Repulsively interacting particles in a periodic potential can form bound composite objects with long lifetimes, as has been observed experimentally [Winkler et al., Nature (London) 441, 853 (2006)]. In this paper, a complete two-particle solution of one-dimensional periodical potential was derived in a strong interaction regime, where the on-site approximation of a two-body interaction in the Bose-Hubbard model (BHM) is extended to include the interaction of nearest neighbors, which results in atom-pair hopping. The energy spectrum of the bound pair is drastically reshaped due to the pair-hopping term, and complex eigenenergy corresponding to metastable states is also found that has not been discovered in the usual BHM. When the absolute value of a center-of-mass quasimomentum wave vector is greater than a critical value ( $|K|>{K}_{c}$ ), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.Repulsively interacting particles in a periodic potential can form bound composite objects with long lifetimes, as has been observed experimentally [Winkler et al., Nature (London) 441, 853 (2006)]. In this paper, a complete two-particle solution of one-dimensional periodical potential was derived in a strong interaction regime, where the on-site approximation of a two-body interaction in the Bose-Hubbard model (BHM) is extended to include the interaction of nearest neighbors, which results in atom-pair hopping. The energy spectrum of the bound pair is drastically reshaped due to the pair-hopping term, and complex eigenenergy corresponding to metastable states is also found that has not been discovered in the usual BHM. When the absolute value of a center-of-mass quasimomentum wave vector is greater than a critical value ($|K|>{K}_{c}$), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.

Physical Review AApr 15, 201028 citations

Analogue simulation of two-body quantum dynamics with classical setup

Maxim A. Gorlach, Marco Fedele Di Liberto, Alessio Recati +3 more

One-dimensional Bose-Hubbard models provide a variety of intriguing predictions including the formation of repulsively bound two-boson pairs, their collapse and revival and the realization of the two-boson topological states. While probing such systems in quantum regime is quite a challenging task, there is another appealing option to explore the properties of repulsively bound bosons based on mapping of the one-dimensional interacting system onto the two-dimensional classical model described by the standard coupled-mode equations. Adopting the latter approach, we develop the procedure to probe the energy of bound boson pairs as well as to perform the tomography of the bound pair quantum state in realistic dissipative systems.One-dimensional Bose-Hubbard models provide a variety of intriguing predictions including the formation of repulsively bound two-boson pairs, their collapse and revival and the realization of the two-boson topological states. While probing such systems in quantum regime is quite a challenging task, there is another appealing option to explore the properties of repulsively bound bosons based on mapping of the one-dimensional interacting system onto the two-dimensional classical model described by the standard coupled-mode equations. Adopting the latter approach, we develop the procedure to probe the energy of bound boson pairs as well as to perform the tomography of the bound pair quantum state in realistic dissipative systems.

Journal of Physics Conference SeriesSep 1, 20181 citation

Quantum dynamics of coupled bosonic wells within the Bose-Hubbard picture

Roberto Franzosi

International Journal of Modern Physics BJan 1, 20003 citations

Quantum Many-Body Dynamics of the Bose-Hubbard System with Artificial and Intrinsic Dissipation

Takafumi Tomita

Mar 25, 20190 citations

|K|>{K}_{c}

), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.