Abstract: The progress in realising ultracold atomic mixtures has greatly revitalised the interest in studying impurities immersed in quantum mediums [1]. Following these developments, and motivated by the possibility of trapping ultracold atoms in optical lattices [2], the theoretical study of impurities in lattice configurations has emerged as a new platform for studying polaron physics. In this direction, recent studies of impurities interacting with bosonic baths have revealed intriguing features across the superfluid-to-Mott insulator transition [3,4].

In this talk  I will first present a numerical study of an impurity interacting with a bosonic bath and immersed in a harmonically confined optical lattice [5]. We reveal that the impurity can form a correlated counterflow state with the bath. This counterflow state [6] shows long-range anti-pair order and displays non-trivial features, including a sudden orthogonality. Then, I will briefly present a related study of an impurity interacting with a spin-1/2 fermonic bath in small lattices, where we show

[1] F. Grusdt, N. Mostaan, E. Demler and L. A. Peña Ardila, Rep. Prog. Phys. 88, 066401 (2025).

[2] I. Bloch, Nat. Phys. 1, 23 (2005).

[3] V. E. Colussi, F. Caleffi, C. Menotti, and A. Recati, Phys. Rev. Lett. 130, 17, 3002  (2023).

[4] R. Alhyder, V. E. Colussi, M. Čufar, J. Brand, A. Recati, G. M. Bruun, SciPost Phys. 19, 002 (2025).

[5] F. Isaule, A. Rojo-Francàs, L. Morales-Molina, and B. Juliá-Díaz, Phys. Rev. Lett. 135, 023404 (2025).

[6] A. B. Kuklov and B. V. Svistunov, Phys. Rev. Lett. 90, 100401 (2003).