the so-called self-evaporation mechanism, where the droplet dissipates energy by releasing atoms, and then we consider the effects of losses due to three-body recombinations and to the balancing of populations in the mixture. We discuss the importance of these three mechanisms in the observed droplet dynamics and their implications for future experiments.

We show that attractive spinor Bose-Einstein condensates under the action of spin-orbit coupling (SOC) and Zeeman splitting form self-sustained stable two- and three-dimensional (2D and 3D) states in free space, even when SOC acts in a lower-dimensional form. We find that two-dimensional states are stabilized by one-dimensional (1D) SOC in a broad range of chemical potentials, for atom numbers (or norm of the spinor wavefunction) exceeding a threshold value, which strongly depends on the SOC strength and vanishes at a critical point. The zero-threshold point is a boundary between single-peaked and striped states, realizing hybrids combining 2D and 1D structural features. In a vicinity of such point, an asymptotic equation describing the bifurcation of the solitons from the linear spectrum is derived and investigated analytically. We show that striped 3D solitary states are as well stabilized by 2D SOC, albeit in a limited range of chemical potentials and norms., Comment: 7 pages, 5 figures, to appear in Physical Review Research

A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Non-classical rotational effects have been searched for a long time also for the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. We study a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, already employed for superfluids. From the measured moment of inertia, we infer a superfluid fraction that is different from zero and of order of unity, providing direct evidence of the superfluid nature of the dipolar supersolid., Comment: 8 pages, 4 figures, revised version

Self-bound quantum droplets are a newly discovered phase in the context of ultracold atoms. In this work we report their experimental realization following the original proposal by Petrov [Phys. Rev. Lett. 115, 155302 (2015)], using an attractive bosonic mixture. In this system spherical droplets form due to the balance of competing attractive and repulsive forces, provided by the mean-field energy close to the collapse threshold and the first-order correction due to quantum fluctuations. Thanks to an optical levitating potential with negligible residual confinement we observe self-bound droplets in free space and we characterize the conditions for their formation as well as their equilibrium properties. This work sets the stage for future studies on quantum droplets, from the measurement of their peculiar excitation spectrum, to the exploration of their superfluid nature.

We consider a homogeneous heteronuclear Bose mixture with contact interactions at the mean-field collapse, i.e. with interspecies attraction equal to the mean geometrical intraspecies repulsion. We show that the Lee-Huang-Yang (LHY) energy functional is accurately approximated by an expression that has the same functional form as in the homonuclear case. The approximated energy functional is characterized by two exponents, which can be treated as fitting parameters. We demonstrate that the values of these parameters which preserve the invariance under permutation of the two atomic species are exactly those of the homonuclear case. Deviations from the exact expression of LHY energy functional are discussed quantitatively and a specific application is described., Comment: 7 pages, 3 figures

We report on the formation of heteronuclear quantum droplets in an attractive bosonic mixture of 41K and 87Rb. We observe long-lived self-bound states, both in free space and in an optical waveguide. In the latter case, the dynamics under the effect of a species-dependent force confirms their bound nature. By tuning the interactions from the weakly to the strongly attractive regime, we study the transition from expanding to localized states, in both geometries. We compare the experimental results with beyond mean-field theory and we find a good agreement in the full range of explored interactions. Our findings open up the production of long-lived droplets with important implications for further research., Comment: 9 pages, 7 figures

Maintaining balance while walking is not a simple task for a humanoid robot because of its complex dynamics. The presence of a persistent disturbance makes this task even more challenging, as it can cause a loss of balance and ultimately lead the the robot to a fall. In this paper, we extend our previously proposed Intrinsically Stable MPC (IS-MPC), which guarantees boundedness of the CoM with respect to the ZMP, to the case of persistent disturbances. This is achieved by designing a disturbance observer whose estimate is used to compute a modified stability constraint included in the QP problem formulation. The method is validated by MATLAB simulations for the LIP as well as dynamic simulations for a NAO humanoid in DART., Comment: 7 pages, 10 figures, submitted to 2019 IEEE-RAS International Conference on Humanoid Robots

