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We study an ultracold atomic gas with attractive interactions in a one-dimensional optical lattice. We find that its excitation spectrum displays a quantum soliton band, corresponding to $N$-particle bound states, and a continuum band of other, mostly extended, states. For a system of a finite size, the two branches are degenerate in energy for weak interactions, while a gap opens above a threshold value for the interaction strength. We find that the interplay between degenerate extended and bound states has important consequences for both static and dynamical properties of the system. In particular, the solitonic states turn out to be protected from spatial perturbations and random disorder. We discuss how such dynamics implies that our system effectively provides an example of a quantum many-body system that, with the variation of the bosonic lattice filling, crosses over from integrable non-ergodic to non-integrable ergodic dynamics, through non-integrable non-ergodic regimes.
We study quantum dynamics of a dark soliton in a one-dimensional Bose gas in an optical lattice within the truncated Wigner approximation. A previous work has revealed that in the absence of quantum fluctuations, dynamical stability of the dark solit
A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton
Motivated by recent experiments, we model the dynamics of bright solitons formed by cold gases in quasi-1D traps. A dynamical variational ansatz captures the far-from equilibrium excitations of these solitons. Due to a separation of scales, the radia
Disorder can profoundly affect the transport properties of a wide range of quantum materials. Presently, there is significant disagreement regarding the effect of disorder on transport in the disordered Bose-Hubbard (DBH) model, which is the paradigm
The dynamics of two penetrating superfluids exhibit an intriguing variety of nonlinear effects. Using two distinguishable components of a Bose-Einstein condensate, we investigate the counterflow of two superfluids in a narrow channel. We present the