We propose to go beyond the usual Hubbard model description of atoms in optical lattices and show how few-body physics can be used to simulate many-body phenomena, e.g., an electron-phonon system. We take one atomic species to be trapped in a deep optical lattice at full-filling and another to be untrapped spin-polarized fermions (which do not see the optical lattice) but to have an $s$ -wave contact interaction with the first species. For large positive scattering length on the order of lattice spacing, the usual two-body bound (dimer) states overlap forming giant orbitals extending over the entire lattice, which can be viewed as an ``electronic'' band for the untrapped species while the trapped atoms become the ``ions'' with their own on-site dynamics, thereby simulating an electron-phonon system with renormalization of the phonon frequencies and Peierls transitions. This setup requires large scattering lengths but minimizes losses, does not need higher bands, and adds degrees of freedom which cannot easily be described in terms of lattice variables, thus opening up intriguing possibilities to explore interesting physics at the interface between few-body and many-body systems.We propose to go beyond the usual Hubbard model description of atoms in optical lattices and show how few-body physics can be used to simulate many-body phenomena, e.g., an electron-phonon system. We take one atomic species to be trapped in a deep optical lattice at full-filling and another to be untrapped spin-polarized fermions (which do not see the optical lattice) but to have an $s$-wave contact interaction with the first species. For large positive scattering length on the order of lattice spacing, the usual two-body bound (dimer) states overlap forming giant orbitals extending over the entire lattice, which can be viewed as an ``electronic'' band for the untrapped species while the trapped atoms become the ``ions'' with their own on-site dynamics, thereby simulating an electron-phonon system with renormalization of the phonon frequencies and Peierls transitions. This setup requires large scattering lengths but minimizes losses, does not need higher bands, and adds degrees of freedom which cannot easily be described in terms of lattice variables, thus opening up intriguing possibilities to explore interesting physics at the interface between few-body and many-body systems.

arXiv:1310.4152Physical Review ASep 24, 20148 citations

Lellouch-Lüscher Relation for Ultracold Few-Atom Systems under Confinement

Jing-Lun Li, Paul S. Julienne, Johannes Hecker Denschlag +1 more

We derive an analog of the Lellouch-Lüscher (LL) relation for few-body bosonic systems, linking few-body scattering loss rates to the energies and widths of the corresponding harmonically trapped few-body states. Three-body numerical simulations show that the LL relation applies across a broad range of interaction strengths and energies and allows the determination of scattering rates within a single partial wave. Our Letter establishes a robust theoretical framework for understanding the role of the finite-volume effect in few-body observables in optical lattice and tweezer experiments, enabling precise determination of multibody scattering rates.We derive an analog of the Lellouch-Lüscher (LL) relation for few-body bosonic systems, linking few-body scattering loss rates to the energies and widths of the corresponding harmonically trapped few-body states. Three-body numerical simulations show that the LL relation applies across a broad range of interaction strengths and energies and allows the determination of scattering rates within a single partial wave. Our Letter establishes a robust theoretical framework for understanding the role of the finite-volume effect in few-body observables in optical lattice and tweezer experiments, enabling precise determination of multibody scattering rates.

arXiv:2511.11906Physical Review LettersApr 21, 20260 citations

s

-wave contact interaction with the first species. For large positive scattering length on the order of lattice spacing, the usual two-body bound (dimer) states overlap forming giant orbitals extending over the entire lattice, which can be viewed as an ``electronic'' band for the untrapped species while the trapped atoms become the ``ions'' with their own on-site dynamics, thereby simulating an electron-phonon system with renormalization of the phonon frequencies and Peierls transitions. This setup requires large scattering lengths but minimizes losses, does not need higher bands, and adds degrees of freedom which cannot easily be described in terms of lattice variables, thus opening up intriguing possibilities to explore interesting physics at the interface between few-body and many-body systems.