Reconstruction of the Joint State of a Two-Mode Bose-Einstein Condensate
We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift, and nonideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beam splitter is exactly balanced. Simulated noisy data from a two-mode coherent state are produced and the state is reconstructed, for 49atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data. {copyright} {ital 1997} {ital The American Physical Society}