# Nonlinear Dynamics of the Cold Atom Analog False Vacuum

## TL;DR

This paper explores the nonlinear dynamics of cold atom systems as quantum simulators for false vacuum decay, revealing how unstable modes influence the system's evolution and phase transition behavior.

## Contribution

It provides a numerical analysis of the nonlinear evolution of unstable modes in a cold atom analog false vacuum, and demonstrates how coupling modulation can induce different phase transitions.

## Key findings

- Unstable short-wavelength modes threaten false vacuum stability.
- Short-scale modifications to the GPE can stabilize the false vacuum.
- Modulating coupling strength induces crossover between phase transition types.

## Abstract

We investigate the nonlinear dynamics of cold atom systems that can in principle serve as quantum simulators of false vacuum decay. The analog false vacuum manifests as a metastable vacuum state for the relative phase in a two-species Bose-Einstein condensate (BEC), induced by a driven periodic coupling between the two species. In the appropriate low energy limit, the evolution of the relative phase is approximately governed by a relativistic wave equation exhibiting true and false vacuum configurations. In previous work, a linear stability analysis identified exponentially growing short-wavelength modes driven by the time-dependent coupling. These modes threaten to destabilize the analog false vacuum. Here, we employ numerical simulations of the coupled Gross-Pitaevski equations (GPEs) to determine the non-linear evolution of these linearly unstable modes. We find that unless a physical mechanism modifies the GPE on short length scales, the analog false vacuum is indeed destabilized. We briefly discuss various physically expected corrections to the GPEs that may act to remove the exponentially unstable modes. To investigate the resulting dynamics in cases where such a removal mechanism exists, we implement a hard UV cutoff that excludes the unstable modes as a simple model for these corrections. We use this to study the range of phenomena arising from such a system. In particular, we show that by modulating the strength of the time-dependent coupling, it is possible to observe the crossover between a second and first order phase transition out of the false vacuum.