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We investigate the effects of a static impurity, modeled by a localized barrier, in a one-dimensional mesoscopic system comprised of strongly correlated repulsive SU($N$)-symmetric fermions. For a mesoscopic sized ring under the effect of an artificial gauge field, we analyze the particle density and the current flowing through the impurity at varying interaction strength, barrier height and number of components. We find a non-monotonic behaviour of the persistent current, due to the competition between the screening of the impurity, quantum fluctuations, and the phenomenon of fractionalization, a signature trait of SU($N$) fermionic matter-waves in mesoscopic ring potentials. This is also highlighted in the particle density at the impurity site. We show that the impurity opens a gap in the energy spectrum selectively, constrained by the total effective spin and interaction. Our findings hold significance for the fundamental understanding of the localized impurity problem and its potential applications for sensing and interferometry in quantum technology., Comment: 5 revtex pages, 3 figures

Many systems, classical or quantum, closed or open, exhibit universal statistical properties. Exciton-polariton condensates, being intrinsically driven-dissipative, offer a promising platform for observing non-equilibrium universal features. By conducting extensive numerical simulations of an incoherently pumped and interacting condensate coupled to an exciton reservoir we show that the effective nonlinearity of the condensate phase dynamics can be finely adjusted across a broad range, by varying the exciton-polariton interaction strength, allowing one to probe three main universal regimes with parameters accessible in current experiments: the weakly nonlinear Edwards-Wilkinson (EW) regime, where the phase fluctuations dominate, but the phase profile does not become rough, the strongly non-linear Kardar-Parisi-Zhang regime, where the condensate phase fluctuations grow in a superdiffusive manner leading to roughening of the phase, and a vortex-dominated phase emerging at stronger interactions, where both density and phase dynamics play significant roles. Our results provide a unified picture of the phase diagram of 2d exciton-polariton condensates under incoherent pumping, and shed light on recent experimental and numerical observations., Comment: 17 pages, 10 figures

We investigate the dynamics of one-dimensional SU(2) ultracold fermions near the Tonks-Girardeau limit, confined in a box potential. The system is driven out of equilibrium by initially preparing the two spin components in a fully separated configuration, and its evolution is described by the Hamiltonian in the presence of strong repulsive interactions. Building on the results in [arXiv:2302.02828, Phys$.$Rev. A, 107, L061301 (2023)], we extend the analysis to out-of-equilibrium dynamics, uncovering the emergence of time-dependent oscillating high-momentum tails in the momentum distribution. These oscillations, due to the finite size of the system, are governed by a nonlocal, high-order spin coherence term, whose amplitude and phase evolve over time. We show that this term initially grows as time to the power N/2 and subsequently follows the spin-mixing dynamics of the system. Notably, when the spin components are fully mixed, the amplitude of this border-to-border spin coherence reaches its maximum value.

We propose an alternative to the Bethe Ansatz method for strongly-interacting fermionic (or bosonic) mixtures on a ring. Starting from the knowledge of the solution for single-component non-interacting fermions (or strongly-interacting bosons), we explicitly impose periodic condition on the amplitudes of the spin configurations. This reduces drastically the number of independent complex amplitudes that we determine by constrained diagonalization of an effective Hamiltonian. This procedure allows us to obtain a complete basis for the exact low-energy many-body solutions for mixtures with a large number of particles, both for $SU(\kappa)$ and symmetry-breaking systems., Comment: 29 pages and 4 figures. Submission to SciPost

Multicomponent quantum mixtures in one dimension can be characterized by their symmetry under particle exchange. For a strongly interacting Bose-Bose mixture, we show that the time evolution of the momentum distribution from an initially symmetry-mixed state is quasiconstant for a SU(2) symmetry conserving Hamiltonian, while it displays large oscillations in time for the symmetry-breaking case where inter- and intraspecies interactions are different. Using the property that the momentum distribution operator at strong interactions commutes with the class-sum operator, the latter acting as a symmetry witness, we show that the momentum distribution oscillations correspond to symmetry oscillations, with a mechanism analogous to neutrino flavor oscillations.

