Wigner Function Flow in Generalized Quantum Harmonic Oscillators
Popo Yang1*, Shin-Tza Wu2, Ray-Kuang Lee1,3,4
1Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
2Department of Physics, National Chung Cheng University, Chiayi, Taiwan
3Institute of Photonics, National Tsing Hua University, Hsinchu, Taiwan
4Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan
* Presenter:Popo Yang, email:popoycr@gmail.com
We develop a continuity equation for Wigner function flow and calculate the corresponding circulation values, for generalized quantum harmonic oscillators with parity-time (PT) symmetry or with parametric optical process. For the PT-symmetric non-Hermitian Hamiltonian, we reveal how a PT -symmetry breaking manifests itself in the phase-space representation through the circulation values of Wigner function flows; while for the optical parametric oscillators (OPO), how the vacuum states evolves into squeezed states and interference inside Schrodinger cat states are revisited through the Wigner function flow.

Keywords: Wigner distribution function, Wigner flow, PT symmetry