regime (as evidenced by the asymmetric sidebands).[]{data-label="bi"}](BISTAB2.eps)

Strong coupling regimes: triple mode splitting and bistability
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The multimode, or at least two mode, self-trapping regime may permit new possibilities for position sensing and for controlling entanglement between two optical modes and the mechanical resonator. Here we investigate regimes where such effects are clearly apparent. The implications of the measurement for the accessible range of optomechanical coupling strengths suggests that multiple hybridization and bistability are quite accessible with reasonable cavity parameters.

In Fig. \[eigensplit\] we investigate the complex behaviour of the eigenmode frequencies of the self-trapped, levitated system. On the left panels (Fig. \[eigensplit\] (a)) we plot the noise spectra of the two optical modes, which exibit sidebands near $\omega
\simeq \omega_M$ since the corresponding optical fields are modulated by the motion of the mechanical oscillator. Here we fix one detuning ($\Delta_1=-1.15$MHz) and look at the behaviour as the other detuning is varied. The sidebands are displaced in frequency and split: one effect is simply due to the dependence of $\omega_M$ on $\Delta_j$ (unique to the levitated system); it arises from the calculation of the equilibrium fields and frequencies. The other effect is due to normal mode mixing (hybridization of light 