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

TL;DR

This paper explores how nonlinear effects in Bose-Einstein quantum droplets within optical lattices lead to impeded Bloch oscillations and asymmetric Landau-Zener tunneling, revealing complex dynamical phenomena due to mean-field and beyond-mean-field interactions.

Contribution

It introduces a detailed analysis of nonlinear Bloch dynamics and Landau-Zener tunneling in quantum droplets, highlighting nonreciprocal tunneling and the role of self-stabilization mechanisms.

Findings

Identification of localization impedance inhibiting dispersion.

Observation of nonreciprocal Landau-Zener tunneling.

Mapping dynamics onto a nonlinear two-level model.

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.