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Quantum vortices are commonly described as funnel-like objects around which the superfluid swirls, and their motion is typically modeled in terms of massless particles. Here, we show that, in Fermi superfluids, the normal component confined in the vortex core provides the vortex with a finite inertial mass. This inertia imparts an unambiguous signature to the dynamic behavior of vortices, specifically manifesting as small-amplitude transverse oscillations which remarkably follow the prediction of a simple point-like model supplemented by an effective mass. We demonstrate this phenomenon through large-scale time-dependent simulations of Fermi superfluids across a wide range of interaction parameters, at both zero and finite temperatures, and for various initial conditions. Our findings pave the way for the exploration of inertial effects in superfluid vortex dynamics., Comment: manuscript and supplementary material

We study the mass exchange between two rotating, quantum massive vortices in a two-component Bose-Einstein condensate. The vortices, in the majority component, exhibit a filled core, where the in-filling minority component undergoes a quantum tunneling effect. Remarkably, we observe that the two-vortex system features stable Josephson oscillations, as well as all the nonlinear phenomena, including the macroscopic quantum self-trapping, that characterize a Bosonic Josephson Junction (BJJ). We propose an analytical model for describing the inter-vortex tunneling, obtained by implementing the a coherent-state representation of the two-mode Bose-Hubbard model. This allows us to give the explicit expression of the model's parameters in terms of the physical macroscopic parameters of the two-vortex system. The comparison of the dynamical scenario predicted by the model with that emerging from the Gross-Pitaevskii equations is very good for sufficiently small particle numbers, while at larger particle numbers it grows less precise, presumably due to the partial exclusion of the many-body interactions from our model. The definition of an effective self-interaction parameter allows us to include the many-body effects, thus restoring a quite good agreement with the numerical results. Interestingly, the recognition of the bosonic Josephson dynamics paves the way to the investigation of new dynamical behaviors in multi-vortex configurations., Comment: 13 pages, 14 figures

We characterize the dynamical instability responsible for the breakdown of regular rows and necklaces of quantized vortices that appear at the interface between two superfluids in relative motion. Making use of a generalized point-vortex model, we identify several mechanisms leading to the suppression of this instability. They include a non-zero mass of the vortex cores, dissipative processes resulting from the interaction between the vortices and the excitations of the superfluid, and the proximity of the vortex array to the sample boundaries. We show that massive vortex cores not only have a mitigating effect on the dynamical instability, but also change the associated scaling law and affect the direction along which it develops. The predictions of our massive and dissipative point-vortex model are eventually compared against recent experimental measurements of the maximum instability growth rate relevant to vortex necklaces in a cold-atom platform., Comment: Revised version after peer review, 26 pages, 13 figures

We consider massive vortices in binary condensates, where the immiscibility condition entails the trapping of the minority component in the vortex cores of the majority component. We study such vortices by means of a 2D point-like model, and show how the relevant dynamical equations exhibit vortex-pair solutions characterized by different vortex masses and circular orbits of different radii $a$ and $b$. These solutions are validated by the simulations of the Gross-Pitaevskii equations for binary condensates. After examining the properties of vortex-pair rotational frequency $\Omega$ as a function of the vortex masses for a given pair geometry, we define the rotational-state diagram $\cal D$, describing all the possible vortex-pair solutions in terms of the orbit radii at given $\Omega$. This includes solutions with equal-mass pairs but $a \ne b$ or with one of the two masses (or both) equal to zero. Also, we analytically find the minimum value of $\Omega$ for the existence of such solutions, and obtain numerically the critical frequency $\Omega_c$ below which $\cal D$ changes its structure and the transition to an unstable vortex-pair regime takes place. Our work highlights an indirect measurement scheme to infer the vortex masses from orbits radii $a$ and $b$, and a link between the vortex masses and the vortex-pair small-oscillation properties., Comment: 16 pages, 24 figures

Recent advances in cold-atom platforms have made real-time dynamics accessible, renewing interest in the motion of superfluid vortices in two-dimensional domains. Here we show that the energy and the trajectories of arbitrary vortex configurations may be computed on a complicated (curved or bounded) surface, provided that one knows a conformal map that links the latter to a simpler domain (like the full plane, or a circular boundary). We also prove that Hamilton's equations based on the vortex energy agree with the complex dynamical equations for the vortex dynamics, demonstrating that the vortex trajectories are constant-energy curves. We use these ideas to study the dynamics of vortices in a two-dimensional incompressible superfluid with an elliptical boundary, and we derive an analytical expression for the complex potential describing the hydrodynamic flow throughout the fluid. For a vortex inside an elliptical boundary, the orbits are nearly self-similar ellipses., Comment: 25 pages, 9 figures | Final version after two rounds of peer-reviewing