We investigate the correlation properties in the steady state of driven-dissipative interacting bosonic systems in the quantum regime, as for example non-linear photonic cavities. Specifically, we consider the Bose-Hubbard model on a periodic chain and with spatially homogeneous one-body loss and pump within the Markovian approximation. The steady state corresponds to an infinite temperature state at finite chemical potential with diagonal spatial correlations. Nonetheless, we observe a nontrivial behaviour of the space-time two-point correlation function in the steady state, obtained by exact diagonalisation. In particular, we find that the decay width of the propagator is not only renormalised at increasing interactions, as it is the case of a single non-linear resonator, but also at increasing hopping strength. We then compute the full spectral function, finding that it contains both a dispersive free-particle like dispersion at low energy and a doublon branch at energy corresponding to the on-site interactions. We compare with the corresponding calculation for the ground state of a closed quantum system and show that the driven-dissipative nature - determining both the steady state and the dynamical evolution - changes the low-lying part of the spectrum, where noticeably, the dispersion is quadratic instead of linear at small wavevectors., Comment: 30 pages, 15 figures

We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this regime, the behaviour of the large wavelength modes is captured by the Kardar-Parisi-Zhang equation, determining universal scaling and statistical properties. We present numerical evidence of the existence of an additional scale-invariant regime, with dynamical scaling exponent $z=1$, emerging at scales which are intermediate between the microscopic, intrinsic to the modulational instability, and the macroscopic ones. We argue that this new regime is a signature of the universality class corresponding to the inviscid limit of the Kardar-Parisi-Zhang equation.

We study the localization dynamics of a SU(2) fermionic wavepacket launched in a (pseudo)random potential. We show that in the limit of strong inter-component repulsions, the total wavepacket exhibits a boomerang-like dynamics, returning near its initial position as expected for non-interacting particles, while separately each spin-component does not. This spin-charge separation effect occurs both in the infinite repulsive limit and at finite interactions. At infinite interactions, the system is integrable and thermalization cannot occur: the two spin-components push each other during the dynamics and their centers of mass stop further from each other than their initial position. At finite interactions, integrability is broken, the two spin-components oscillate and mix, with their center-of-mass positions converging very slowly to the center of mass of the whole system. This is a signature that the final localized state is a fully spin-mixed thermalized state.

In the absence of vortices or phase slips, the phase dynamics of exciton-polariton condensates was shown to map onto the Kardar-Parisi-Zhang (KPZ) equation, which describes the stochastic growth of a classical interface. This implies that the coherence of such non-equilibrium quasi-condensates decays in space and time following stretched exponentials, characterized by KPZ universal critical exponents. In this work, we focus on the time evolution of the average phase of a one-dimensional exciton-polariton condensate in the KPZ regime and determine the frequency of its evolution, which is given by the blueshift, i.e. the non-equilibrium analog of the chemical potential. We determine the stochastic corrections to the blueshift within Bogoliubov linearized theory and find that while this correction physically originates from short scale effects, and depends both on density and phase fluctuations, it can still be related to the effective large-scale KPZ parameters. Using numerical simulations of the full dynamics, we investigate the dependence of these blueshift corrections on both noise and interaction strength, and compare the results to the Bogoliubov prediction. Our finding contributes both to the close comparison between equilibrium and non-equilibrium condensates, and to the theoretical understanding of the KPZ mapping.

We consider a one-dimensional driven-dissipative exciton-polariton condensate under incoherent pump, described by the stochastic generalized Gross-Pitaevskii equation. It was shown that the condensate phase dynamics maps under some assumptions to the Kardar-Parisi-Zhang (KPZ) equation, and the temporal coherence of the condensate follows a stretched exponential decay characterized by KPZ universal exponents. In this work, we determine the main mechanisms which lead to the departure from the KPZ phase, and identify three possible other regimes: (i) a soliton-patterned regime at large interactions and weak noise, populated by localized structures analogue to dark solitons; (ii) a vortex-disordered regime at high noise and weak interactions, dominated by point-like phase defects in space-time; (iii) a defect-free reservoir-textured regime where the adiabatic approximation breaks down. We characterize each regime by the space-time maps, the first-order correlations, the momentum distribution and the density of topological defects. We thus obtain the phase diagram at varying noise, pump intensity and interaction strength. Our predictions are amenable to observation in state-of-art experiments with exciton-polaritons.

