A bosonic Josephson junction connects two reservoirs of identical bosons through a weak link. In the mean-field approximation — valid when the particle number is large — the population imbalance between the two sides exhibits two dynamical regimes. At small imbalances, the population oscillates back and forth, Josephson-style. At large imbalances, above a critical threshold set by the ratio of interaction energy to tunneling energy, the population locks: it oscillates around a nonzero value but never crosses zero. The system is macroscopically self-trapped. The atoms pile up on one side and stay there, despite the tunnel coupling that should allow them to flow to the other side.
This self-trapping is a prediction of the mean-field theory — the Gross-Pitaevskii equation applied to two modes. The mean-field theory treats the bosonic field as a classical variable and ignores quantum fluctuations. The self-trapping is permanent in this approximation: once trapped, the population imbalance persists forever.
Bardin, Minguzzi, and Salasnich (arXiv 2602.22857, February 2026) solve the full quantum problem exactly — the two-mode Bose-Hubbard Hamiltonian with a finite number of particles — and find that macroscopic quantum self-trapping always breaks down after a finite time. Always. For any number of particles and any initial state.
The mechanism is quantum tunneling through the energy barrier that the mean-field theory predicts is insurmountable. The exact quantum spectrum has a discrete set of energy levels, and the energy differences between them set the timescales for recurrence. At finite particle number, these energy spacings are finite, and the system eventually explores all accessible quantum states. The population imbalance, which appears trapped in the mean-field picture, undergoes quantum revival — it returns to zero after a time that grows with particle number but is always finite.
The timescale for breakdown increases exponentially with the number of particles, which is why the mean-field prediction works well for large systems over experimentally accessible times. A Josephson junction with ten thousand atoms would appear self-trapped for all practical purposes — the breakdown time is astronomically long. But for the mesoscopic systems studied in ultracold atom experiments — tens to hundreds of atoms — the breakdown occurs on observable timescales.
The result clarifies the relationship between classical and quantum dynamics in many-body systems. The mean-field theory is not wrong — it captures the short-time dynamics correctly. But it misses the long-time behavior because it replaces a discrete quantum spectrum with a continuous classical one. The classical system has genuine fixed points where the population imbalance is permanently locked. The quantum system has approximate fixed points that hold for a time proportional to the exponential of the particle number, then release. The self-trapping is real but temporary. The trap has a quantum leak.