Wave-packet dynamics in nonlinear Schrödinger equations
S. Moulieras1, A. G. Monastra2,3, M. Saraceno2, P. Leboeuf 1
Published under licence by PHYSICAL REVIEW A
1 Laboratoire de Physique Théorique et Modèles Statistiques, Centre National de la Recherche Scientifique, Université Paris Sud, Unite Mixte de Recherche No. 8626, 91405 Orsay Cedex, France
2 Gerencia Investigación y Aplicaciones, Comisión Nacional de Energía Atómica, Avenida General Paz 1499, 1650 San Martín, Argentina
3 Consejo Nacional de Investigaciones Científicas y Técnicas, Avenida Rivadavia 1917, 1033 Buenos Aires, Argentina
Abstract
Coherent states play an important role in quantum mechanics because of their unique properties under time evolution. Here we explore this concept for one-dimensional repulsive nonlinear Schrödinger equations, which describe weakly interacting Bose-Einstein condensates or light propagation in a nonlinear medium. It is shown that the dynamics of phase-space translations of the ground state of a harmonic potential is quite simple: The center follows a classical trajectory whereas its shape does not vary in time. The parabolic potential is the only one that satisfies this property. We study the time evolution of these nonlinear coherent states under perturbations of their shape or of the confining potential. A rich variety of effects emerges. In particular, in the presence of anharmonicities, we observe that the packet splits into two distinct components. A fraction of the wavepacket is transferred toward incoherent high-energy modes, while the amplitude of oscillation of the remaining coherent component is damped toward the bottom of the well.