Lattice polarons across the superfluid to Mott insulator transition

Mobile impurities interacting with a few one-dimensional lattice bosons

“…We perform a comprehensive study of the ground-state properties of the impurities across a wide range of inter-atomic interactions across the bath's SF to MI transition, particularly the binding energies. Our results complement and bridge the gap between recent few- [65,66] and many-body [58,64] calculations of Bose lattice polarons. In the case of two impurities, we also examine the onset of diimpurity dimer states by examining their sizes, where we find that insulating baths induce tightly bound dimers.…”

“…where E 0 and E 1 correspond to the ground-state energies of the system with zero and one impurity, respectively, and E I is the energy of a single free impurity. We note that even though the rigorous picture of polarons is not fulfilled in optical lattices, particularly with insulating baths, E p is still also referred to as the polaron energy for the close connection with Bose polarons [58,64].…”

“…In tight lattices where the optical potential depth is sufficiently large to confine the system to the lowest Bloch band [8], this SF to MI transition is naturally described by the Bose-Hubbard model [55,56]. In this direction, Hubbard models can be straightforwardly extended to include impurities [57], enabling the study of impurities across the SF to MI transition [58]. It is worth pointing out that while optical lattices do not support phonon excitations [48], and thus the traditional picture of polarons is not fulfilled, condensates introduce Bogoliubov phonons [59] which induce polaron-like features in SF baths [57].…”

Mobile impurities interacting with a few one-dimensional lattice bosons

“…In the future, we intend to study impurities in larger one-and two-dimensional Bose lattice gases by performing Monte Carlo [77] and DMRG [78] simulations. This will enable us to further examine polaron and bipolaron properties across the SF to MI transition, complementing related perturbative studies [54]. We also intend to study impurities immersed in lattices loaded with spin 1/2 fermions and two-component bosons.…”

“…This transition is naturally described by the Bose-Hubbard model [51,52]. In this direction, Hubbard models can be straightforwardly extended to include impurities [53], enabling the study of impurities across the SF to MI transition [54].…”