Measurement of complete and continuous Wigner functions for discrete atomic systems

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.

It is shown that the negativity of this newly defined Wigner function (for arbitrary spin systems) is closely related to the purity of the state, but the interpretation of its physical meaning deserves further studies (not as apparent as in the CV case). Accepted by PRA

References in corpus (8)

• Quantum homodyne tomography of a two-photon Fock state
• Energy distribution and cooling of a single atom in an optical tweezer
• Analysis of dephasing mechanisms in a standing wave dipole trap
• Coherence properties and quantum state transportation in an optical conveyor belt
• Probing the negative Wigner function of a pulsed single photon point by point
• Visualizing operators of coupled spin systems
• Towards a complete, continuous, Wigner function for an ensemble of spins or qubits
• Loss-based Experimental Test of Bohr's Complementarity Principle with Single Neutral Atom

Cited by in corpus (1)

• Overview of the phase space formulation of quantum mechanics with application to quantum technologies