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Phase Retrieval From Two-Dimensional Absorption Images Of Bose-Einstein Condensates

Introduction Phase retrieval involves determining the phase of a complex wavefunction using information about its modulus.

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Phase Retrieval From Two-Dimensional Absorption Images Of Bose-Einstein Condensates

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  1. Introduction Phase retrieval involves determining the phase of a complex wavefunction using information about its modulus. We develop a generalised Gerchberg-Saxton algorithm for retrieving the phase of a (2+1)-dimensional complex scalar wave-field obeying a known non-linear parabolic differential equation. Here we will apply the algorithm to recover the wavefunction, , of a Bose-Einstein Condensate (BEC) from simulated absorption images. The wavefunction satisfies a non-linear Schrödinger equation: • Generalised Gerchberg-Saxton Algorithm • is a unitary non-linear evolution operator defined by • is a projection operator that replaces the modulus of the wavefunction on which it acts with the known modulus • This algorithm can be represented for three images as: SCHOOL OF PHYSICS and MATERIALS ENGINEERING Simulated modulus and phase (left column). Retrieved modulus and phase (right column), using 5 images separated by 50 timesteps. FIG. 1: Results from noise-free retrievals 3 images - 100 timesteps 5-25 Case I (with g = 0): Simulated modulus (left) and phase (centre). Retrieved phase (right), using 3 images separated by 200 timesteps. 9-25 3-50 9-50 5-50 Simulated modulus and phase (left column). Retrieved modulus and phase (right column), using 9 images separated by 100 timesteps. FIG. 2: Noise-free retrieval for Case I (with g = 1000) using different retrieval parameters. “I-T” indicates retrieval using I images with T timesteps between images. Case I (with g = 1000): Simulated modulus (left) and phase (centre). Retrieved phase (right), using 5 images separated by 50 timesteps. Case II (with g = 100): Simulated modulus (left) and phase (centre). Retrieved phase (right), using 9 images separated by 100 timesteps. Yaw-Ren E. Tan, David M. Paganin, Rotha P. Yu and Michael J. Morgan, “Wavefunction reconstruction of complex fields obeying non-linear parabolic equations”, Phys. Rev. E (2003) (Submitted 26/06/2003). Reference Phase Retrieval From Two-Dimensional Absorption Images Of Bose-Einstein Condensates Yaw-Ren E. Tan, David Paganin, Rotha Yu and Michael Morgan School of Physics and Materials Engineering, Monash University, Victoria 3800, Australia E-mail: eugene.tan@australia.edu Simulating a BEC Case I: Two spatially separated BECs expand and overlap, showing interference patterns. This is similar to Young’s double slit experiment. Case II: A BEC in a trap is stirred with a laser, nucleating quantised vortices. This is similar to stirring a bucket of water with a stick. Table 1: Wavefunction retrieval with Poisson noise. (*with vortices present)

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