Measuring the Quantum State of a Large Angular Momentum

Abstract

We demonstrate a general method to measure the quantum state of an angular momentum of arbitrary magnitude. The $(2F+1)\times (2F+1)$ density matrix is completely determined from a set of Stern-Gerlach measurements with $(4F+1)$ different orientations of the quantization axis. We implement the protocol for laser cooled Cesium atoms in the ${6S}_{1/2}(F=4\mathrm{})$ hyperfine ground state and apply it to a variety of test states prepared by optical pumping and Larmor precession. A comparison of input and measured states shows typical reconstruction fidelities $F\gtrsim 0.95$.