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

We study the motion of superfluid vortices with filled massive cores. Previous point-vortex models already pointed out the impact of the core mass on the vortex dynamical properties, but relied on an assumption that is questionable in many physical systems where the immiscibility condition is barely satisfied: the fact that the massive core always lays at the very bottom of the effective confining potential constituted by the hosting vortex. Here, we relax this assumption and present a new point-vortex model where quantum vortices are harmonically coupled to their massive cores. We thoroughly explore the new dynamical regimes offered by this improved model; we then show that the functional dependence of the system normal modes on the microscopic parameters can be correctly interpreted only within this new generalized framework. Our predictions are benchmarked against the numerical simulations of coupled Gross-Pitaevskii equations for a realistic mixture of atomic Bose-Einstein condensates., Comment: 29 pages, 9 figures

Ghost vortices constitute an elusive class of topological excitations in quantum fluids since the relevant phase singularities fall within regions where the superfluid density is almost zero. Here we present a platform that allows for the controlled generation and observation of such vortices. Upon rotating an imbalanced mixture of two-component Bose-Einstein condensates (BECs), one can obtain necklaces of real vortices in the majority component whose cores get filled by particles from the minority one. The wavefunction describing the state of the latter is shown to harbour a number of ghost vortices which are crucial to support the overall dynamics of the mixture. Their arrangement typically mirrors that of their real counterpart, hence resulting in a ``dual" ghost-vortex necklace, whose properties are thoroughly investigated in the present paper. We also present a viable experimental protocol for the direct observation of ghost vortices in a ${}^{23}\mathrm{Na}$ $+$ ${}^{39}\mathrm{K}$ ultracold mixture. Quenching the inter-component scattering length, some atoms are expelled from the vortex cores and, while diffusing, swirl around unpopulated phase singularities, thus turning them directly observable., Comment: 13 pages, 8 figures

We study a superfluid in a planar annulus hosting vortices with massive cores. An analytical point-vortex model shows that the massive vortices may perform radial oscillations on top of the usual uniform precession of their massless counterpart. Beyond a critical vortex mass, this oscillatory motion becomes unstable and the vortices are driven towards one of the edges. The analogy with the motion of a charged particle in a static electromagnetic field leads to the development of a plasma orbit theory that provides a description of the trajectories which remains accurate even beyond the regime of small radial oscillations. These results are confirmed by the numerical solution of coupled two-component Gross-Pitaevskii equations. The analysis is then extended to a necklace of vortices symmetrically arranged within the annulus., Comment: 36 pages, 12 figures

Quantum vortices are often endowed with an effective inertial mass, due, for example, to massive particles in their cores. Such "massive vortices" display new phenomena beyond the standard picture of superfluid vortex dynamics, where the mass is neglected. In this work, we demonstrate that massive vortices are allowed to collide, as opposed to their massless counterparts. We propose a scheme to generate controllable, repeatable, deterministic collisional events in pairs of quantum vortices. We demonstrate two mass-driven fundamental processes: (i) the annihilation of two counter-rotating vortices and (ii) the merging of two co-rotating vortices, thus pointing out new mechanisms supporting incompressible-to-compressible kinetic energy conversion, as well as doubly-quantized vortices stabilization in flat superfluids., Comment: 6 pages, 4 figures (+ 2 pages for Supplemental Material)

We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential $\propto r^k$ can be experimentally realized with recent advances in optical-trapping techniques. Our analysis encompasses both empty-core and filled-core vortices. In the latter case, the vortex acquires a mass due to the presence of distinguishable atoms located in its core. The axisymmetry allows us to reduce the coupled dynamical equations of motion to a single radial equation with an effective potential $V_{\rm eff}$. In many cases, $V_{\rm eff}$ has a single minimum, where the vortex precesses uniformly. The dynamics of the vortex and the localized massive core arises from the dependence of the energy on the radial position of the vortex and from the $r^k$ trap potential. We find that a positive vortex with small mass orbits in the positive direction, but the sense of precession can reverse as the core mass increases. Early experiments and theoretical studies on two-component vortices found some qualitatively similar behavior., Comment: 10 pages, 7 figures

We consider the effect of a local interatomic repulsion on synthetic heterostructures where a discrete synthetic dimension is created by Raman processes on top of $SU(N)$-symmetric two-dimensional lattice systems. At a filling of one fermion per site, increasing the interaction strength, the system is driven towards a Mott state which is adiabatically connected to a band insulator. The chiral currents associated with the synthetic magnetic field increase all the way to the Mott transition, where they reach the maximum value, and they remain finite in the whole insulating state. The transition towards the Mott-band insulator is associated with the opening of a gap within the low-energy quasiparticle peak, while a mean-field picture is recovered deep in the insulating state., Comment: 27 Pages, 10 Figures

