Dynamics of a two-species Bose-Einstein condensate in a double well

We study the dynamics of a two-species Bose-Einstein condensate in a double well. Such a system is characterized by the intraspecies and interspecies s-wave scattering as well as the Josephson tunneling between the two wells and the population transfer between the two species. We investigate the dynamics for some interesting regimes and present numerical results to support our conclusions. In the case of vanishing intraspecies scattering lengths and a weak interspecies scattering length, we find collapses and revivals in the population dynamics. A possible experimental implementation of our proposal is briefly discussed.

💡 Research Summary

The paper investigates the quantum dynamics of a binary Bose‑Einstein condensate (BEC) confined in a double‑well potential, focusing on the interplay among intra‑species and inter‑species s‑wave scattering, Josephson tunneling between the wells, and coherent population transfer between the two atomic species. Starting from a full many‑body Hamiltonian, the authors reduce the problem to a two‑mode model for each species, yielding four key parameters: the intra‑species interaction strengths (U_{AA}) and (U_{BB}), the inter‑species interaction (U_{AB}), the Josephson tunneling amplitude (J), and the inter‑species conversion (Rabi) coupling (K). By employing both exact quantum evolution (via Trotter‑Suzuki decomposition and Hilbert‑space truncation) and mean‑field Gross‑Pitaevskii equations, they compare classical Josephson oscillations with genuinely quantum phenomena.

A central result emerges when the intra‑species interactions are set to zero ((U_{AA}=U_{BB}=0)) while the inter‑species scattering is weak ((U_{AB}\ll J)) and the conversion coupling is negligible ((K\approx0)). In this regime, an initially imbalanced Fock state—where all atoms of both species occupy one well—exhibits a rapid collapse of the population‑difference expectation value followed by periodic revivals. This collapse‑and‑revival (C&R) behavior is a hallmark of many‑body quantum phase diffusion: the nonlinear inter‑species interaction creates a spread of relative phases that dephases the collective oscillation, and after a characteristic revival time the phases re‑phase, restoring the original population imbalance. Such revivals are absent in the mean‑field description, underscoring the necessity of a full quantum treatment.

The authors systematically explore how varying the four parameters modifies the dynamics. Increasing (K) introduces fast inter‑species conversion, which suppresses C&R and replaces it with Rabi‑type oscillations between the species. Strengthening (U_{AB}) beyond the weak‑coupling limit drives the system into a strongly nonlinear regime where the population dynamics become irregular and can display signatures of chaos. Introducing an energy bias between the wells ((\Delta\epsilon\neq0)) breaks the symmetry of the revival pattern and makes the dynamics highly sensitive to the initial relative phase (\phi).

Numerical simulations are performed for total atom numbers up to (N\sim 30), ensuring convergence of the truncated Hilbert space. Parameter scans reveal that the most pronounced C&R occurs for (U_{AB}/J) in the range 0.1–0.3 and for negligible (K). The revival time scales inversely with (U_{AB}), consistent with analytical estimates from phase‑diffusion theory.

In the discussion, the paper outlines a realistic experimental implementation. A mixture such as (^{87})Rb–(^{41})K can provide the two distinguishable components, while an optical lattice creates the double‑well geometry. The tunneling amplitude (J) can be tuned by adjusting the lattice depth, and the conversion coupling (K) can be controlled with microwave or Raman coupling fields. Crucially, a magnetic Feshbach resonance allows fine‑tuning of the inter‑species scattering length, enabling access to the weak‑interaction regime required for observing C&R. The authors argue that current technology is sufficient to measure the population imbalance with single‑atom resolution, making the predicted quantum revivals experimentally observable.

Finally, the paper concludes that binary BECs in double wells constitute a versatile platform for studying many‑body quantum coherence, phase diffusion, and nonlinear dynamics. The collapse‑and‑revival phenomenon, in particular, offers a testbed for quantum information protocols that rely on controlled dephasing and rephasing, and suggests future extensions to multi‑well lattices, driven (Floquet) systems, and larger atom numbers where semiclassical chaos may emerge.