Tachyonic and parametric instabilities in an extended bosonic Josephson junction

We study the decay of phase coherence in an extended bosonic Josephson junction realized via two tunnel-coupled Bose-Einstein condensates. Specifically, we focus on the π π -trapped state of large population and phase imbalance, which, similar to the breakdown of macroscopic quantum self-trapping, becomes dynamically unstable due to the amplification of quantum fluctuations. We analytically identify early tachyonic and parametric instabilities connected to the excitation of atom pairs from the condensate to higher momentum modes along the extended direction. Furthermore, we perform Truncated Wigner numerical simulations to observe the build-up of non-linearities at later times and explore realistic experimental parameters.