Coherent Two-State Oscillations in False Vacuum Decay Regimes

Coherent two-state oscillations are observed in numerical simulations of the one-dimensional transverse-longitudinal-field Ising model (TLFIM) within false vacuum decay regimes. Starting from the false vacuum (a nearly fully polarized ferromagnetic state), we show that in moderate-sized systems, at resonances $h\approx 2J/n$ (with longitudinal field $h$, transverse field $J$, and an integer $n$), the expected decay can give way to coherent oscillations between the false vacuum and a symmetric resonant state. The oscillation frequency, i.e., the tunneling splitting, is observed notably to exhibit a superradiant-like $\sqrt{L}$ enhancement, as confirmed by a Schrieffer-Wolff analysis. In large chains, coherence remains for $n\gtrsim L/2$ due to bubble-size blockade and is robust against stronger transverse fields; for small $n$, long-range interactions can stabilize the oscillations by lifting multi-bubble degeneracies, establishing a robust many-body coherence mechanism beyond perturbative and finite-size limits.