The existence of a paradoxical supersolid phase of matter, possessing the apparently incompatible properties of crystalline order and superfluidity, was predicted 50 years ago. Solid helium was the natural candidate, but there supersolidity has not been observed yet, despite numerous attempts. Ultracold quantum gases have recently shown the appearance of the periodic order typical of a crystal, due to various types of controllable interactions. A crucial feature of a D-dimensional supersolid is the occurrence of up to D+1 gapless excitations reflecting the Goldstone modes associated with the spontaneous breaking of two continuous symmetries: the breaking of phase invariance, corresponding to the locking of the phase of the atomic wave functions at the origin of superfluid phenomena, and the breaking of translational invariance due to the lattice structure of the system. The occurrence of such modes has been the object of intense theoretical investigations, but their experimental observation is still missing. Here we demonstrate the supersolid symmetry breaking through the appearance of two distinct compressional oscillation modes in a harmonically trapped dipolar Bose-Einstein condensate, reflecting the gapless Goldstone excitations of the homogeneous system. We observe that the two modes have different natures, with the higher frequency mode associated with an oscillation of the periodicity of the emergent lattice and the lower one characterizing the superfluid oscillations. Our work paves the way to explore the two quantum phase transitions between the superfluid, supersolid and solid-like configurations that can be accessed by tuning a single interaction parameter.

We introduce an exactly integrable nonlinear model describing the dynamics of spinor solitons in space-dependent matrix gauge potentials of rather general types. The model is shown to be gauge equivalent to the integrable system of vector nonlinear Schr\"odinger equations known as the Manakov model. As an example we consider a self-attractive Bose-Einstein condensate with random spin-orbit coupling (SOC). If Zeeman splitting is also included, the system becomes nonintegrable. We illustrate this by considering the random walk of a soliton in a disordered SOC landscape. While at zero Zeeman splitting the soliton moves without scattering along linear trajectories in the random SOC landscape, at nonzero splitting it exhibits strong scattering by the SOC inhomogeneities. For a large Zeeman splitting the integrability is recovered. In this sense the Zeeman splitting serves as a parameter controlling the crossover between two different integrable limits., Comment: 8 pages (with Supplemental Material), 4 figures

We report on the study of binary collisions between quantum droplets formed by an attractive mixture of ultracold atoms. We distinguish two main outcomes of the collision, i.e. merging and separation, depending on the velocity of the colliding pair. The critical velocity $v_c$ that discriminates between the two cases displays a different dependence on the atom number $N$ for small and large droplets. By comparing our experimental results with numerical simulations, we show that the non-monotonic behavior of $v_c(N)$ is due to the crossover from a compressible to an incompressible regime, where the collisional dynamics is governed by different energy scales, i.e. the droplet binding energy and the surface tension. These results also provide the first evidence of the liquid-like nature of quantum droplets in the large $N$ limit, where their behavior closely resembles that of classical liquid droplets.

We study the motion of a self-attractive Bose-Einstein condensate with pseudo-spin 1/2 driven by a synthetic Rabi (Zeeman-like) field. This field triggers the pseudo-spin dynamics resulting in a density redistribution between its components and, as a consequence, in changes of the overall density distribution. In the presence of an additional external potential, the latter produces a net force acting on the condensate and activates its displacement. As an example, here we consider the case of a one-dimensional condensate in a random potential., Comment: Phys. Rev. A, accepted

The competition of dipole-dipole and contact interactions leads to exciting new physics in dipolar gases, well-illustrated by the recent observation of quantum droplets and rotons in dipolar condensates. We show that the combination of the roton instability and quantum stabilization leads under proper conditions to a novel regime that presents supersolid properties, due to the coexistence of stripe modulation and phase coherence. In a combined experimental and theoretical analysis, we determine the parameter regime for the formation of coherent stripes, whose lifetime of a few tens of milliseconds is limited by the eventual destruction of the stripe pattern due to three-body losses. Our results open intriguing prospects for the development of long-lived dipolar supersolids., Comment: Revised version with a theoretical analysis not present in the previous version

We report on the production of a 41K-87Rb dual-species Bose-Einstein condensate in a hybrid trap, consisting of a magnetic quadrupole and an optical dipole potential. After loading both atomic species in the trap, we cool down 87Rb first by magnetic and then by optical evaporation, while 41K is sympathetically cooled by elastic collisions with 87Rb. We eventually produce two-component condensates with more than 10^5 atoms and tunable species population imbalance. We observe the immiscibility of the quantum mixture by measuring the density profile of each species after releasing them from the trap., Comment: 7 pages, 8 figures

We investigate theoretically the dynamics of a spin-orbit coupled soliton formed by a self- interacting Bose-Einstein condensate immersed in a random potential, in the presence of an artificial magnetic field. We find that due to the anomalous spin-dependent velocity, the synthetic Zeeman coupling can play a critical role in the soliton dynamics by causing its localization or delocalization, depending on the coupling strength and on the parameters of the random potential. The observed effects of the Zeeman coupling qualitatively depend on the type of self-interaction in the condensate since the spin state and the self-interaction energy of the condensate are mutually related if the invariance of the latter with respect to the spin rotation is lifted., Comment: reference added

