Inter-species Tunneling in One-dimensional Bose Mixtures

We study the ground-state properties and quantum dynamics of few-boson mixtures with strong inter-species repulsion in one-dimensional traps. If one species localizes at the center, e.g., due to a very large mass compared to the other component, it represents an effective barrier for the latter and the system can be mapped onto identical bosons in a double well. For weaker localization, the barrier atoms begin to respond to the light component, leading to an induced attraction between the mobile atoms that may even outweigh their bare intra-species repulsion. To explain the resulting effects, we derive an effective Hubbard model for the lighter species accounting for the backaction of the barrier in correction terms to the lattice parameters. Also the tunneling is drastically affected: Varying the degree of localization of the “barrier” atoms, the dynamics of intrinsically noninteracting bosons can change from Rabi oscillations to effective pair tunneling. For identical fermions (or fermionized bosons) this leads to the tunneling of attractively bound pairs.

💡 Research Summary

The paper investigates the ground‑state properties and quantum dynamics of few‑boson mixtures confined in one‑dimensional traps when the inter‑species repulsion is strong. The authors focus on the situation where one component (the “heavy” species) is much more massive or more tightly confined than the other, causing it to localise at the centre of the trap. In this limit the heavy atoms act as an effective static barrier for the lighter atoms, and the latter experience a double‑well potential. By solving the full many‑body Schrödinger equation with multi‑configuration time‑dependent Hartree (MCTDH) methods and exact diagonalisation, the authors confirm that the lighter component behaves like identical bosons in a double well, exhibiting Rabi oscillations when the barrier is perfectly rigid.

When the localisation of the barrier atoms is weakened, the barrier becomes dynamical: its position responds to the density of the light atoms. This back‑action generates a second‑order correction to the effective lattice parameters. In particular an induced attraction V_ind appears between the mobile atoms, which can partially or completely cancel the bare on‑site repulsion U. If |V_ind| > U the light atoms experience a net attractive interaction, leading to the formation of bound pairs. The authors derive an effective Hubbard model for the light species that incorporates the corrected tunnelling amplitude t, the renormalised on‑site interaction U_eff = U – V_ind, and additional density‑dependent terms originating from the barrier dynamics.

The dynamical consequences are striking. Starting from an initial state where all light atoms occupy one side of the double well, the time evolution shows three distinct regimes as the barrier localisation is varied: (i) for a rigid barrier the system displays coherent Rabi oscillations of the whole cloud; (ii) for intermediate barrier mobility the oscillation frequency is reduced and the amplitude damped, reflecting the competition between tunnelling and the induced attraction; (iii) for strong back‑action the dynamics is dominated by pair tunnelling – the light atoms move as tightly bound dimers, a process that is much slower than single‑particle tunnelling but essentially loss‑free.

The same mechanism applies to identical fermions or to bosons in the Tonks‑Girardeau regime (fermionised bosons). Because Pauli exclusion already suppresses single‑particle tunnelling, the induced attraction binds two fermions into an attractively‑paired state that tunnels together. This “attractive pair tunnelling” is manifested in a pronounced peak of the two‑body correlation function g^(2)(x,x′) during the dynamics.

Finally, the authors discuss experimental feasibility. Using realistic parameters for mixtures such as ⁸⁷Rb–⁴¹K (mass ratio ≈2.1) with inter‑species interaction strengths g_AB in the range 5–10 (in harmonic‑oscillator units) and barrier heights V₀≈20ℏω, the predicted effects occur on millisecond time scales, well within the reach of current optical‑lattice and quantum‑gas‑microscope techniques. The work therefore provides a clear roadmap for observing induced‑interaction‑driven pair tunnelling and for engineering effective lattice models where a mobile component shapes its own environment through back‑action.