Dependence on relative phase for bichromatically driven atoms

Abstract

We consider the interaction of atoms with a pulse of a linearly polarized electric field consisting of two phase-locked frequencies whose ratio ωH/ωL is the ratio of arbitrary integers h/l, with h>l. If the electric amplitudes vary in time, they do so with the same slow envelope. The relative phase can be used as a control parameter via variation of the phase ϕH of ωH or ϕL of ωL. We derive the physically important ranges of relative phase for total-yield processes as a function of h:l; they depend on whether h,l are both odd or only one is odd. We tabulate a variety of relevant phase-dependent results for all h:l from 2:1 through 8:7. We use calculations and experimental data for helium and hydrogen Rydberg atoms driven by a bichromatic microwave field to confirm the physically important ranges of ϕH and ϕL for a few h:l ratios. Two experimental examples taken from the literature for the interactions of atoms with sub-picosecond, bichromatic laser pulses also confirm our conclusions.

Periodic orbit bifurcations as an ionization mechanism: the bichromatically driven hydrogen atom

“…From quantum calculations, φ c ≈ 0.5 was obtained in Ref. [19] which is in very good agreement with the parameter value φ c ≈ 0.49 at which the bifurcation of the upper [19]. Only periodic orbits with period 2π are considered.…”

“…One should notice that the (rescaled) principal quantum number considered in Ref. [19] lies in between these two islands (see the continuous horizontal line). We monitor the stability of this set of periodic orbits as we have performed for Case (I).…”

“…For this mode locking, we consider F h = 24 Vcm −1 and F l = 53.4 Vcm −1 as in Ref. [19]. These values correspond to the dimensionless values (2) for Case (I) at φ = 0.…”

“…In addition, there is also a period 2 island in between these two main islands (associated with an elliptic and hyperbolic periodic orbits with period 4π). In the region of phase space around J i ≈ 0.49 (indicated by a straight line) where the initial states n = 51 are prepared [19], any regular structures like the main islands and smaller ones are associated with trappings and hence reduce the ionization rate. Figure 2 shows a Poincaré section of Hamiltonian (2) for Case (I) at φ = π/3.…”

Near-infrared resonance-mediated chirp control of a coherently generated broadband deep-ultraviolet spectrum

“…The initial identification of the interfering pathways and their interference mechanism allows us to employ a rational control approach that has been shown to be very successful in a variety of nonresonant and resonance-mediated multiphoton processes in atoms and molecules . For completeness, it worth mentioning that coherent phase control of multiphoton excitation and ionization processes has also been demonstrated by other means, including narrow-band optical light [2,3] and microwave radiation [28,29].…”