Detecting a long lived false vacuum with quantum quenches

Distinguishing whether a system supports alternate low-energy (locally stable) states -- stable (true vacuum) versus metastable (false vacuum) -- by direct observation can be difficult when the lifetime of the state is very long but otherwise unknown. Here we demonstrate, in a tractable model system, that there are physical phenomena on much shorter time scales that can diagnose the difference. Specifically, we study the spectral density following a quench in the tilted quantum Ising model, and show that the evolution of the spectral density is a powerful diagnostic. Small transition bubbles are more common than large ones, and we see characteristic differences in the size dependence of bubble lifetimes even well below the critical size for false vacuum decay. We expect this sort of behavior to be generic in systems of this kind. We identify a scaling limit that connects the discrete, simulatable model to continuum quantum field theory.