Stability and decay of Bloch oscillations in presence of time-dependent   nonlinearity
  We consider Bloch oscillations of Bose-Einstein condensates in presence of a time-modulated s-wave scattering length. Generically, interaction leads to dephasing and decay of the wave packet. Based on a cyclic-time argument, we find---additionally to the linear Bloch oscillation and a rigid soliton solution---an infinite family of modulations that lead to a periodic time evolution of the wave packet. In order to quantitatively describe the dynamics of Bloch oscillations in presence of time-modulated interactions, we employ two complementary methods: collective-coordinates and the linear stability analysis of an extended wave packet. We provide instructive examples and address the question of robustness against external perturbations. 
Christopher Gaul, Elena D\'iaz, Rodrigo P. A. Lima, Francisco   Dom\'inguez-Adame, Cord A. M\"uller
cond-mat.quant-gas