We study one- and two-magnon dynamics in a spin-$1/2$ XX chain coupled to a tunable Bose-Hubbard bath. The XX Hamiltonian transports the magnons, while the bath dresses their motion and mediates an effective attraction. A single magnon forms a mobile polaron whose retarded bosonic cloud reduces its velocity below the static Lang-Firsov prediction and generates magnon-boson entanglement. In the weak-dressing, off-resonant mobile regime, the residual velocity deficit and entanglement are governed by the excitation weight of the cloud, as captured by perturbation theory and tensor network-based real-time simulations. Transport therefore provides a model-calibrated proxy for entanglement without joint-state reconstruction. When two clouds overlap, the bath mediates a finite-range attraction, yielding finite-size evidence for a compact two-magnon bound state and a transient post-scattering signature. On-site bath interactions suppress local boson number fluctuations and stiffen the bath response, reducing entanglement and weakening ground-state binding. Bath deformability thus emerges as a common control parameter for magnon transport, entanglement, and bath-mediated pairing.
We study one- and two-magnon dynamics in a spin-1/2 XX chain coupled to a tunable Bose-Hubbard bath. The XX Hamiltonian transports the magnons, while the bath dresses their motion and mediates an effective attraction. A single magnon forms a mobile polaron whose retarded bosonic cloud reduces its velocity below the static Lang-Firsov prediction and generates magnon-boson entanglement. In the weak-dressing, off-resonant mobile regime, the residual velocity deficit and entanglement are governed by the excitation weight of the cloud, as captured by perturbation theory and tensor network-based real-time simulations. Transport therefore provides a model-calibrated proxy for entanglement without joint-state reconstruction. When two clouds overlap, the bath mediates a finite-range attraction, yielding finite-size evidence for a compact two-magnon bound state and a transient post-scattering signature. On-site bath interactions suppress local boson number fluctuations and stiffen the bath response, reducing entanglement and weakening ground-state binding. Bath deformability thus emerges as a common control parameter for magnon transport, entanglement, and bath-mediated pairing.
We investigate how the coherence and spatial dressing of a single impurity evolve in the two-dimensional Bose-Hubbard model when the impurity couples attractively to the bath. Using large-scale, sign-problem-free worm-algorithm quantum Monte Carlo, we measure the impurity winding, bath superfluid response and compressibility, and impurity-bath density correlations. In a compressible superfluid bath (Ub/t=13.3), strengthening attraction drives an interaction-controlled \emph{winding-collapse self-trapping crossover}: a mobile light polaron evolves continuously into a heavy polaron and ultimately into a bound cluster with vanishing winding, while the bath remains globally superfluid. In incompressible Mott-insulating baths, by contrast, extended density rearrangements are suppressed and the dressing cloud collapses; we compare the resulting short-range deformation patterns for both attractive and repulsive couplings. Across the SF-MI transition at fixed moderate attraction (Uib/t=−8.0), the impurity crosses over from a mobile polaron with an extended deformation cloud to a nearly free defect with minimal dressing in the Mott background; for this coupling it does not lock into a fully self-trapped defect even deep in the insulator. Together with our companion Letter [Impurity Self-Trapping in Lattice Bose systems] on repulsive couplings, these results provide a unified microscopic picture of impurity self-trapping in correlated lattice bosons, connecting interaction-driven winding collapse in the superfluid to compressibility-controlled undressing across the SF-MI transition.
The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fröhlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov approximation which includes the local repulsion between bosons and thereby stabilizes the Bose polaron even near and beyond the scattering resonance. We show that the Bose polaron energy remains bounded from below across the resonance and the size of the polaron dressing cloud stays finite. Our results demonstrate how the dressing cloud replaces the attractive impurity potential with an effective many-body potential that excludes binding. We find that at resonance, including the effects of boson repulsion, the polaron energy depends universally on the effective range. Moreover, while the impurity contact is strongly peaked at positive scattering length, it remains always finite. Our solution highlights how Bose polarons are self-stabilized by repulsion, providing a mechanism to understand quench dynamics and nonequilibrium time evolution at strong coupling.