The elementary excitations in weakly interacting quantum fluids have a non-trivial nature which is at the basis of defining quantum phenomena such as superfluidity. These excitations and the physics they lead to have been explored in closed quantum systems at thermal equilibrium both theoretically within the celebrated Bogoliubov framework, and experimentally in quantum fluids of ultracold atoms. Over the past decade, the relevance of Bogoliubov excitations has become essential to understand quantum fluids of interacting photons. Their driven-dissipative character leads to distinct properties with respect to their equilibrium counterparts. For instance, the condensate coupling to the photonic vacuum environment leads to a non-zero generation rate of elementary excitations with many striking implications. In this work, considering that quantum fluids of light are often hosted in solid-state systems, we show within a joint theory-experiment analysis that the vibrations of the crystal constitute another environment that the condensate is fundamentally coupled to. This coupling leads to a unique heat transfer mechanism, resulting in a large generation rate of elementary excitations in typical experimental conditions, and to a fundamental non-zero contribution at vanishing temperatures. Our work provides a complete framework for solid-embedded quantum fluids of light, which is invaluable in view of achieving a regime dominated by photon vacuum fluctuations., Comment: Main text: 24 pages 6 figures, Supplementary Information : 4 pages, 3 figures

We discuss an interferometric scheme employing interference of bright solitons formed as specific bound states of attracting bosons on a lattice. We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102, 010403 (2009)] for using the scattering of a quantum matter-wave soliton on a barrier in order to create a coherent superposition state of the soliton being entirely to the left of the barrier and being entirely to the right of the barrier. In that proposal, it was assumed that the scattering is perfectly elastic, i.e.\ that the center-of-mass kinetic energy of the soliton is lower than the chemical potential of the soliton. Here we relax this assumption: By employing a combination of Bethe ansatz and DMRG based analysis of the dynamics of the appropriate many-body system, we find that the interferometric fringes persist even when the center-of-mass kinetic energy of the soliton is above the energy needed for its complete dissociation into constituent atoms., Comment: arXiv admin note: substantial text overlap with arXiv:2201.10479

The statistics of the fluctuations of quantum many-body systems are highly revealing of their nature. In driven-dissipative systems displaying macroscopic quantum coherence, as exciton polariton condensates under incoherent pumping, the phase dynamics can be mapped to the stochastic Kardar-Parisi-Zhang (KPZ) equation. However, in two dimensions (2D), it was theoretically argued that the KPZ regime may be hindered by the presence of vortices, and a non-equilibrium BKT behavior was reported close to condensation threshold. We demonstrate here that, when a discretized 2D polariton system is considered, universal KPZ properties can emerge. We support our analysis by extensive numerical simulations of the discrete stochastic generalized Gross-Pitaevskii equation. We show that the first-order correlation function of the condensate exhibits stretched exponential behaviors in space and time with critical exponents characteristic of the 2D KPZ universality class, and find that the related scaling function accurately matches the KPZ theoretical one, stemming from functional Renormalization Group. We also obtain the distribution of the phase fluctuations and find that it is non-Gaussian, as expected for a KPZ stochastic process., Comment: revised version, an appendix added, 14 pages, 8 figures

We study the equilibrium properties of a one-dimensional mixture of two Tonks-Girardeau gases on a ring geometry in the limit of strongly-repulsive inter-species interactions. We derive the exact many-body wavefunction and compare it to the $SU(2)$ solution where intra- and inter-species interactions are also diverging but equal. We focus on the role of the $SU(2)$-symmetry breaking on the behaviour of the large- and short-distance correlations by studying the zero-momentum occupation number and the Tan's contact from the asymptotic behavior of the momentum distribution. Although the symmetry is only weakly broken, it has important consequences on spin correlations in the system as the reduction by a factor of two of the zero-momentum occupation number with respect to the $SU(2)$ case in the thermodynamic limit and the decrease of the Tan's contact., Comment: 9 pages, 5 figures

We provide a measurement protocol to estimate 2- and 4-point fermionic correlations in ultra-cold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical landscapes, with high-resolution imaging systems such as quantum gas microscopes. We illustrate our results in the context of the variational quantum eigensolver algorithm for solving quantum chemistry problems.

We revisit the proposal of Castin and Weiss [Phys. Rev. Lett. vol. 102, 010403 (2009)] for using the scattering of a quantum matter-wave soliton on a barrier in order to create a coherent superposition state of the soliton being entirely to the left of the barrier and being entirely to the right of the barrier. In that proposal, is was assumed that the scattering is perfectly elastic, i.e. that the center-of-mass kinetic energy of the soliton is lower than the chemical potential of the soliton. Here we relax this assumption. Also, we introduce an interferometric scheme, which uses interference of soltions, that can be used to detect the degree of coherence between the reflected and transmitted part of the soliton. Using exact diagonalization, we numerically simulate a complete interferometric cycle for a soliton consisting of six atoms. We find that the interferometric fringes persist even when the center-of-mass kinetic energy of the soliton is above the energy needed for complete dissociation of the soliton into constituent atoms., Comment: 9 pages, 3 figures

