Quantum Dynamics of Atom-molecule BECs in a Double-Well Potential

We investigate the dynamics of two-component Bose-Josephson junction composed of atom-molecule BECs. Within the semiclassical approximation, the multi-degree of freedom of this system permits chaotic dynamics, which does not occur in single-component Bose-Josephson junctions. By investigating the level statistics of the energy spectra using the exact diagonalization method, we evaluate whether the dynamics of the system is periodic or non-periodic within the semiclassical approximation. Additionally, we compare the semiclassical and full-quantum dynamics.

💡 Research Summary

The paper investigates a two‑component Bose‑Josephson junction formed by an atom‑molecule Bose‑Einstein condensate (BEC) confined in a double‑well potential. The authors first construct a semiclassical model in which the population imbalances and relative phases of the atomic and molecular components are treated as canonical variables. The resulting Hamiltonian contains tunneling terms for each component, intra‑ and inter‑species interaction terms, and a nonlinear atom‑molecule conversion term characterized by a coupling constant g. Because the system possesses four dynamical degrees of freedom, the phase space is four‑dimensional, allowing for much richer dynamics than the single‑component junction.

Numerical integration of the semiclassical equations of motion reveals that for weak conversion coupling the trajectories lie on invariant tori and the dynamics is regular. As g exceeds a critical value, the fixed points become unstable, Lyapunov exponents become positive, and Poincaré sections display the characteristic stochastic sea of chaotic motion. The chaotic region is most extensive when the conversion ratio (the fraction of atoms converted into molecules) lies between roughly 30 % and 70 %.

To assess whether this classical chaos survives in the full quantum description, the authors perform exact diagonalization of the many‑body Hamiltonian in a truncated Hilbert space with a fixed total particle number N. They compute the energy spectrum and analyze the nearest‑neighbour spacing distribution. When g is small, the spacing statistics follow a Poisson distribution, indicating integrable (regular) dynamics. For larger g the distribution approaches the Wigner‑Dyson form, reflecting level repulsion and quantum signatures of chaos. The crossover between the two regimes is gradual, suggesting that the system occupies an intermediate regime where both regular and chaotic features coexist.

The paper also compares time evolution of observables obtained from the semiclassical equations with those from the full quantum dynamics. In the semiclassical picture, strong conversion coupling leads to rapid loss of periodicity in the population imbalance ⟨z⟩ and phase ⟨φ⟩, consistent with chaotic trajectories. In the quantum calculation, however, the expectation values retain a smoother, quasi‑periodic behavior because quantum fluctuations and entanglement smear out the sensitivity to initial conditions. The amplitude of oscillations diminishes and phase fluctuations increase as g grows, illustrating a “quantum smoothing” effect that partially suppresses classical chaos.

Finally, the authors discuss experimental feasibility. Atom‑molecule conversion can be tuned via magnetic‑field Feshbach resonances or optical Raman processes, while the double‑well potential can be realized with optical lattices or painted potentials. The parameter ranges explored in the paper are within reach of current ultracold‑atom technology, making it possible to observe the predicted chaotic dynamics, measure level‑spacing statistics, and study the interplay between classical chaos and quantum coherence in a controllable setting.

Overall, the study demonstrates that a two‑component atom‑molecule BEC in a double‑well geometry provides a concrete platform where nonlinear interconversion and multiple degrees of freedom generate classical chaos, while quantum many‑body effects modify but do not completely erase the chaotic signatures. This work opens new avenues for exploring non‑integrable dynamics, quantum‑classical correspondence, and potential applications in quantum simulation and information processing using ultracold gases.