A. Privitera

We study the problem of three ultracold fermions in different hyperfine states loaded into a lattice with spatial dimension $D=1,2$. We consider SU(3)-symmetric attractive interactions and also eventually include a three-body constraint, which mimics the effect of three-body losses in the strong-loss regime. We combine exact diagonalization with the Lanczos algorithm, and evaluate both the eigenvalues and the eigenstates of the problem. In $D=1$, we find that the ground state is always a three-body bound state (trion) for arbitrarily small interaction, while in $D=2$, due to the stronger influence of finite-size effects, we are not able to provide conclusive evidence of the existence of a finite threshold for trion formation. Our data are, however, compatible with a threshold value which vanishes logarithmically with the size of the system. Moreover, we are able to identify the presence of a fine structure inside the spectrum, which is associated with off-site trionic states. The characterization of these states shows that only the long-distance behavior of the eigenstate wave functions provides clear-cut signatures about the nature of bound states and that on-site observables are not enough to discriminate between them. The inclusion of a three-body constraint due to losses promotes these off-site trions to the role of lowest-energy states, at least in the strong-coupling regime. DOI: http://dx.doi.org/10.1103/PhysRevA.87.023617 ©2013 American Physical Society

We generalize the application of small polaron theory to ultracold gases [M. Bruderer, A. Klein, S. R. Clark, and D. Jaksch, New J. Phys. 10, 033015 (2008)] to the case of Bose-Fermi mixtures, where both components are loaded into an optical lattice. In a suitable range of parameters, the mixture can be described within a Bogoliubov approach in the presence of fermionic (dynamic) impurities; an effective description in terms of polarons applies. In the dilute limit of the slow-impurity regime, the hopping of fermionic particles is exponentially renormalized due to polaron formation, regardless of the sign of the Bose-Fermi interaction. This should lead to clear experimental signatures of polaronic effects, once the regime of interest is reached. The validity of our approach is analyzed in the light of currently available experiments. We provide results for the hopping renormalization factor for different values of temperature, density, and Bose-Fermi interaction for three-dimensional ${}^{87}\mathrm{Rb}$-${}^{40}\mathrm{K}$ mixtures in an optical lattice. DOI: http://dx.doi.org/10.1103/PhysRevA.82.063614 © 2010 The American Physical Society