Quantum correlations can be used as a resource for quantum computing, eg for quantum state manipulation, and for quantum sensing, eg for creating non-classical states which allow to achieve the quantum advantage regime. This review collects the predictions coming from a family of exact solutions which allows to describe the many-body wavefunction of strongly correlated quantum fluids confined by a tight waveguide and subjected to any form of longitudinal confinement. It directly describes the experiments with trapped ultracold atoms where the strongly correlated regime in one dimension has been achieved. The exact solution applies to bosons, fermions and mixtures. It allows to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach. It also predicts the exact quantum dynamics at all the times, including the small oscillations regime yielding the collective modes of the system and the large quench regime where the system parameters are changed considerably. The solution can be extended to describe finite-temperature conditions, spin and magnetization effects. The review illustrates the idea of the solution, presents the key theoretical achievements and the main experiments on strongly correlated one-dimensional quantum gases., Comment: 22 pages, 19 figures

Revealing universal behaviors is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces, of interfaces in bacterial colonies, and spin transport in quantum magnets all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. This universality stems from a common underlying effective dynamics governed by the non-linear stochastic Kardar-Parisi-Zhang (KPZ) equation. Recent theoretical works suggest that this dynamics also emerges in the phase of out-of-equilibrium systems displaying macroscopic spontaneous coherence. Here, we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space-time scaling laws, combined with a theoretical microscopic analysis that consistently reveals the other key signatures of this universality class, together with the possible resilience of KPZ dynamics to the presence of space-time vortices. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a new paradigm for exploring universal behaviors in open systems.

We study the spin-mixing dynamics of a one-dimensional strongly repulsive Fermi gas under harmonic confinement. By employing a mapping onto an inhomogeneous isotropic Heisenberg model and the symmetries under particle exchange, we follow the dynamics till very long times. Starting from an initial spin-separated state, we observe superdiffusion, spin-dipolar large amplitude oscillations and thermalization. We report a universal scaling of the oscillations with particle number N^1/4, implying a slow-down of the motion and the decrease of the zero-temperature spin drag coefficient as the particle number grows., Comment: 10 pages, 7 figures

Atomtronics is an emerging field that aims to manipulate ultracold atom moving in matter wave circuits for both fundamental studies in quantum science and technological applications. In this colloquium, we review recent progress in matter-wave circuitry and atomtronics-based quantum technology. After a short introduction to the basic physical principles and the key experimental techniques needed to realize atomtronic systems, we describe the physics of matter-waves in simple circuits such as ring traps and two-terminal systems. The main experimental observations and outstanding questions are discussed. We also present possible applications to a broad range of quantum technologies, from quantum sensing with atom interferometry to future quantum simulation and quantum computation architectures., Comment: 33 revtex pages; 10 figs. To be published in Reviews of Modern Physics

We study the Bose polaron problem in a nonequilibrium setting, by considering an impurity embedded in a quantum fluid of light realized by exciton-polaritons in a microcavity, subject to a coherent drive and dissipation on account of pump and cavity losses. We obtain the polaron effective mass, the drag force acting on the impurity, and determine polaron trajectories at a semiclassical level. We find different dynamical regimes, originating from the unique features of the excitation spectrum of driven-dissipative polariton fluids, in particular a non-trivial regime of acceleration against the flow. Our work promotes the study of impurity dynamics as an alternative testbed for probing superfluidity in quantum fluids of light., Comment: Submitted to SciPost Physics; corrected typos, added references, results are unchanged

Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum eigensolver is one of the aforementioned algorithms designed to determine the ground-state of many-body Hamiltonians. Here, we apply the variational quantum eigensolver to study the ground-state properties of $N$-component fermions. With such knowledge, we study the persistent current of interacting SU($N$) fermions, which is employed to reliably map out the different quantum phases of the system. Our approach lays out the basis for a current-based quantum simulator of many-body systems that can be implemented on noisy intermediate-scale quantum computers., Comment: 24 pages, 8 figures

The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement in quantum many-body-systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins., Comment: 7 + 10 pages with 3 + 3 figures. Accepted version with additional analytical expressions for statistical errors of arbitrary order polynomials of the density matrix estimated via classical shadows. Code available at https://github.com/bvermersch/RandomMeas

