Realization of a degenerate parametric oscillator in electromechanical systems

E. Jansen, J. D.P. Machado, Ya M. Blanter

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
122 Downloads (Pure)


We consider an electromechanical system in which a microwave cavity is coupled to a mechanical resonator, with a mechanical frequency twice the microwave frequency. In this regime, the effective photon-phonon interaction is equivalent to that of a degenerate parametric amplifier, instead of the typical radiation pressure interaction. If the mechanical resonator is strongly driven, it undergoes a phase transition to a state in which the energy pumped into the mechanical mode is entirely converted to the photonic mode. Quantum fluctuations smear this phase transition. We describe these effects with a steady-state Fokker-Planck equation in the complex P representation and compute the photonic field intensity and quadrature variances, as well as the mechanical amplitude. This Fokker-Planck method performs better than the standard linearization results when compared to numerical simulations.

Original languageEnglish
Article number045401
Number of pages7
JournalPhysical Review B
Issue number4
Publication statusPublished - 2019


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