We summarize the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with ESA and national space and research funding agencies., Comment: Summary of the Community Workshop on Cold Atoms in Space and corresponding Road-map: https://indico.cern.ch/event/1064855/

We analyze two different fermionic systems that defy Mott localization showing a metallic ground state at integer filling and very large Coulomb repulsion. The first is a multiorbital Hubbard model with a Hund's coupling, where this physics has been widely studied and the new metallic state is called a Hund's metal, and the second is a SU(3) Hubbard model with a patterned single-particle potential designed to display a similar interaction-resistant metal in a set-up which can be implemented with SU($N$) ultracold atoms. With simple analytical arguments and exact numerical diagonalization of the Hamiltonians for a minimal three-site system, we demonstrate that the interaction-resistant metal emerges in both cases as a compromise between two different insulating solutions which are stabilized by different terms of the models. This provides a strong evidence that the Hund's metal is a specific realization of a more general phenomenon which can be realized in various strongly correlated systems., Comment: 11 pages, 11 figures

We study the massive point-vortex model introduced in Ref. [Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core., Comment: 10 pages, 5 figures

We investigate a notable class of states peculiar to a bosonic binary mixture featuring repulsive intraspecies and attractive interspecies couplings. We evidence that, for small values of the hopping amplitudes, one can access particular regimes marked by the fact that the interwell boson transfer occurs in a jerky fashion. This property is shown to be responsible for the emergence of a staircase-like structure in the phase diagram of a mixture confined in a ring trimer and to strongly resemble the mechanism of the superfluid-Mott insulator transition. Under certain conditions, in fact, we show that it is possible to interpret the interspecies attraction as an effective chemical potential and the supermixed soliton as an effective particle reservoir. Our investigation is developed both within a fully quantum approach based on the analysis of several quantum indicators and by means of a simple analytical approximation scheme capable of capturing the essential features of this ultraquantum effect., Comment: 16 pages, 10 figures

We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating box-like circular trap, i.e. states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully-analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying them their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting., Comment: 11 pages, 8 figures

We investigate the phase separation mechanism of bosonic binary mixtures in spatially-fragmented traps, evidencing the emergence of phases featuring a different degree of mixing. The analysis is initially carried out by means of a semiclassical approach which transparently shows the occurrence of critical phenomena. These predictions are actually corroborated by the study of genuinely quantum indicators, including, but not limited to, the energy levels' structure and the entanglement between the species. The scope of our work goes also beyond the ground state's properties, as it comprises excited states and the dynamical evolution thereof. In particular, after introducing an indicator to monitor the degree of mixing, we show that several dynamical regimes feature persistent demixing in spite of their remarkably chaotic character., Comment: 11 pages, 8 figures

We investigate the mechanism of formation of supermixed soliton-like states in bosonic binary mixtures loaded in ring lattices. We evidence the presence of a common pathway which, irrespective of the number of lattice sites and upon variation of the interspecies attraction, leads the system from a mixed and delocalized phase to a supermixed and localized one, passing through an intermediate phase where the supermixed soliton progressively emerges. The degrees of mixing, localization and quantum correlation of the two condensed species, quantified by means of suitable indicators commonly used in Statistical Thermodynamics and Quantum Information Theory, allow one to reconstruct a bi-dimensional mixing-supermixing phase diagram featuring two characteristic critical lines. Our analysis is developed both within a semiclassical approach capable of capturing the essential features of the two-step mixing-demixing transition and with a fully-quantum approach., Comment: 12 pages, 8 figures

We derive the complete mixing-demixing phase-diagram relevant to a bosonic binary mixture confined in a ring trimer and modeled within the Bose-Hubbard picture. The mixing properties of the two quantum fluids, which are shown to be strongly affected by the fragmented character of the confining potential, are evaluated by means of a specific indicator imported from Statistical Thermodynamics and are shown to depend only on two effective parameters incorporating the asymmetry between the heteronuclear species. To closely match realistic experimental conditions, our study is extended also beyond the pointlike approximation of potential wells by describing the systems in terms of two coupled Gross-Pitaevskii equations. The resulting mean-field analysis confirms the rich scenario of mixing-demixing transitions of the mixture and also constitutes an effective springboard towards a viable experimental realization. We additionally propose an experimental realization based on a realistic optical-tweezers system and on mixtures of bosonic $^{23}\mathrm{Na}$ and $^{39}\mathrm{K}$, thanks to the large tunability of their intra- and inter-species scattering lengths., Comment: 14 pages, 8 figures

