title: Wave-function reconstruction of complex fields obeying nonlinear parabolic equations.
abstract: We present a generalized Gerchberg-Saxton (GS) algorithm for reconstructing a (2+1)-dimensional complex scalar wave field which obeys a known nonlinear nondissipative parabolic differential equation, given knowledge of the wave-field modulus at three or more values of an evolution parameter such as time. This algorithm is used to recover the complex wave function of a (2+1)-dimensional Bose-Einstein condensate (BEC) from simulated modulus data. The Gross-Pitaveskii equation is used to model the dynamics of the BEC, with the modulus information being provided by a temporal sequence of simulated absorption images of the condensate. The efficacy of the generalized GS algorithm is examined for a wide range of simulation conditions, including strong nonlinearities, vortex states and Poisson noise. The general form of this algorithm, which allows one to reconstruct a time-dependent wave function, will be useful for studying the phase dynamics of topological defects in coherent quantum systems.
authors.affiliation: School of Physics and Materials Engineering, Monash University, Victoria 3800, Australia.
authors.forename: Yaw-Ren E
authors.initials: YR
authors.lastname: Tan
authors.forename: David M
authors.initials: DM
authors.lastname: Paganin
authors.forename: Rotha P
authors.initials: RP
authors.lastname: Yu
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Morgan