Abstract
In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules. This method allows us to display quantum correlations (entanglement) between spin and spatial degrees of freedom (spin-orbit coupling) and between spin degrees of freedom, as well as more complex combinations of spin and spatial entanglement. This is important as there is growing recognition that such properties affect the physical characteristics, and chemistry, of atoms and molecules. Our visualizations are sufficiently accessible that, with some preparation, those with a nontechnical background can gain an appreciation of subtle quantum properties of atomic and other systems. By providing insights and modeling capability, our phase-space representation will be of great utility in understanding aspects of atomic physics and chemistry not available with current techniques.
Highlights
Despite its fundamental flaws, the Rutherford description of the atom as electrons orbiting a nucleus is an established icon of the physical sciences
In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules
By providing insights and modeling capability, our phase-space representation will be of great utility in understanding aspects of atomic physics and chemistry not available with current techniques
Summary
The Rutherford description of the atom as electrons orbiting a nucleus is an established icon of the physical sciences This provides a familiar image with which to start a discussion of matter at the subatomic level. In such discussions one rapidly moves towards a more sophisticated view of a set of atomic and molecular orbitals, generally displayed as the 90th percentile of the probability density of the associated quantum-mechanical energy eigenstate. These images represent a much more accurate view; some simplifications remain They are unable to display the entanglement of spin and spatial degrees of freedom due to coupling between the spin of an electron and its orbital angular momentum. It is with these future applications in mind that we demonstrate a more accurate visualization of the atom: one that is familiar, yet at the same time offers more insight into the internal entanglement effects that determine many atomic properties [2,3,4,10,27]
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