Multimode optomechanics to reach and evade displacement sensitivity limits*

The measurement of mechanical oscillators' displacement is at the basis of many fundamental physics experiments. Fundamental sensitivity limits, where the measurement process becomes the dominant source of measured fluctuations, can nowadays be reached. Optomechanics has recently explored a path to reach and surpass these limits: coupling the displacement to contingent degrees of freedom, and redistribute fluctuations towards these rather than the observable of interest. This idea first emerged with the two motional quadratures of a mechanical oscillator, limiting the quantity of interest to one quadrature only. More recently, optomechanical systems involving multiple modes have extended this concept beyond the measurement of a single motional quadrature.

We will first present how optomechanical systems involving two aluminum drum resonators coupled to two on-chip microwave cavities can provide quantum-limited, phase-insensitive, directional microwave amplification adapted to displacement measurement in microwave-optomechanical systems. We will then show how the same systems can be used to reduce the fluctuations of one mechanical oscillator along the principle of a refrigerator, at the expense of exciting another oscillator. Finally, this system also allows to dynamically couple a pair non-commutating motional quadratures, which therefore make up an artificial oscillator. This proposes a measurement simultaneously evading backaction for these two quadratures, which is famously impossible for pairs commutating quantities. This technique, directly adapted to the detection of continuous variable entanglement, is used to verify the stabilized quantum entanglement of two drum resonators deeper than had been possible before for macroscopic mechanical oscillators.