Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, this leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical resonances in the isomerizing system CN-Li
⇆Li-CN. By using a correlation diagram of eigenenergies versus Planck constant, we show the existence of different series of avoided crossings, leading to the corresponding series of quantum resonances, which represent the quantum manifestations of the classical resonances. Moreover, the extrapolation of these series to
ℏ=0 unveils the correspondence between the bifurcation energy of classical resonances and the energy of the series of quantum resonances in the semiclassical limit
ℏ→0. Additionally, in order to obtain analytical expressions for our results, a semiclassical theory is developed.
We present experimental measurements of the mean energy in the vicinity of the first and second quantum resonances of the atom-optics kicked rotor for a number of different experimental parameters. Our data are rescaled and compared with the one-parameter
(ϵ) classical scaling function developed to describe the quantum resonance peaks. Additionally, experimental data are presented for the ``classical'' resonance which occurs in the limit as the kicking period goes to zero. This resonance is found to be analogous to the quantum resonances, and a similar one-parameter classical scaling function is derived, and found to match our experimental results. The widths of the quantum and classical resonance peaks are compared, and their sub-Fourier nature examined.