Measuring the quantum state of a large angular momentum

We demonstrate a general method to measure the quantum state of an angular momentum of arbitrary magnitude. The (2F + 1) X (2F + 1) density matrix is completely determined from a set of Stern-Gerlach measurements with (4F + 1 ) different orientations of the quantization axis. We implement the protoco l for laser cooled Cesium atoms in the 6S(1/2)(F = 4) hyperfine ground stat e and apply it to a variety of test states: prepared by optical pumping and Larmor precession. A comparison of input and measured states shows; typica l reconstruction fidelities F greater than or similar to 0.95.