Sum rules predict the largest off-resonance electronic nonlinear susceptibility allowed by quantum mechanics. The range between (10 -3/2 to 1) times the physical limit level has until now not been penetrated experimentally and has become known as the quantum gap. We report the first measured second hyperpolarizability to breach the quantum gap. Through cross-linking, the C60-polymer film reported used delocalized electrons from neighboring three-dimensional C60 molecules and realized significant red shift of its energy levels. An ultrafast second hyperpolarizability of 9.6 × 10-32 esu (55% of the physical limit) has been achieved.

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Journal Nano Letters
Chen, Q. (Qiying), Kuang, L. (Li), Wang, Z.Y, & Sargent, E.H. (Edward H.). (2004). Cross-linked C60 polymer breaches the quantum gap. Nano Letters, 4(9), 1673–1675. doi:10.1021/nl049159q