Measurement of complete and continuous Wigner functions for discrete atomic systems. (arXiv:1706.08676v4 [quant-ph] UPDATED)

We measure complete and continuous Wigner functions of a two-level cesium
atom in both a nearly pure state and highly mixed states. We apply the method
[T. Tilma et al., Phys. Rev. Lett. 117, 180401 (2016)] of strictly constructing
continuous Wigner functions for qubit or spin systems. We find that the Wigner
function of all pure states of a qubit has negative regions and the negativity
completely vanishes when the purity of an arbitrary mixed state is less than
$\frac{2}{3}$. We experimentally demonstrate these findings using a single
cesium atom confined in an optical dipole trap, which undergoes a nearly pure
dephasing process. Our method can be applied straightforwardly to multi-atom
systems for measuring the Wigner function of their collective spin state.

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