We investigate several dynamical regimes characterizing a bosonic binary mixture loaded in a ring trimer, with particular reference to the persistence of demixing. The degree of phase separation is evaluated by means of the "Entropy of mixing", an indicator borrowed from Statistical Thermodynamics. Three classes of demixed stationary configurations are identified and their energetic and linear stability carefully analyzed. An extended set of trajectories originating in the vicinity of fixed points are explicitly simulated and chaos is shown to arise according to three different mechanisms. In many dynamical regimes, we show that chaos is not able to disrupt the order imposed by phase separation, i.e. boson populations, despite evolving in a chaotic fashion, do not mix. This circumstance can be explained either with energetic considerations or in terms of dynamical restrictions., Comment: 21 pages, 9 figures

Bosonic two-ring ladders constitute an important class of atomtronic circuits, where coherent current flows not only can offer a new insight into many-body physics, but also can play the role of actual degrees of freedom, and hence allow for a viable implementation of cold-atom based devices and qubit systems. In this work, we exhaustively investigate the ground state properties and the low-lying energy spectrum of two linearly coupled Bose-Hubbard rings. We show that the competition among interactions, intra- and inter-ring hopping processes gives place to a rather rich physical scenario, where Mott-like states and (different kinds of) superfluid-like states emerge. The latter ones depend also on the (in)commensurate filling of the atoms. Our analysis, carried out within a simple analytical framework and by means of the exact numerical diagonalization of the system Hamiltonian, provides one with a rather complete characterization of the static properties of the two-ring ladder, including, but not limited to, coherence, fragmentation, correlations, and entanglement. We complement our investigation by studying how these indicators depend on the commensurability of the total number of bosons with respect to the total number of sites and show that the two stacked rings are always entangled for an odd number of atoms., Comment: v2: improved version. Accepted for publication in Journal of Physics B

We show that, depending on the ratio between the inter- and the intra-species interactions, a binary mixture trapped in a three-well potential with periodic boundary conditions exhibits three macroscopic ground-state configurations which differ in the degree of mixing. Accordingly, the corresponding quantum states feature either delocalization or a Schr\"odinger cat-like structure. The two-step phase separation occurring in the system, which is smoothed by the activation of tunnelling processes, is confirmed by the analysis of the energy spectrum that collapses and rearranges at the two critical points. In such points, we show that also Entanglement Entropy, a quantity borrowed from quantum-information theory, features singularities, thus demonstrating its ability to witness the double mixining-demixing phase transition. The developed analysis, which is of interest to both the experimental and theoretical communities, opens the door to the study of the demixing mechanism in complex lattice geometries., Comment: 14 pages, 9 figures

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the bipartite residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerably good approximation of the entanglement entropy. Finally, we show that the effectiveness of bipartite residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates., Comment: 18 pages, 9 figures

We investigate the weak excitations of a system made up of two condensates trapped in a Bose-Hubbard ring and coupled by an interspecies repulsive interaction. Our approach, based on the Bogoliubov approximation scheme, shows that one can reduce the problem Hamiltonian to the sum of sub-Hamiltonians $\hat{H}_k$, each one associated to momentum modes $\pm k$. Each $\hat{H}_k$ is then recognized to be an element of a dynamical algebra. This uncommon and remarkable property allows us to present a straightforward diagonalization scheme, to find constants of motion, to highlight the significant microscopic processes, and to compute their time evolution. The proposed solution scheme is applied to a simple but still very interesting closed circuit, the trimer. The dynamics of low-energy excitations, corresponding to weakly-populated vortices, is investigated considering different choices of the initial conditions, and the angular-momentum transfer between the two condensates is evidenced. Finally, the condition for which the spectral collapse and dynamical instability are observed is derived analytically., Comment: 11 pages, 7 figures

We study the quantum dynamics of the Bose-Hubbard model on a ladder formed by two rings coupled by tunneling effect. By implementing the Bogoliubov approximation scheme, we prove that, despite the presence of the inter-ring coupling term, the Hamiltonian decouples in many independent sub-Hamiltonians $\hat{H}_k$ associated to momentum-mode pairs $\pm k$. Each sub-Hamiltonian $\hat{H}_k$ is then shown to be part of a specific dynamical algebra. The properties of the latter allow us to perform the diagonalization process, to find energy spectrum, the conserved quantities of the model, and to derive the time evolution of important physical observables. We then apply this solution scheme to the simplest possible closed ladder, the double trimer. After observing that the excitations of the system are weakly-populated vortices, we explore the corresponding dynamics by varying the initial conditions and the model parameters. Finally, we show that the inter-ring tunneling determines a spectral collapse when approaching the border of the dynamical-stability region., Comment: 14 pages, 9 figures