Mode-selective multiphoton excitation in a model system

A computational study is made of mode-selective multiphoton excitation in a model nonseparable anharmonic-oscillator system. The time evolution of quantal wave packets on the Hénon-Heiles potential surface is treated via Floquet theory; periodicity of the classical laser field, $E_{0}cos\omega t$, is utilized to formulate the propagator for the state amplitudes. In a previous study by Hose and Taylor, a criterion was developed by which the quantum states corresponding to the classical quasiperiodic motion are identified. Two types of quasiperiodic states exist in the Hénon-Heiles system: $Q^{\mathrm{I}}$, the normal mode and $Q^{\mathrm{II}}$, a local (bond) mode; highly mode-mixed states are designated as $N$ (nonquasi-periodic). In the present study it is found that efficient multiphoton excitation into a subset of the $Q^{\mathrm{I}}$ states lying between the classical critical energy and the dissociation barrier is obtained, provided that the field strength is not too large and the frequency of the laser is tuned to the fundamental of the $Q^{\mathrm{I}}$ ladder. Implications for mode-selective excitation in real systems are discussed.