Tachyonic and parametric instabilities in an extended bosonic Josephson junction

TL;DR

This paper investigates the dynamical instabilities, including tachyonic and parametric resonance types, in extended bosonic Josephson junctions of Bose-Einstein condensates, revealing how quantum fluctuations destabilize mean-field stable states.

Contribution

It identifies and analyzes tachyonic and parametric instabilities in bosonic Josephson junctions, combining linearized analysis and numerical simulations to understand their role in quantum phase coherence decay.

Findings

Tachyonic instabilities are linked to imaginary dispersion relations.

Parametric resonance instabilities are triggered by oscillations in phase and population.

Numerical simulations confirm the development of instabilities and their nonlinear evolution.

Abstract

We study the dynamics and decay of quantum phase coherence for Bose-Einstein condensates in tunnel-coupled quantum wires. The two elongated Bose-Einstein condensates exhibit a wide variety of dynamic phenomena where quantum fluctuations can lead to a rapid loss of phase coherence. We investigate the phenomenon of self-trapping in the relative population imbalance of the two condensates, particularly $\pi$-trapped oscillations that occur when also the relative phase is trapped. Though this state appears stable in mean-field descriptions, the $\pi$-trapped state becomes dynamically unstable due to quantum fluctuations. Nonequilibrium instabilities result in the generation of pairs excited from the condensate to higher momentum modes. We identify tachyonic instabilities, which are associated with imaginary parts of the dispersion relation, and parametric resonance instabilities that are triggered by oscillations of the relative phase and populations. At early times, we compute the instability chart of the characteristic modes through a linearized analysis and identify the underlying physical process. At later times, the primary instabilities trigger secondary instabilities due to the build-up of non-linearities. We perform numerical simulations in the Truncated Wigner approximation in order to observe the dynamics also in this non-linear regime. Furthermore, we discuss realistic parameters for experimental realizations of the $\pi$-trapped state in ultracold atom setups.