Period tripling due to Josephson parametric down-conversion beyond the rotating-wave approximation

Abstract

Parametrically driven oscillators can display period tripling in response to a drive at thrice the resonance frequency. In contrast to the parametric instability for period doubling, the symmetric fixed point corresponding to the state of rest remains stable at arbitrary strong driving for the tripling transition. Previously, it has been shown that fluctuations can circumvent this and induce a period-tripling instability. In this article, we explore an alternative way of inducing a period-tripling transition by investigating properties of period tripling due to parametric down-conversion beyond the rotating-wave approximation. We show that despite the absence of an instability threshold, off-resonant frequency contributions can induce a period-tripling transition by activating the parametric down-conversion. Moreover, we study the subsequent period-tripled states of the Josephson potential and discuss the asymmetry between the clockwise and counterclockwise rotating fixed points that only arises beyond the rotating-wave approximation.

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