In quantum mechanics, each particle is described by a complex valued wave-function characterized by amplitude and phase. When many particles interact each other, cooperative phenomena give rise to a quantum many-body state with a specific quantum coherence. What is the interplay between single-particle's phase coherence and many-body quantum coherence? Over the years, such question has been object of profound analysis in quantum physics. Here, we demonstrate how the time-dependent interference formed by releasing an interacting degenerate Fermi gas from a specific matter-wave circuit in an effective magnetic field can tell apart the two notions. Single-particle phase coherence, indicated by the first-order correlator, and many-body quantum coherence, indicated by the density-density correlator, are displayed as distinct features of the interferogram. Single particle phase coherence produces spiral interference of the Fermi orbitals at intermediate times. Many-body quantum coherence emerges as long times interference. The interplay between single-particle coherence and many-body coherence is reflected in a stepwise dependence of the interference pattern on the effective magnetic field., Comment: 13 pages, 10 figures

We study a quantum many-body system of attracting bosons confined in a ring-shaped potential and interrupted by a weak link. With such architecture, the system defines atomtronic quantum interference devices harnessing quantum solitonic currents. We demonstrate that the system is characterized by the specific interplay between the interaction and the strength of the weak link. In particular, we find that, depending on the operating conditions, the current can be a universal function of the relative size between the strength of the impurity and interaction. The low lying many-body states are studied through a quench dynamical protocol that is the atomtronic counterpart of Rabi interferometry. With this approach, we demonstrate how our system defines a two level system of coupled solitonic currents. The current states are addressed through the analysis of the momentum distribution.

Exciton-polariton condensates under driven-dissipative conditions are predicted to belong to the Kardar-Parisi-Zhang (KPZ) universality class, the dynamics of the condensate phase satisfying the same equation as for classical stochastic interface growth at long distance. We show that by engineering an external confinement for one-dimensional polaritons we can access two different universality sub-classes, which are associated to the flat or curved geometry for the interface. Our results for the condensate phase distribution and correlations match with great accuracy with the exact theoretical results for KPZ: the Tracy-Widom distributions (GOE and GUE) for the one-point statistics, and covariance of Airy processes (Airy1 and Airy2) for the two-point statistics. This study promotes the exciton-polariton system as a compelling platform to investigate KPZ universal properties., Comment: 16 pages, 14 figures. Updated Fig. 2 and added Fig. 5 and Fig. 6, minor review done

We study the persistent currents of an attractive Fermi gas confined in a tightly-confining ring trap and subjected to an artificial gauge field all through the BCS-BEC crossover. At weak attractions, on the BCS side, fermions display a parity effect in the persistent currents, ie their response to the gauge field is paramagnetic or diamagnetic depending on the number of pairs on the ring. At resonance and on the BEC side of the crossover we find a doubling of the periodicity of the ground-state energy as a function of the artificial gauge field and disappearance of the parity effect, indicating that persistent currents can be used to infer the formation of tightly-bound bosonic pairs. Our predictions can be accessed in ultracold atoms experiments through noise interferograms., Comment: 7 pages, 5 figures

We propose a protocol for creating moving, robust dispersive shock waves in interacting one-dimensional Bose fluids. The fluid is prepared in a moving state by phase imprinting and sent against the walls of a box trap. We demonstrate that the thus formed shock wave oscillates for several periods and is robust against thermal fluctuations. We show that this large amplitude dynamics is universal across the whole spectrum of the interatomic interaction strength, from weak to strong interactions, and it is fully controlled by the sound velocity inside the fluid. Our work provides a generalization of the dispersive-shock-wave paradigm to the many-body regime. The shock waves we propose are within reach for ultracold atom experiments.

In transition metal dichalcogenides layers of atomic scale thickness, the electron-hole Coulomb interaction potential is strongly influenced by the sharp discontinuity of the dielectric function across the layer plane. This feature results in peculiar non-hydrogenic excitonic states, in which exciton-mediated optical nonlinearities are predicted to be enhanced as compared to their hydrogenic counterpart. To demonstrate this enhancement, we performed optical transmission spectroscopy of a MoSe$_2$ monolayer placed in the strong coupling regime with the mode of an optical microcavity, and analyzed the results quantitatively with a nonlinear input-output theory. We find an enhancement of both the exciton-exciton interaction and of the excitonic fermionic saturation with respect to realistic values expected in the hydrogenic picture. Such results demonstrate that unconventional excitons in MoSe$_2$ are highly favourable for the implementation of large exciton-mediated optical nonlinearities, potentially working up to room temperature.

