| Summary: | Cavity optomechanics offers quantum ground state cooling, control and measurement of small mechanical oscillators. However optomechanical backactions disturb the oscillator motions: they shift mechanical frequencies and, for a levitated oscillator, rotate the spatial orientation of the mechanical modes. This introduces added imprecisions when sensing the orientation of an external force. For a nanoparticle trapped in a tweezer in a cavity populated only by coherently scattered (CS) photons, we investigate experimentally mode orientation, via the S_{xy}(ω) mechanical cross-correlation spectra, as a function of the nanoparticle position in the cavity standing wave. We show that the CS field rotates the mechanical modes in the opposite direction to the cavity backaction, canceling the effect of the latter. It also opposes optical spring effects on the frequencies. We demonstrate a cancellation point, where it becomes possible to lock the modes near their unperturbed orientations and frequencies, independent of key experimental parameters, while retaining strong light-matter couplings that permit ground state cooling. This opens the way to sensing of directionality of very weak external forces, near quantum regimes.
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