Density matrix reconstruction of atoms with large angular momentum

Summary form only given. Determining the unknown state of a quantum system from measurements of observables, a question first posed by Pauli, is a nontrivial task, which does not always permit a solution. The few examples where this inverse problem was experimentally solved include light fields, molecular vibrations, the motion of trapped ions and free atomic waves. We describe a method to reconstruct the complete density matrix of a generally mixed spin state of trapped neutral atoms. Compared to spin- 1/2 systems, the reconstruction of the spin density matrix for a large angular momentum is a much more challenging task. In our system with cesium atoms in the hyperfine ground state, a reconstruction of the 9/spl times/9 density matrix requires 80 real numbers to be experimentally determined. This can be achieved by measuring the 2F+1=9 populations along 4F+1=17 carefully chosen orientations of a Stern-Gerlach apparatus. A numerical simulation of the reconstruction shows this method to be robust against expected experimental uncertainties. We report on an experiment in progress to implement this measurement protocol in a standard laser cooling and trapping arrangement of neutral cesium atoms.