Visualizing the Quantum Interaction Picture in Phase Space
Bahar Mehmani, Andrea Aiello

TL;DR
This paper demonstrates how the quantum Interaction Picture's evolution can be visualized as local and global transformations of the Wigner function in phase space, using a driven harmonic oscillator model.
Contribution
It provides a novel phase space visualization of the quantum Interaction Picture and derives exact time-evolution operators using the Magnus series.
Findings
Interaction Picture corresponds to local phase space transformations.
Exact time-evolution operator derived for a driven harmonic oscillator.
Phase space visualization clarifies quantum dynamics in the Interaction Picture.
Abstract
We illustrate the correspondence between the quantum Interaction Picture-evolution of the state of a quantum system in Hilbert space and a combination of local and global transformations of its Wigner function in phase space. To this aim, we consider the time-evolution of a quantized harmonic oscillator driven by both a linear and a quadratic (in terms of bosonic creation and annihilation operators) potentials and employ the Magnus series to derive the exact form of the time-evolution operator. In this case, the Interaction Picture corresponds to a local transformation of phase space-reference frame into the one that is co-moving with the Wigner function.
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