Solitonic eigenstates of the chaotic Bose–Hubbard Hamiltonian

Detection of avoided crossings by fidelity

“…6% of regular levels, in good agreement with counting 7 regular levels out of 132 by direct inspection of the spectrum. Except for the identification of single regular levels [27], this has so far not been detected in the tilted Bose-Hubbard model by other statistical measures. The reported results are obtained for periodic boundary conditions applied to the Hamiltonian of Eq.…”

Robust states of ultracold bosons in tilted optical lattices

“…Associated with these structures are the solitonic states, which are distinguished by a strong localization on the lattice as well as in the Fock space, which barely changes with the tilt strength. Unlike other studies on energetically isolated bound states [12,13,14], this property results from the solitonic states' weak coupling to the bulk of energy levels [32]. Based on the inverse participation ratio, evaluated in the fixed as well as in the adiabatic basis of the Bose-Hubbard Hamiltonian, we compared the dynamical stability of these solitonic states to an ensemble of neighboring states in the bulk of the spectrum, as the tilt was ramped with different slew rates.…”

“…In the previous section, we numerically confirmed the dynamical stability of the solitonic states, as suggested by their parametric level evolution. We now turn to the discussion of the underlying mechanism [32]. The existence of eigenstates of a many-body system with all particles localized close to each other, despite the presence of repulsive interparticle interactions U , was experimentally first demonstrated for pairs of atoms [12].…”

Fock Space Localization of Many-Body States in the Tilted Bose-Hubbard Model

“…The desired dynamical stability may follow from the robustness of the state structure against perturbations in the Hamiltonian parameters. Remarkably, such an example was found recently in the tilted Bose-Hubbard model [18][19][20], for which a set of states that are strongly localized in Fock and real space, and well embedded in the energy spectrum, exhibited a significant stability to dynamical changes in the tilt strength.…”

“…The localized manifold induces characteristic bulk-traversing linear trajectories in the evolution of the energy spectrum as a function of F/U , as reported in Refs. [18][19][20]. Such linear dependence stems from the conserved centre of mass of the bosonic density in the localized eigenstates, as it follows from the application of Hellmann-Feynman's theorem [40] to the TBHH, ∂E/∂F = lln l .…”