We theoretically investigate how the presence of a reservoir of incoherent excitations affects the superfluidity properties of resonantly driven polariton fluids. While in the absence of reservoir the two cases of a defect moving in a fluid at rest and of a fluid flowing against a static defect are linked by a formal Galilean transformation, here the reservoir defines a privileged reference frame attached to the semiconductor structure and causes markedly different features between the two settings. The consequences on the critical velocity for superfluidity are highlighted and compared to experiments in resonantly driven excitons polaritons., Comment: 13 pages, 7 figures

We propose a method to generate multi-mode N00N states with arrays of ultracold atoms. Our protocol requires a strong relative offset among the wells and a drive of the interparticle interaction at a frequency resonant with the offsets. The proposal is demonstrated by a numerical and a Floquet analysis of the quantum dynamics of a ring-shaped atomtronics circuit made of M weakly coupled optical traps. We generate a hierarchy of energy scales down to very few low-energy states where N00N dynamics takes place, making multi-mode N00N states appear at nearly regular time intervals. The production of multi-mode N00N states can be probed by time-of-flight imaging. Such states may be used to build a multiple beam splitter., Comment: 15 pages, 14 figures. Revised manuscript with new material

We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave Ansatz of the wave function. We obtain energies and correlation functions of the system both for repulsive and attractive interactions. In contrast with the one-dimensional continuous theory described by the Lieb-Liniger model, in the lattice case we prove that the center of mass of the two particles is coupled with its relative coordinate. Distinctive features clearly emerge in the persistent current of the system. While for repulsive bosons the persistent current displays a periodicity given by the standard flux quantum for any interaction strength, in the attractive case the flux quantum becomes fractionalized in a manner that depends on the interaction. We also study the density after the long time expansion of the system which provides an experimentally accessible route to detect persistent currents in cold atom settings. Our results can be used to benchmark approximate schemes for the many-body problem.

We consider a system of weakly interacting bosons confined on a planar double lattice ring subjected to two artificial gauge fields. This system is known to display three phases, the Meissner phase where the flow of particles is carried at the edges of the system without transverse current, a vortex phase characterized by non-zero transverse current, and a biased-ladder phase, characterized by an imbalance of the population of the two rings. We use the Bogoliubov approximation to determine the excitation spectrum in the three phases, the dynamic structure factor and the quantum fluctuation corrections to the first-order correlation function. Our analysis reveals supersolid features as well as Josephson modes, corresponding to out-of-phase modes of the finite ring., Comment: 11 pages, 12 figures

We study the time evolution of a supercurrent imprinted on a one-dimensional ring of interacting bosons in the presence of a defect created by a localized barrier. Depending on interaction strength and temperature, we identify various dynamical regimes where the current oscillates, is self-trapped or decays with time. We show that the dynamics are captured by a dual Josephson model and involve phase slips of thermal or quantum nature., Comment: 10 pages, 3 figures

Quantum mechanics is characterized by quantum coherence and entanglement. After having discovered how these fundamental concepts govern physical reality, scientists have been devoting intense efforts to harness them to shape future science and technology. This is a highly nontrivial task because most often quantum coherence and entanglement are difficult to access. Here, we demonstrate the enhancement of the sensitivity of a quantum many-body system with specific coherence and entanglement properties. Our physical system is made of strongly correlated attracting neutral bosons flowing in a ring-shaped potential of mesoscopic size. Because of attractive interactions, quantum analogs of bright solitons are formed. As a genuine quantum-many-body feature, we demonstrate that angular momentum fractionalization occurs. As a consequence, the matter-wave current in our system can react to very small changes of rotation or other artificial gauge fields. We work out a protocol to entangle such quantum solitonic currents, allowing them to operate rotation sensors and gyroscopes to Heisenberg-limited sensitivity., Comment: 8 pages, 4 figures

Exciton-polaritons in semiconductor microcavities constitute the archetypal realization of a quantum fluid of light. Under coherent optical drive, remarkable effects such as superfluidity, dark solitons or the nucleation of hydrodynamic vortices have been observed. These phenomena can be all understood as a specific manifestation of collective excitations forming on top of the polariton condensate. In this work, we performed a Brillouin scattering experiment to measure their dispersion relation $\omega(\mathbf{k})$ directly. The result, such as a speed of sound which is apparently twice too low, cannot be explained upon considering the polariton condensate alone. In a combined theoretical and experimental analysis, we demonstrate that the presence of a reservoir of long-lived excitons interacting with polaritons has a dramatic influence on the nature and characteristic of the quantum fluid, and that it explains our measurement quantitatively. This work clarifies the role of such a reservoir in the different polariton hydrodynamics phenomena occurring under resonant optical drive. It also provides an unambiguous tool to determine the condensate-to-reservoir fraction in the quantum fluid, and sets an accurate framework to approach novel ideas for polariton-based quantum-optical applications.

