Interaction-induced anomalous transport behavior in one dimensional optical lattice

The non-equilibrium dynamics of spin impurity atoms in a strongly interacting one-dimensional (1D) Bose gas under the gravity field is studied. We show that due to the non-equilibrium preparation of the initial state as well as the interaction between the impurity atoms and other bosons, a counterintuitive phenomenon may emerge: the impurity atoms could propagate upwards automatically in the gravity field . The effects of the strength of interaction, the gradient of the gravity field, as well as the different configurations of the initial state are investigated by studying the time-dependent evolution of the 1D strongly interacting bosonic system using time-evolving block decimation (TEBD) method. A profound connection between this counterintuitive phenomenon and the repulsive bound pair is also revealed.

💡 Research Summary

The authors investigate the non‑equilibrium dynamics of a single spin‑impurity atom moving through a strongly interacting one‑dimensional Bose gas that is subjected to a linear gravitational potential. The system is modeled by a two‑component Bose‑Hubbard Hamiltonian in which only the impurity experiences the tilt G·i, while the background “trap” atoms remain confined by a magnetic harmonic trap. An initial Mott‑insulating state with unit filling is prepared, and a radio‑frequency pulse flips the spin on a single lattice site, creating a localized impurity (↓) amidst the background (↑). This state is far from any eigenstate of the Hamiltonian, so its time evolution is studied using the time‑evolving block decimation (TEBD) algorithm (L = 33 sites, χ = 80, Δτ = 0.05).

For zero interspecies interaction (U = 0) the impurity’s centre‑of‑mass (COM) remains stationary because Bloch oscillations of opposite‑momentum components cancel each other. When U > 0 the COM drifts downwards (with the gravity) and settles at a quasi‑equilibrium position; when U < 0 the COM moves upwards against the gravitational tilt. The displacement is maximal around |U|/t ≈ 2, indicating an optimal conversion of interaction energy into potential energy. Larger tilt G pushes the final COM to higher positions and the oscillation period follows the Bloch period 2π/G.

To rationalise the upward motion for attractive interactions, the authors map the bosonic model to hard‑core fermions via a Jordan‑Wigner transformation and then perform a particle‑hole transformation on the background atoms. The initial configuration becomes a “doublon” (impurity plus a trap‑hole on the same site) with high interaction energy ˜U. For ˜U ≫ t the doublon behaves like a repulsively bound pair and remains localized; for ˜U ≲ t the excess interaction energy can be released by raising the impurity in the gravitational field, thereby conserving total energy. TEBD calculations of the doublon variance and total double occupancy confirm this picture: variance shrinks and double occupancy approaches one for strong ˜U, while both quantities change rapidly for weak ˜U, signalling doublon breakup and upward impurity motion.

The authors also explore different initial conditions. If the background is a quasi‑superfluid (filling < 1) the trap‑hole is delocalised, no high‑energy doublon exists, and the impurity does not move upward. Conversely, preparing multiple impurities or a Mott plateau within a harmonic trap reproduces the upward‑motion effect, showing its dependence on the presence of a high‑energy bound state.

A phase‑diagram‑like sketch summarises four regimes: (I) upward motion for moderate attractive U, (II) downward motion for moderate repulsive U, (III) a trapped exciton (doublon) for strong attractive U, and (IV) a trapped exciton for strong repulsive U. The transitions are cross‑overs rather than sharp phase transitions. The work highlights that in isolated quantum many‑body systems, dynamics are governed by the competition between energy conservation and entropy maximisation, allowing high‑energy excitations to drive counter‑intuitive transport such as “negative‑mass” motion. The predictions are experimentally accessible via time‑resolved tomography of impurity density, offering a clear platform to study interaction‑induced anomalous transport in optical lattices.