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

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