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arXiv · 1204.1302

Visualizing the Quantum Interaction Picture in Phase Space

Bahar Mehmani·Andrea Aiello
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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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Bahar Mehmani, Andrea Aiello. 2012-04-05. Visualizing the Quantum Interaction Picture in Phase Space. https://doi.org/10.1088/0143-0807%2F33%2F5%2F1367

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