# Measurement of complete and continuous Wigner functions for discrete atomic systems

## TL;DR

This paper experimentally measures complete Wigner functions of a two-level cesium atom, revealing negativity in pure states and its disappearance in mixed states, using a method applicable to multi-atom systems.

## Contribution

It demonstrates a practical method for measuring continuous Wigner functions of atomic systems, including mixed states, and explores negativity properties related to state purity.

## Key findings

- Pure states exhibit negative regions in their Wigner functions.
- Negativity vanishes when state purity drops below 2/3.
- Method is applicable to multi-atom collective spin states.

## Abstract

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.