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A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint.

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We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis… Click to show full abstract

We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but it has not been defined explicitly for quantum nonlinear oscillators. In this study, we define the asymptotic phase for quantum oscillatory systems by using the eigenoperator of the backward Liouville operator associated with the fundamental oscillation frequency. By using the quantum van der Pol oscillator with a Kerr effect as an example, we illustrate that the proposed asymptotic phase appropriately yields isochronous phase values in both semiclassical and strong quantum regimes.

Keywords: quantum nonlinear; nonlinear oscillators; asymptotic phase; phase quantum; phase

Journal Title: Chaos
Year Published: 2022

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