Collective dynamics in circuit optomechanical systems*

Optomechanical systems are polyvalent platforms suited for controlling an extremely long-lived mechanical degree of freedom, realizing high-precision sensors, and benchmarking quantum mechanics at a macroscopic scale. Nevertheless, most of their implementation fails to harvest the advantages of multimode systems, mainly due to challenges in realizing reproducible mechanical and optical (microwave) resonances. Here, we investigate multiple nearly degenerate mechanical oscillators optomechanically coupled to a shared microwave cavity, implemented by superconducting mechanically compliant vacuum gap capacitors shunted by spiral inductors. We show that the mechanical resonators undergo a transition from individual to collective dynamics as their optomechanical interactions are enhanced. We finally study the sideband collective cooling of multimode mechanical systems, where one collective mechanical mode is efficiently cooled down while the individual modes remain the large phonon occupations.