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

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.

arXiv comment8 pages, 7 Figures

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• Echoes in a Single Quantum Kerr-nonlinear Oscillator
• Nonlinear effects on the dynamics of quantum harmonic modes coupled through angular momentum
• Exponential unitary integrators for nonseparable quantum Hamiltonians
• Lindblad Superoperators from Wigner's Phase Space Continuity Equation
• Wigner's Phase Space Current for Variable Beam Splitters -Seeing Beam Splitters in a New Light-
• Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems
• Truncated Wigner approximation as a non-positive Kraus map
• Isospectral mapping for quantum systems with energy point spectra to polynomial quantum harmonic oscillators
• On the Formation of Lines in Quantum Phase Space