Saturation of black hole lasers in Bose-Einstein condensates

Understand

To obtain the end-point evolution of the so-called black hole laser instability, we study the set of stationary solutions of the Gross-Pitaevskii equation for piecewise constant potentials which admit a homogeneous solution with a supersonic flow in the central region between two discontinuities.

• When the distance between them is larger than a critical value, we recover that the homogeneous solution is unstable, and we identify the lowest energy state.
• We show that it can be viewed as determining the saturated value of the first (node-less) complex frequency mode which drives the instability.
• We also classify the set of stationary solutions and establish their relation both with the set of complex frequency modes and with known soliton solutions.