We revisit the dynamics of a Bose-Einstein condensate in a double-well potential, from the regime of Josephson plasma oscillations to the self-trapping regime, by means of the Bogoliubov quasiparticle projection method. For very small imbalance between left and right wells only the lowest Bogoliubov mode is significantly occupied. In this regime the system performs plasma oscillations at the corresponding frequency, and the evolution of the condensate is characterized by a periodic transfer of population between the ground and the first excited state. As the initial imbalance is increased, more excited modes -- though initially not macroscopically occupied -- get coupled during the evolution of the system. Since their population also varies with time, the frequency spectrum of the imbalance turns out to be still peaked around a single frequency, which is continuously shifted towards lower values. The nonlinear mixing between Bogoliubov modes eventually drives the system into the the self-trapping regime, when the population of the ground state can be transferred completely to the excited states at some time during the evolution. For simplicity, here we consider a one-dimensional setup, but the results are expected to hold also in higher dimensions., Comment: 7 pages, 5 figures

We produce Bose-Einstein condensates of $^{162}$Dy atoms employing an innovative technique based on a resonator-enhanced optical trap that allows efficient loading from the magneto-optical trap and fast evaporation. We characterize the scattering properties of the ultracold atoms for magnetic fields between 6 and 30 G. In addition to the typical chaotic distribution of narrow Feshbach resonances in Lanthanides, we discover two rather isolated broad features at around 22 G and 27 G. A characterization using the complementary measurements of losses, thermalization, anisotropic expansion and molecular binding energy points towards resonances of predominant s-wave character. Such resonances will ease the investigation of quantum phenomena relying on the interplay between dipole and contact interactions.

We consider an effective scaling approach for the free expansion of a one-dimensional quantum wave packet, consisting in a self-similar evolution to be satisfied on average, i.e. by integrating over the coordinates. A direct comparison with the solution of the Gross-Pitaevskii equation shows that the effective scaling reproduces with great accuracy the exact evolution - the actual wave function is reproduced with a fidelity close to unity - for arbitrary values of the interactions. This result represents a proof-of-concept of the effectiveness of the scaling ansatz, which has been used in different forms in the literature but never compared with the exact evolution., Comment: 4 pages, 4 figures - revised version, accepted on PRA

Quantum phase slips are the primary excitations in one-dimensional superfluids and superconductors at low temperatures. They have been well characterized in most condensed-matter systems, and signatures of their existence has been recently observed in superfluids based on quantum gases too. In this review we briefly summarize the main results obtained on the investigation of phase slips from superconductors to quantum gases. In particular we focus our attention on recent experimental results of the dissipation in one-dimensional Bose superfluids flowing along a shallow periodic potential, which show signatures of quantum phase slips., Comment: 10 pages, 6 figures

We investigate the correspondence between the tight-binding Floquet Hamiltonian of a periodically modulated honeycomb lattice and the Haldane model. We show that - though the two systems share the same topological phase diagram, as reported in a breakthrough experiment with ultracold atoms in a stretched honeycomb lattice [Jotzu et al., Nature 515, 237 (2014)] - the corresponding Hamiltonians are not equivalent, the one of the shaken lattice presenting a much richer structure., Comment: 8 pages, 7 figures

Quantum phase slips, i.e the primary excitations in one-dimensional superfluids at low temperature, have been well characterized in most condensed-matter systems, with the notable exception of ultracold quantum gases. Here we present our experimental investigation of the dissipation in onedimensional Bose superfluids flowing along a periodic potential, which show signatures of the presence of quantum phase slips. In particular, by controlling the velocity of the superfluid and the interaction between the bosons we are apparently able to drive a crossover from a regime of thermal phase slips into a regime of quantum phase slips. Achieving a good control of quantum phase slips in ultracold quantum gases requires to keep under control other phenomena such as the breaking of superfluidity at the critical velocity or the appearance of a Mott insulator in the strongly correlated regime. Here we show our current results in these directions., Comment: 11 pages, 7 figures

We consider spin- and density-related properties of single-particle states in a one-dimensional system with random spin-orbit coupling. We show that the presence of an additional Zeeman field $\Delta$ induces both nonlinear spin polarization and delocalization of states localized at $\Delta=0$, corresponding to a random macroscopic analogue of the Paschen-Back effect. While the conventional Paschen-Back effect corresponds to a saturated $\Delta-$dependence of the spin polarization, here the gradual suppression of the spin-orbit coupling effects by the Zeeman field is responsible both for the spin saturation and delocalization of the particles., Comment: 8 pages, 7 figures