Lattice impurities have recently emerged as a platform in which polarons unveil new quantum many-body states absent in free space and can serve to probe strongly correlated matter. In this work, we investigate two-dimensional lattice polarons with strong on-site repulsion and tunable nearest-neighbor interactions using a variational approach including up to one excitation of the medium. We show that extended interactions qualitatively modify the quasiparticle structure beyond the conventional attractive and repulsive polaron picture. A direct analysis of the eigenvalue spectrum reveals the presence of dark impurity states, orthogonal to the bare impurity and therefore spectroscopically dark. These states exhibit nontrivial internal structure, including dipolar symmetries in real space. Our results demonstrate that long-range interactions generate multiple quasiparticle excitations with distinct symmetry properties, highlighting the crucial role of interaction range and lattice geometry. This work opens new avenues for probing hidden quasiparticle states in lattice systems through spectroscopic and wave-function-resolved measurements.
Lattice impurities have recently emerged as a platform in which polarons unveil new quantum many-body states absent in free space and can serve to probe strongly correlated matter. In this work, we investigate two-dimensional lattice polarons with strong on-site repulsion and tunable nearest-neighbor interactions using a variational approach including up to one excitation of the medium. We show that extended interactions qualitatively modify the quasiparticle structure beyond the conventional attractive and repulsive polaron picture. A direct analysis of the eigenvalue spectrum reveals the presence of dark impurity states, orthogonal to the bare impurity and therefore spectroscopically dark. These states exhibit nontrivial internal structure, including dipolar symmetries in real space. Our results demonstrate that long-range interactions generate multiple quasiparticle excitations with distinct symmetry properties, highlighting the crucial role of interaction range and lattice geometry. This work opens new avenues for probing hidden quasiparticle states in lattice systems through spectroscopic and wave-function-resolved measurements.
Quasiparticles and their interactions are a key part of our understanding of quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced our understanding of isolated quasiparticles, but so far they have provided limited information regarding their interactions and possible bound states. Here, we show how exploring mobile impurities immersed in a Bose-Einstein condensate (BEC) in a two-dimensional lattice can address this problem. First, the spectral properties of individual impurities are examined, and in addition to the attractive and repulsive polarons known from continuum gases, we identify a new kind of quasiparticle stable for repulsive boson-impurity interactions. The spatial properties of polarons are calculated showing that there is an increased density of bosons at the site of the impurity both for repulsive and attractive interactions. We then derive an effective Schrödinger equation describing two polarons interacting via the exchange of density oscillations in the BEC, which takes into account strong impurity-boson two-body correlations. Using this, we show that the attractive nature of the effective interaction between two polarons combined with the two-dimensionality of the lattice leads to the formation of bound states - i.e. bipolarons. The wave functions of the bipolarons are examined showing that the ground state is symmetric under particle exchange and therefore relevant for bosonic impurities, whereas the first excited state is doubly degenerate and odd under particle exchange making it relevant for fermionic impurities. Our results show that quantum gas microscopy in optical lattices is a promising platform to explore the spatial properties of polarons as well as to finally observe the elusive bipolarons.
Abstract Lattice polarons, quasiparticles arising from the interaction between an impurity and its surrounding bosonic environment confined to a lattice system, have emerged as a platform for generating complex few-body states, probing many-body phenomena, and addressing long-standing problems in physics. In this study, we employ a variational ansatz to investigate the quasiparticle and spectral properties of an impurity coupled to a condensate gas of hard-core bosons in a two-dimensional optical lattice. Our findings demonstrate that the polaron features can be tuned by adjusting the filling factor of the bath, revealing intriguing polaron characteristics in the strongly interacting regime. These results offer valuable insights for lattice polaron experiments with ultracold gases and can serve as a guide for new experiments in emergent quantum devices, such as moiré materials, where optical excitations can be described in terms of hard-core bosons.
Polarons, quasiparticles resulting from the interaction between an impurity and the collective excitations of a medium, play a fundamental role in physics, mainly because they represent an essential building block for understanding more complex many-body phenomena. In this manuscript, we study the spectral properties of a single impurity mixed with identical bosons in a one-dimensional lattice with power-law hopping. In particular, based on the so-called T-matrix approximation, we show the existence of well-defined quasiparticle branches for several tunneling ranges and for both repulsive and attractive impurity-boson interactions. Furthermore, we demonstrate the persistence of the attractive polaron branch when the impurity-boson bound state is absorbed into the two-body continuum and that the attractive polaron becomes more robust as the range of the hopping increases. The results discussed here are relevant for the understanding of the equilibrium properties of quantum systems with power-law interactions.
An impurity particle interacting with a Bose-Einstein condensate (BEC) leads to the formation of a quasiparticle known as the Bose polaron. We investigate the properties of the two-dimensional Bose polaron, applying a variational ansatz that contains up to three Bogoliubov excitations of the BEC. Similar to its three-dimensional counterpart, we observe the existence of two quasiparticle branches, namely, the attractive and the repulsive polarons, at different coupling strengths. We find that their energies agree well with recent quantum Monte Carlo calculations. In particular, we observe that the inclusion of three excitations is crucial to capture the attractive polaron energy towards the regime of strong attraction, where the quasiparticle properties are dominated by few-body correlations. We also calculate the attractive polaron effective mass and residue, where we find significant differences between considering a weakly interacting Bose medium and taking the noninteracting limit, signaling enhanced impurity dressing by excitations in the latter case. By contrast, the spectral weight of the metastable repulsive polaron is largely insensitive to the interactions in the BEC and the number of Bogoliubov excitations. Our model may be experimentally realized in dilute atomic vapors and atomically thin semiconductors.
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.
In this thesis, we investigated the spectral properties of polaronic quasiparticles resulting from the coupling of a charge carrier to the bosonic excitations of ordered environments. Holstein polarons, describing an electron locally coupled to dispersionless phonons, and spin polarons in hole-doped antiferromagnets are considered. The Green's function of the Holstein polaron in a lattice with various kinds of impurities is calculated using the momentum average approximation. The main finding is that the scenario where the mere effect of the coupling to phonons is to enhance the electron's effective mass is incomplete as the phonons are found to also renormalize the impurity potential the polaron interacts with. This formalism is applied first to the case of a single impurity and the range of parameters where the polaron's ground state is localized is identified. The lifetime of the polaron due to scattering from weak but extended disorder is then studied and it is shown that the renormalization of the disorder potential leads to deviation of the strong coupling results from Fermi's golden rule's predictions. Motivated by the hole-doped cuprate superconductors, the motion of a hole in a two-dimensional Ising antiferromagnet and its binding to an attractive impurity is studied next, based on a variational scheme that allows for configurations with a certain maximum number of spin flips. The role of the magnetic sublattices in determining the symmetry of the resulting bound states is discussed. Next, a more realistic model describing a hole in a CuO₂ layer which retains the O explicitly, is considered. By neglecting the fluctuations of the Cu spins and using a variational principle similar to that of the previous chapter, a semi-analytic solution for the Green's function of the hole in an infinite 2D lattice is constructed. The resulting quasiparticle dispersion shows the proper ground state and other features observed in experiments. The lack of importance of the background spin fluctuations is justified based on the hole's ability to move on the O sublattice without disturbing the Cu spins. Finally, the model is generalized to gauge the importance of other relevant O orbitals.