We map out the global phase diagram of a single mobile impurity in the two-dimensional Bose-Hubbard model, spanning the bath evolution from a compressible superfluid (SF) to an incompressible Mott insulator (MI) and the full range of impurity-bath coupling. Using sign-problem-free worm-algorithm quantum Monte Carlo, we identify two distinct self-trapping mechanisms that organize the entire diagram. In the compressible SF, increasing impurity-bath coupling ∣Uib∣ drives an interaction-driven self-trapping crossover signaled by a collapse of the \emph{impurity} winding number: a light, extended polaron evolves continuously into a heavy polaron and ultimately into a self-trapped state -- a repulsive \emph{saturated bubble} or an attractive \emph{bound cluster} -- even while the bath remains globally superfluid, demonstrating self-trapping without any bath phase transition. By contrast, when the bath is tuned across the SF-MI transition at fixed Uib, localization is compressibility controlled. The vanishing bath compressibility quenches long-wavelength density redistribution and suppresses polaronic dressing, converting the SF polaron into a weakly dressed, nearly free defect upon entering the MI when ∣Uib∣≤8.0. Then increasing ∣Uib∣ triggers a distinct Mott-specific route: the impurity binds a quantized vacancy or particle excitation, manifested by discrete changes ΔNb=±1 in the total bath occupation. Together, our results provide a unified microscopic picture of impurity self-trapping in correlated lattice bosons, governed by winding collapse in the SF and by compressibility loss and defect quantization across the SF-MI boundary.
We investigate the zero-temperature properties of a mobile impurity immersed in a bath of bosonic particles confined to a square lattice. We analyze the regimes of attractive and repulsive coupling between the impurity and the bath particles for different strengths of boson-boson interactions in the bath, using exact large-scale quantum Monte-Carlo simulations in the grand canonical ensemble. For weak coupling, the polaron mass ratio is found to decrease around the Mott insulator (MI) to superfluid (SF) transition of the bath, as predicted by recent theory, confirming the possible use of the impurity as a probe for the transition. For strong coupling in the MI regime, instead, the impurity is found to modify the bath density by binding to an extra bath particle or a hole, depending on the sign of the polaron-bath interactions. While the binding prevent the aforementioned use of the polaron mass ratio as an MI-SF transition probe, we show that it can be used instead as a probe of the binding itself. Our exact numerical results provide a benchmark for comparing lattice Bose polaron theories and are relevant for experiments with cold atoms trapped in optical lattices, where the presence of a confining harmonic potential can be modeled by a slowly varying local chemical potential.
The most recent advances in the ultracold atoms experimental techniques allowed the production of the ultracold gases mixtures in the laboratory.Motivated by these developments, in this project we study systems involving two ultracold atoms mixtures.In the first part, we consider a Bose-Einstein condensate (BEC) with a vortex lattice weakly interacting with another utracold dilute bosonic gas.We apply the Bose-Hubbard (BH) model to describe the atoms of the minority species trapped in the vortex lattice.As occurs in a static optical lattice, we predict the quantum phase transition between the Mott insulator to superfluid phases, which now can be controlled by changing the intra and inter-species scattering length.Considering the intrinsic lattice dynamics, the Tkachenko modes of the vortex lattice, we derive an extended BH Hamiltonian and analyzed new properties in the phase diagram that arise from a long-range attractive potential and density-dependent hopping.In the second part, we study the properties of a mobile impurity living in two dimensions and interacting with a 2 and 3 BEC cloud.The resulting impurity-bath interaction leads to the formation of a polaron (particle "dressed" by the phonon excitations of the BEC), which is characterized by its spectral function.We determine the energy dispersion, spectral weight, effective mass and lifetime of the polaron.These analysis allowed us to identify a dissipative regime for higher impurity velocities, with an increasing scattering rate of phonons.In addition, we observe a self-localization regime for lower impurity velocities which may be a signature for molecular formation.In spite of qualitatively similar results obtained for the 2 and 3 bath, we had differences related to the self-localization and dissipation limits, that allowed us to conclude that a 2 BEC bath would be a better candidate to observe stable quasi-particle properties.
Predicting the emergent properties of impurities immersed in a quantum bath is a fundamental challenge that can defy quasiparticle treatments. Here, we measure the spectral properties and real-time dynamics of mobile impurities injected into a weakly interacting homogeneous Bose-Einstein condensate, using two broad Feshbach resonances to tune both the impurity-bath and intrabath interactions. For attractive impurity-bath interactions, the impurity spectrum features a single branch, which away from the resonance corresponds to a well-defined attractive polaron; near the resonance, we observe dramatic broadening of this branch, suggesting a breakdown of the quasiparticle picture. For repulsive impurity-bath interactions, the spectrum features two branches: the attractive branch that is dominated by excitations with energy close to that of the Feshbach dimer, but has a many-body character, and the repulsive polaron branch. Our measurements show that the behavior of impurities in weakly interacting baths is remarkably universal, controlled only by the bath density and a single dimensionless interaction parameter.