Quantum limits of nonlinear susceptibilities, and beyond

We study the limits of susceptibilities as measured with hyper Rayleigh scattering (HRS). We find that octupolar molecules also obey the quantum sum rules, as predicted by the theory. All conceivable molecular engineering approaches, designed to break these limits, are most likely futile because the sum rules take into account all interactions that can be written by a potential energy function. As such, any molecule or system whose Hamiltonian is given by electromagnetic interactions will be bounded by the theory. Since the sum rules can not be violated (because such a violation is equivalent to a violation of the Schrodinger equation) perhaps the only fruitful avenues to approach are to consider slightly resonantly enhanced susceptibilities or molecules that go beyond the dipole approximation.