“…For optically levitated nanoparticles, where ω 0 / ∼ 10 2 [4,30,31], and x 0 ∼ 10 −12 m, the condition reads σ 10 nm, which is not compatible with optical potentials where σ is lower bounded by an optical wavelength. Therefore, levitated nanoparticles require either longer coherence times, achievable by evolution in the absence of recoil heating from laser light (quasielectrostatic traps [32][33][34][35][36], magnetic traps [37][38][39], or in free fall [40,41] where the quartic potential is only applied after the state has sufficiently broadened) or the use of electromagnetic forces near surfaces [42][43][44] such that σ can be potentially smaller than an optical wavelength. Instead of aiming for stronger nonquadratic potentials or longer decoherence times one could also speed up the broadening of the initially prepared state by introducing an inverted harmonic potential [44,45] at the center of the quartic trap, that is, using a double-well potential.…”