Quantum collective motion of macroscopic mechanical oscillators

Collective phenomena in physics emerge from interactions among numerous components in a complex system, leading to behaviors distinct from those of individual parts. This domain includes classical phenomena like synchronization and extends to quantum phenomena such as Bose-Einstein condensation and super-radiance. Studying these phenomena in controlled artificial systems allows for simulating complex natural systems. Solid-state mechanical oscillators, controllable via optomechanical coupling, have been proposed for exploring collective phenomena, but experimental realizations face the challenge of requiring nearly degenerate mechanical oscillators. In this work, we present the collective behavior of six mechanical oscillators coupled to a common cavity in a superconducting circuit optomechanical platform. We experimentally demonstrate that increasing the optomechanical coupling rates induces a transition from individual mechanical oscillators to a collective mode, characterized by equal amplitude and relative phase of the oscillators. By utilizing the finite non-degeneracy of mechanical frequencies and rapidly quenching the optomechanical couplings, we directly measure the amplitude and relative phase of the oscillators in the collective mode. We find that the coupling rate of such mode to the cavity increases with the number of coupled oscillators, similar to a Tavis-Cummings system. Further increasing the coupling rates pushes this collective mode into the strong coupling regime with the cavity. We demonstrate sideband ground-state cooling of the collective mode, achieving a 0.4 quanta occupation, and observe quantum sideband asymmetry for this mode. Observing collective optomechanical phenomena in the quantum regime opens avenues for studying synchronization, investigating topological phases of sound, and achieving multipartite phonon-phonon and photon-phonon entanglement.