We study the ground state of a bosonic ring ladder under a gauge flux in the vortex phase, corresponding to the case where the single-particle dispersion relation has two degenerate minima. By combining exact diagonalization and an approximate fermionization approach we show that the ground state of the system evolves from a fragmented state of two single-particle states at weak interparticle interactions to a fragmented state of two Fermi seas at large interactions. Fragmentation is inferred from the study of the eigenvalues of the reduced single-particle density matrix as well as from the calculation of the fidelity of the states. We characterize these nonclassical states by the momentum distribution, the chiral currents and the current-current correlations.

We consider molecules made of two one-dimensional short-range-interacting bosonic atoms. We show that in the process of scattering of these molecules off a narrow barrier, odd incident waves produce \emph{no unbound atoms, even when the incident energy exceeds the dissociation threshold}. This effect is a consequence of a prohibition on chemical reactions acting in a generally unphysical Bethe Ansatz integrable system of a $C_{2}$-type, with which our system shares the spatially odd eigenstates. We suggest several experimental implementations of the effect. We also propose to use the monomer production as an alternative read-out channel in an atom interferometer: unlike in the standard interferometric schemes, no spatial separation of the output channels will be required.

We show that the contact parameter of N harmonically-trapped interacting 1D bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N-body effects can be almost factorized. The small deviations observed between our analytical results and DMRG calculations are more pronounced when the interaction energy is maximal (i.e. at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe Ansatz. The rescaled two-body solution is so close to the exact ones, that is possible, within a simple expression interpolating the rescaled two-boson result to the local-density, to obtain N-boson contact and ground state energy functions in very good agreement with DMRG calculations. Our results suggest a change of paradigm in the study of interacting quantum systems, giving to the contact parameter a more fundamental role than energy., Comment: 7 pages, 4 figures. Revised version

We study an ultracold atomic gas with attractive interactions in a one-dimensional optical lattice. We find that its excitation spectrum displays a quantum soliton band, corresponding to $N$-particle bound states, and a continuum band of other, mostly extended, states. For a system of a finite size, the two branches are degenerate in energy for weak interactions, while a gap opens above a threshold value for the interaction strength. We find that the interplay between degenerate extended and bound states has important consequences for both static and dynamical properties of the system. In particular, the solitonic states turn out to be protected from spatial perturbations and random disorder. We discuss how such dynamics implies that our system effectively provides an example of a quantum many-body system that, with the variation of the bosonic lattice filling, crosses over from integrable non-ergodic to non-integrable ergodic dynamics, through non-integrable non-ergodic regimes., Comment: To be published in Physical Review Letters

Frank W. J. Hekking performed his PhD work on "Aspects of Electron Transport in Semiconductor Nanostructures" at the TU Delft in 1992. He then worked as a postdoc at the University of Karlsruhe, the University of Minnesota, the Cavendish Laboratory at the University of Cambridge, and the Ruhr University at Bochum. In 1999 he joined the LPMMC (Laboratoire de Physique et Mod\' elisation des Milieux Condens\' es) in Grenoble and was appointed Professor at the Universit\' e Joseph Fourier and afterwards Universit\' e Grenoble Alpes. Frank Hekking was nominated as a member of the Institut Universitaire de France, for the periods 2002-2007 and 2012-2017. This review provides an overview of his scientific contributions to several fields of mesoscopic electron transport and superconductivity as well as atomic gases, and is organized along sections describing the different themes.

The universal Tan relations connect a variety of microscopic features of many-body quantum systems with two-body contact interactions to a single quantity, called the contact. The latter has become pivotal in the description of quantum gases.We provide a complete characterization of the Tan contact of the harmonically trapped Lieb-Liniger gas for arbitrary interactions and temperature.Combining thermal Bethe ansatz, local-density approximation, and exact quantum Monte Carlo calculations,we show that the contact is a universal function of only two scaling parameters, and determine the scaling function.We find that the temperature dependence of the contact, or equivalently the interaction dependence of the entropy, displays a maximum. The presence of this maximum provides an unequivocal signature of the crossover to the fermionized regime and it is accessible in current experiments.

