MEASURING THE QUANTUM STATE OF A BOSE-EINSTEIN CONDENSATE

We describe an atomic interferometer based on Raman transitions betwee n two hyperfine states. We show how atom count probabilities at the ou tput of the interferometer can be used to reconstruct the joint multip article state of a two-mode Bose-Einstein condensate. Two data collect ion schemes are compared, via numerical solution for the density matri x from the probability data and analytical estimates of the errors are made. In the first scheme, only the phase of the interferometer is va ried. We prove that state reconstruction is impossible for the case of a balanced beam splitter; otherwise, the problem is ill-conditioned, In the second scheme, both the phase and transmission parameters are v aried, the Q function can be measured directly, and the reconstruction of the state is well conditioned.