Abstract We report a comprehensive study of the ground-state properties of one and two bosonic impurities immersed in small one-dimensional optical lattices loaded with a few interacting bosons. We model the system with a two-component Bose–Hubbard model and solve the problem numerically by means of the exact diagonalization method. We report binding energies of one and two impurities across the superfluid (SF) to Mott-insulator transition and confirm the formation of two-body bound states of impurities induced by repulsive interactions. In particular, we found that an insulator bath induces tightly bound di-impurity dimers, whereas a SF bath induces shallower bound states.
We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.
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.
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 study the formation of bound states in a binary mixture of a few bosons in small square optical lattices. Using the exact diagonalization method, we find that bound clusters of all available bosons can form. We provide a comprehensive numerical examination of these bound states for a wide range of repulsive intraspecies and attractive interspecies interactions. In contrast to binary mixtures in one-dimensional chains, we reveal that the binding energy of the clusters shows a nonmonotonic dependence on the interspecies interaction strengths for small tunneling rates, developing a local minimum for intermediate attractive interactions. The findings of this work highlight the difference between the binding mechanisms of binary bosonic mixtures in one- and higher-dimensional lattices.
This work examines a mobile impurity interacting with a bath of a few spin- ↑ and spin- ↓ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method, where the system is modeled by a three-component Fermi Hubbard Hamiltonian. We find that in addition to the standard phase separation between a strongly repulsive impurity and the bath, a strongly attractive impurity also phase separates with the fermionic holes due to the particle-hole symmetry. Furthermore, we find that the impurity can show an oscillatory pattern in its density for intermediate attractive and repulsive bath-impurity interactions, which are induced by Friedel oscillations in the finite-size fermionic bath. This rich behavior of the impurity could be probed with fermionic ultracold mixtures in optical lattices.