Bifurcation trees of Stark-Wannier ladders for accelerated BECs in an optical lattice

TL;DR

This paper investigates how increasing nonlinearity in a periodic potential causes bifurcations in Stark-Wannier ladders, leading to a dense spectrum and a transition to quantum chaos, with explicit bifurcation sequences provided.

Contribution

It introduces a detailed analysis of bifurcation trees in Stark-Wannier ladders within the semiclassical regime, revealing the transition to quantum chaos.

Findings

Bifurcation trees cause the spectrum to become dense.

Transition from regular to chaotic dynamics is observed.

Explicit bifurcation sequences are derived.

Abstract

In this paper we show that in the semicassical regime of periodic potential large enough, the Stark-Wannier ladders become a dense energy spectrum because of a cascade of bifurcations while increasing the ratio between the effective nonlinearity strength and the tilt of the external field; this fact is associated to a transition from regular to quantum chaotic dynamics. The sequence of bifurcation points is explicitly given.