We consider a system of weakly interacting bosons confined on a planar double ring lattice subjected to two artificial gauge fields. We determine its ground state by solving coupled discrete non-linear Schr\"odinger equations at mean field level. At varying inter-ring tunnel coupling, flux and interactions we identify the vortex, Meissner and biased-ladder phases also predicted for a bosonic linear ladder by a variational Ansatz. We also find peculiar features associated to the ring geometry, in particular parity effects in the number of vortices, and the appearance of a single vortex in the Meissner phase. We show that the persistent currents on the rings carry precise information on the various phases. Finally, we propose a way of observing the Meissner and vortex phases via spiral interferogram techniques.

Exciton-polaritons under driven-dissipative conditions exhibit a condensation transition which belongs to a different universality class than equilibrium Bose-Einstein condensates. By numerically solving the generalized Gross-Pitaevskii equation with realistic experimental parameters, we show that one-dimensional exciton-polaritons display fine features of Kardar-Parisi-Zhang (KPZ) dynamics. Beyond the scaling exponents, we show that their phase distribution follows the Tracy-Widom form predicted for KPZ growing interfaces. We moreover evidence a crossover to the stationary Baik-Rains statistics. We finally show that these features are unaffected on a certain timescale by the presence of a smooth disorder often present in experimental setups., Comment: 4 pages, 4 figures

We consider a one-dimensional bosonic gas on a ring lattice, in the presence of a localized barrier, and under the effect of an artificial gauge field. By means of exact diagonalization we study the persistent currents at varying interactions and barrier strength, for various values of lattice filling. While generically the persistent currents are strongly suppressed in the Mott insulator phase, they show a resonant behaviour when the barrier strength becomes of the order of the interaction energy. We explain this phenomenon using an effective single-particle model. We show that this effect is robust at finite temperature, up the temperature scale where persistent currents vanish., Comment: 8 pages, 7 figures; added refs and Editors' teaser

We consider multi-component quantum mixtures (bosonic, fermionic, or mixed) with strongly repulsive contact interactions in a one-dimensional harmonic trap. In the limit of infinitely strong repulsion and zero temperature, using the class-sum method, we study the symmetries of the spatial wave function of the mixture. We find that the ground state of the system has the most symmetric spatial wave function allowed by the type of mixture. This provides an example of the generalized Lieb-Mattis theorem. Furthermore, we show that the symmetry properties of the mixture are embedded in the large-momentum tails of the momentum distribution, which we evaluate both at infinite repulsion by an exact solution and at finite interactions using a numerical DMRG approach. This implies that an experimental measurement of the Tan's contact would allow to unambiguously determine the symmetry of any kind of multi-component mixture., Comment: 19 pages, 6 figures

Semiconductor microcavities in the strong-coupling regime exhibit an energy scale in the THz frequency range, which is fixed by the Rabi splitting between the upper and lower exciton-polariton states. While this range can be tuned by several orders of magnitude using different excitonic medium, the transition between both polaritonic states is dipole forbidden. In this work we show that in Cadmium Telluride microcavities, the Rabi-oscillation driven THz radiation is actually active without the need for any change in the microcavity design. This feature results from the unique resonance condition which is achieved between the Rabi splitting and the phonon-polariton states, and leads to a giant enhancement of the second order nonlinearity., Comment: 6 pages, 2 figures

We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the Lieb-Liniger model of $\delta$-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasi-momenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength $\gamma_c\simeq 3.816$, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths.

We theoretically consider ultracold polar molecules in a wave guide. The particles are bosons, they experience a periodic potential due to an optical lattice oriented along the wave guide and are polarised by an electric field orthogonal to the guide axis. The array is mechanically unstable by opening the transverse confinement in the direction orthogonal to the polarizing electric field and can undergo a transition to a double-chain (zigzag) structure. For this geometry we derive a multi-mode generalized Bose-Hubbard model for determining the quantum phases of the gas at the mechanical instability taking into account the quantum fluctuations in all directions of space. Our model limits the dimension of the numerically relevant Hilbert subspace by means of an appropriate decomposition of the field operator, which is obtained from a field theoretical model of the linear-zigzag instability. We determine the phase diagrams of small systems using exact diagonalization and find that, even for tight transverse confinement, the aspect ratio between the two transverse trap frequencies controls not only the classical but also the quantum properties of the ground state in a non-trivial way. Convergence tests at the linear-zigzag instability demonstrate that our multi-mode generalized Bose-Hubbard model can catch the essential features of the quantum phases of dipolar gases in confined geometries with a limited computational effort., Comment: 11 pages, 7 figures