Instability of Holographic Superfuids in Optical Lattice

TL;DR

This paper investigates the instability of holographic superfluids in optical lattices, identifying critical flow parameters and analyzing the nonlinear evolution leading to chaos and eventual stabilization.

Contribution

It introduces a holographic model to study superfluid instability in optical lattices, revealing critical flow conditions and nonlinear dynamics including chaos and soliton formation.

Findings

Existence of a critical Bloch wave vector $k_c$ for superflow stability.

Unstable superflows evolve into chaotic states with solitons.

System stabilizes with lower current and larger condensate after instability.

Abstract

The instability of superfluids in optical lattice has been investigated using the holographic model. The static and steady flow solutions are numerically obtained from the static equations of motion and the solutions are described as Bloch waves with different Bloch wave vector $k$. Based on these Bloch waves, the instability is investigated at two levels. At the linear perturbation level, we show that there is a critical $k_{c}$ above which the superflow is unstable. At the fully nonlinear level, the intermediate state and final state of unstable superflow are identified through numerical simulation of the full equations of motion. The results show that during the time evolution, the unstable superflow will undergo a chaotic state, where solitons will appear and disappear. The system will settle down to a stable state with $k<k_{c}$ eventually, with a smaller current and a larger condensate.