Abstract

Much recent interest in the new dilute alkali Bose-Einstein condensate stems from the idea that the multiparticle state may be highly squeezed due to collisions.¹ The internal states of the atoms can serve as a probe of this squeezing. Motivated by the success of homodyne tomography in measuring the quantum state of light, we propose to obtain the complete density matrix of a two-mode condensate from repeated atom-counting measurements. All that is required is an atom beam splitter, similar to the output coupler,² and two atom counters. By varying the phase shift and transmission of the beam splitter, histograms of probability are obtained. From these, the density matrix of a condensate with a fixed total number of atoms can be computed, using a fast Fourier transform and matrix pseudoinverses.³ An exception is that the reconstruction algorithm fails when data are obtained from an exactly balanced beam splitter.

© 1998 Optical Society of America