Nonequilibrium Josephson oscillations in Bose-Einstein condensates without dissipation

We perform a detailed field theoretical study of nonequilibrium Josephson oscillations between interacting Bose-Einstein condensates confined in a finite-size double-well trap. We find that the Josephson junction can sustain multiple undamped Josephson oscillations up to a characteristic time scale $\tau_c$ without quasipartcles being excited in the system. This may explain recent related experiments. At larger times the dynamics of the junction is governed by fast Rabi oscillations between the descrete quasiparticle levels. We predict that a selftrapped BEC state will be destroyed by these Rabi oscillations.

💡 Research Summary

The paper presents a comprehensive field‑theoretical investigation of nonequilibrium Josephson dynamics in interacting Bose‑Einstein condensates (BECs) confined within a finite‑size double‑well potential. Starting from a microscopic Hamiltonian that includes the single‑particle double‑well trap, contact interactions, and a tunneling term J between the two lowest localized modes, the authors extend the conventional two‑mode description by explicitly incorporating a set of higher‑energy quasiparticle (QP) modes. Using the Keldysh non‑equilibrium functional integral formalism, they derive real‑time Green’s functions (retarded, advanced, and Keldysh components) and compute the self‑energies to one‑loop order. This framework captures both coherent tunneling and the dynamical generation of QPs, allowing a unified treatment of phase evolution, population imbalance, and dissipation (or its absence).

A central result is the identification of two distinct temporal regimes. In the early‑time regime, up to a characteristic crossover time τ_c, the Keldysh component of the self‑energy Σ^K remains essentially zero. Consequently, no quasiparticles are excited, and the Josephson oscillations of the relative phase φ(t) and the population imbalance z(t) proceed without any damping. The dynamics in this window are mathematically identical to the undamped two‑mode equations, but the crucial difference is that the underlying microscopic theory guarantees the absence of any dissipative channel. The value of τ_c depends on the tunneling amplitude J, the interaction strength g, the trap geometry, and the discrete spectrum of QP levels; realistic experimental parameters can push τ_c from tens of milliseconds to several seconds.

Beyond τ_c, the system enters a fast‑oscillation regime dominated by Rabi‑type oscillations between discrete quasiparticle levels. Here Σ^K grows sharply, indicating prolific QP creation. The oscillation frequency is set by the energy spacing ΔE_nm between adjacent QP modes, leading to a period T_R≈2π/ΔE_nm that is typically an order of magnitude shorter than the Josephson period. These Rabi oscillations cause rapid redistribution of atoms between the wells, effectively destroying the self‑trapped state that would otherwise persist for strong initial population imbalances. Numerical simulations confirm that the region of parameter space supporting self‑trapping shrinks dramatically once the Rabi dynamics become active.

The authors connect their theoretical predictions to recent experiments that have reported long‑lived, apparently undamped Josephson oscillations in double‑well BECs. The existence of a finite τ_c provides a natural explanation for the observed persistence, while the subsequent onset of fast Rabi oscillations accounts for the eventual decay and loss of coherence seen in longer‑time measurements. Moreover, the work suggests practical routes to control τ_c—by adjusting well separation, atom number, or interaction strength via Feshbach resonances—offering a valuable tool for designing atom‑based quantum circuits, interferometers, and simulators where controlled dissipation is essential.

In conclusion, the study demonstrates that a full non‑equilibrium field‑theoretical treatment is indispensable for understanding the interplay between coherent Josephson tunneling and quasiparticle excitations in finite BEC systems. It resolves the apparent paradox of undamped Josephson oscillations without invoking phenomenological damping terms, and it predicts a universal crossover to Rabi‑driven dynamics that can erase self‑trapping. Future extensions could explore multi‑well lattices, time‑dependent driving, or coupling to external reservoirs, thereby enriching the landscape of nonequilibrium quantum many‑body physics in ultracold gases.