Fig. 3: Two-dimensional state purity μ for the motion of a nanoparticle in the tweezer transverse plane.
From: High purity two-dimensional levitated mechanical oscillator
We show the results obtained in different experiments as a function of the overlap parameter \(s=2({g}_{x}^{2}+{g}_{y}^{2})/\kappa \delta\). Green dots: ref. 8. Magenta squares: ref. 29. Blue triangles: ref. 9. Red diamonds: this work, including the additional data sets. In order to provide an indication of the two-dimensional correlations present in the mechanical system, we also show the contour plot of the symmetrized quantum discord \(0.5({{\mathcal{D}}}_{X\leftarrow Y}+{{\mathcal{D}}}_{Y\leftarrow X})\), calculated with the following parameters: gx/2π = gy/2π = 12400 Hz, Γx/2π = Γy/2π varying between 100 Hz and 300 kHz, Δ = − 0.5(ΩX + ΩY). The other parameters are chosen similar to those of the present work for s > 0.7, while for s < 0.7 they change to keep realistic ranges. In details, for s > 0.7 we use κ/2π = 57 kHz and (ΩX + ΩY)/4π = 116 kHz. For s < 0.7, both the cavity width and the mean oscillation frequency increase, reaching κ/2π = 330 kHz and (ΩX + ΩY)/4π = 246 kHz when s = 0.07, thus approaching the parameters of ref. 9. The variations laws are κ/2π = [57 + (330 − 57)x4] kHz and (ΩX + ΩY)/4π = [116 + (246 − 116)x2] kHz where x = (s − 0.7)/(0.07 − 0.7). In the full graph, the frequency splitting δ is determined by s according to \(s=2({g}_{x}^{2}+{g}_{y}^{2})/\kappa \delta\).
