From harmonic trap to optical lattice: Adiabatic loading of a quasi-one-dimensional interacting Bose gas

Ultracold atoms in optical lattices offer a highly controllable platform for studying diverse quantum phases. In three dimensions, Bose gases exhibit Bose–Einstein condensation (BEC) below a critical temperature $T_c$, while in optical lattices, a superfluid–Mott insulator transition emerges at zero temperature. In contrast, quasi-one-dimensional (quasi-1D) trapped Bose gases do not exhibit true condensation in the thermodynamic limit but can display finite-size condensate features and have been tested by experiments. In this work, we investigate the adiabatic loading of a harmonically trapped quasi-1D Bose gas initially prepared in the quasi-BEC phase into an optical lattice with confinement-induced resonance (CIR) interactions. By combining the thermodynamic Bethe ansatz with a lattice phonon model — whose phonon spectrum is obtained from the discrete nonlinear Schrödinger equation (DNLSE) — we investigate how interaction strength and lattice depth jointly influence the adiabatic loading process. In particular, we analyze the resulting final temperature $T_f$ and the most probable site occupation number $n_L^{\ast }$ that characterize the equilibrium state in the optical lattice. We find that $T_f$ generally exceeds the initial temperature $T_i$ due to entropy redistribution when the filling is not fixed. Crucially, we identify that the loss of superfluidity is not solely caused by on-site interactions, as usually assumed, but is also strongly influenced by interaction-induced tunneling. As this term becomes appreciable at strong coupling, it induces dynamical instabilities that can destroy the superfluid phase even in regimes previously deemed stable. Our results clarify how combined lattice potentials and interatomic interactions shape the thermodynamic behavior and stability of ultracold atomic systems in low dimensions.