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arXiv · 1811.02952

Quantum Kerr oscillators' evolution in phase space: Wigner current, symmetries, shear suppression and special states

Maxime Oliva·Ole Steuernagel
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Abstract

The creation of quantum coherences requires a system to be anharmonic. The simplest such continuous 1D quantum system is the Kerr oscillator. It has a number of interesting symmetries we derive. Its quantum dynamics is best studied in phase space, using Wigner's distribution W and the associated Wigner phase space current J. Expressions for the continuity equation governing its time evolution are derived in terms of J and it is shown that J for Kerr oscillators follows circles in phase space. Using J we also show that the evolution's classical shear in phase space is quantum suppressed by an effective `viscosity'. Quantifying this shear suppression provides measures to contrast classical with quantum evolution and allows us to identify special quantum states.

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Maxime Oliva, Ole Steuernagel. 2019-03-19. Quantum Kerr oscillators' evolution in phase space: Wigner current, symmetries, shear suppression and special states. https://doi.org/10.1103/physreva.99.032104

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