Coherent Two-State Oscillations in False Vacuum Decay Regimes

Abstract: Coherent two-state oscillations are observed in numerical simulations of one-dimensional transverse- and longitudinal-field Ising model within the false vacuum decay regimes. Starting from the false vacuum state with all spins up, in moderate-sized systems with a small transverse field, we find conventional decay dynamics at resonance conditions $ h\approx 2J/n$ can change into coherent oscillations between the false vacuum and a symmetric resonant state, manifested by a sub-leading eigenstate overlap approaching $0.5$ and periodic vanishing of the Loschmidt echo. Notably, the oscillation frequency shows a superradiant-like $\sqrt{L}$ enhancement compared to the earlier Schrieffer-Wolff predictions. In larger systems, we find these oscillations persist for $n \gtrsim L/2$ (enabled by a bubble size blockade effect) or when long-range interactions lift multi-bubble degeneracies, revealing a robust many-body coherence mechanism transcending perturbative treatments and finite-size limitations.