Approximate nonlinear wave solutions of the coupled two-component Gross–Pitaevskii equations with spin–orbit interaction

Abstract

Recent experimental observations of spin–orbit coupling (SOC) in Bose–Einstein condensates (BECs) open the way for investigating novel physics of nonlinear waves with promising applications in atomic physics and condensed matter physics. The interplay between atomic interactions and SOC are crucial for the understanding of the dynamics of nonlinear waves in BECs with SOC. Here, in the small linear coupling regime, an approach is presented which allows us to derive an infinite number of novel approximate solutions of the Gross–Pitaevskii equations (GPEs) in one and two dimensions including SOCs, time-dependent external potentials, and nonlinearities leading to breathers and periodic as well as quasiperiodic nonlinear waves. To verify the theoretical predictions we perform numerical simulations which show for several cases a very good agreement with the analytics. For the case of one spatial dimension, it is shown that functions describing the external potential and nonlinearities cannot be chosen independently. The management of the solutions is clarified along with some important physical properties such as Josephson oscillations and Rosen–Zener oscillations.