Coherent Features of Resonance-Mediated Two-Photon Absorption Enhancement by Varying the Energy Level Structure,Laser Spectrum Bandwidth and Central Frequency

The femtosecond pulse shaping technique has been shown to be an effective method to control the multi-photon absorption by the light–matter interaction. Previous studies mainly focused on the quantum coherent control of the multi-photon absorption by the phase, amplitude and polarization modulation, but the coherent features of the multi-photon absorption depending on the energy level structure, the laser spectrum bandwidth and laser central frequency still lack in-depth systematic research. In this work, we further explore the coherent features of the resonance-mediated two-photon absorption in a rubidium atom by varying the energy level structure, spectrum bandwidth and central frequency of the femtosecond laser field. The theoretical results show that the change of the intermediate state detuning can effectively influence the enhancement of the near-resonant part, which further affects the transform-limited （TL）-normalized final state population maximum. Moreover, as the laser spectrum bandwidth increases, the TL-normalized final state population maximum can be effectively enhanced due to the increase of the enhancement in the near-resonant part, but the TL-normalized final state population maximum is constant by varying the laser central frequency. These studies can provide a clear physical picture for understanding the coherent features of the resonance-mediated two-photon absorption, and can also provide a theoretical guidance for the future applications.

A NUMERICAL METHOD FOR SECOND ORDER MEAN FORCES AND SLOWLY VARYING FORCES ON A FLOATING STRUCTURE

Existing far field expressions of second order potentials are by no means complete.Hence there has been no exact far field expression of second order potentials.In this paper the far field expression for Φ_d^((2)) is purposely avoided in deducing the formulae of second order forces and a series of functions Φ_(dRn)^((?)) are used.The far field expression of is given,which for (x,U,z)∈Σ,φ_(dRn)^((2))(?) φ_d^((2)).Using these properties formulae for calculating second order diffraction forces are obtained.To calculate the integral ∫∫_(?)1/g f_(?)Ψ_(?)ds it is divided into two parts.One is the integral over a finite domain and the function under the integral is continuous,so the usual approximate integration formulae may be used. The other is the integral over an infinite domain.Using the far field expression of first order potentials,formulae for calculating the integral to meet given accuracies are given. The mooring force in surge direction is used for comparison between numerical predictions and experimental measurements.The predicted results are checked against the measured value in a specially designed test.In the low frequency domain of interest,the mooring forces in surge,for calculated and experimental spectra are in good consistency so long as the damping coefficients is choosen appropriately.

ADIABATIC INVARIANTS OF SLOWLY VARYING THREE－DIMENSIONAL SYSTEMS AND EXISTENCE OF INVARIANT TORI OF LOTKA－VOLTERRA EQUATION

In this paper, we use the theory of generalized Poisson bracket (GPB) to build the Poisson structure of three-dimensional 'frozen' systems Of Hamiltonian systems with slow time variable,and show that under proper conditions, there exists an adiabatic invariant on every closed simply connected symplectic leaf for the time-dependent Hamiltonian systems. If the Hamiltonian H(p,q,τ) on these symplectic leaves are periodic with respect to τ and the frozen systems are in some sense strictly nonisochronous, then there are perpetual adiabatic invariants. To illustrate these results, we discuss the classical Lotka-Volterra equation with slowly periodic time-dependent coefficients modeling the interactions of three species.