Chapter Six - Efficient Description of Bose–Einstein Condensates in Time-Dependent Rotating Traps

Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable sources for the coherent matter waves in these devices are Bose–Einstein condensates. A reliable prediction of their dynamics, which is governed by the Gross–Pitaevskii equation, requires suitable analytical and numerical methods, which take into account the center-of-mass motion of the condensate, its rotation, and its spatial expansion by many orders of magnitude. In this chapter, we present an efficient way to study their dynamics in time-dependent rotating traps that meet this objective. Both an approximate analytical solution for condensates in the Thomas–Fermi regime and dedicated numerical simulations on a variable adapted grid are discussed. We contrast and relate our approach to previous alternative methods and provide further results, such as analytical expressions for the one- and two-dimensional spatial density distributions and the momentum distribution in the long-time limit that are of immediate interest to experimentalists working in this field of research.