Impeded Bloch Oscillation and Nonreciprocal Landau-Zener Tunneling of Bose-Einstein Quantum Droplets in Optical Lattices

Abstract: We investigate the nonlinear Bloch dynamics and Landau-Zener tunneling of quantum droplets in optical lattices, where the interplay between mean-field repulsion and beyond-mean-field attraction from Lee-Huang-Yang corrections introduces a localization impedance that inhibits dynamical dispersion. This self-stabilizing mechanism is crucial to droplet mobility and nonlinear dephasing under external driving. In the deep-lattice regime, simulation in tight-binding reduction reveals breathing modes, self-trapping, and nonlinear Bloch oscillations. In the shallow-lattice regime, we reformulate the problem in momentum space and map the dynamics onto a nonlinear two-level model with time-dependent detuning. The adiabatic spectrum features looped bands and multiple fixed points, parallelly captured by the phase-space structure through a classical Josephson analogy. Applying Hamilton-Jacobi theory, we quantify the tunneling probabilities and demonstrate nonreciprocal Landau-Zener tunneling. The transition probability from the lower to upper band differs from that of the reverse process, even under the same sweeping protocol. This asymmetry arises from nonlinearly induced band gap modulation, highlighting rich dynamical behavior beyond the linear and adiabatic regimes.