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Register a new userHow periodic orbit bifurcations drive multiphoton ionization
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The multiphoton ionization of hydrogen by a strong bichromatic microwave field is a complex process prototypical for atomic control research. Periodic orbit analysis captures this complexity: Through the stability of periodic orbits we can match qualitatively the variation of experimental ionization rates with a control parameter, the relative phase between the two modes of the field. Moreover, an empirical formula reproduces quantum simulations to a high degree of accuracy. This quantitative agreement shows how short periodic orbits organize the dynamics in multiphoton ionization.
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We investigate the multiphoton ionization of hydrogen driven by a strong bichromatic microwave field. In a regime where classical and quantum simulations agree, periodic orbit analysis captures the mechanism: Through the linear stability of periodic orbits we match qualitatively the variation of experimental ionization rates with control parameters such as the amplitudes of the two modes of the field or their relative phases. Moreover, we discuss an empirical formula which reproduces quantum simulations to a high degree of accuracy. This quantitative agreement shows the mechanism by which short periodic orbits organize the dynamics in multiphoton ionization. We also analyze the effect of longer pulse durations. Finally we compare our results with those based on the peak amplitude rule. Both qualitative and quantitative analyses are implemented for different mode locked fields. In parameter space, the localization of the period doubling and halving allows one to predict the set of parameters (amplitudes and phase lag) where ionization occurs.
We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios on the Poincare surface of section. Uniform approximations for the density of states for an integrable Hamiltonian system with two degrees of freedom are derived and successfully reproduce the numerical quantum-mechanical results.
We present a control procedure to reduce the stochastic ionization of hydrogen atom in a strong microwave field by adding to the original Hamiltonian a comparatively small control term which might consist of an additional set of microwave fields. This modification restores select invariant tori in the dynamics and prevents ionization. We demonstrate the procedure on the one-dimensional model of microwave ionization.
Coupled map lattices have been widely used as models in several fields of physics, such as chaotic strings, turbulence, and phase transitions, as well as in other disciplines, such as biology (ecology, evolution) and information processing. This paper investigates properties of periodic orbits in two coupled Tchebyscheff maps. The zeta function cycle expansions are used to compute dynamical averages appearing in Becks theory of chaotic strings. The results show close agreement with direct simulation for most values of the coupling parameter, and yield information about the system complementary to that of direct simulation.
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this letter these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.
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