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Physical Review A

Limitations on quantum ladder climbing in complex systems

Rutger B. Vrijen, D. Duncan, Lambertus D. Noordam

Published Sep 1, 1997• 18 citations

Abstract

The use of cesium Rydberg atoms as a test system for quantum ladder climbing with chirped laser pulses is described. Quantum ladders can be used in the coherent control of chemical reactions; for instance, by exciting a specific molecular bond by climbing its vibrational ladder. A Rydberg atom is an easy test system because of the large transition dipole moments between Rydberg states. The Rydberg states are easy to access and to analyze. Picosecond far-infrared laser pulses around a wavelength of 50 \ensuremath{\mu}m, with peak intensities of ${10}^{9}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2},$ from the free-electron laser for infrared experiments (FELIX) at Nieuwegein, The Netherlands, were used. It is found that the complexity of the system puts severe limits on the allowed intensities that are used to drive the ladder. At high intensity the ladder is distorted due to coupling with states outside the ladder. This distortion frustrates efficient climbing.

DOI: 10.1103/physreva.56.2205

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The use of cesium Rydberg atoms as a test system for quantum ladder climbing with chirped laser pulses is described. Quantum ladders can be used in the coherent control of chemical reactions; for instance, by exciting a specific molecular bond by climbing its vibrational ladder. A Rydberg atom is an easy test system because of the large transition dipole moments between Rydberg states. The Rydberg states are easy to access and to analyze. Picosecond far-infrared laser pulses around a wavelength of 50 \ensuremath{\mu}m, with peak intensities of

{10}^{9}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2},

from the free-electron laser for infrared experiments (FELIX) at Nieuwegein, The Netherlands, were used. It is found that the complexity of the system puts severe limits on the allowed intensities that are used to drive the ladder. At high intensity the ladder is distorted due to coupling with states outside the ladder. This distortion frustrates efficient climbing.

The theory of vibrational ladder climbing excitation by coherent stimulated nonresonant Raman using chirped laser pulses is developed. We analytically obtain the conditions for inverting the population to a final preselected vibrational state and the restrictions that apply in the linear chirp regime. By controlling both the shape of the laser pulses and the chirp profile, the ladder climbing process can be accelerated without reducing the yield of the selective excitation. Numerical results are presented for selection of moderately excited vibrational levels in Na 2, where the important contribution of several excited electronic states is also clarified.

Excitation of a quantum ladder system by frequency-swept (-chirped) laser pulses has been investigated by studying an atomic model system, the 5s-5p-5d ladder of rubidium. The population transfer is significantly enhanced when the frequency is swept such that it follows the spacing of the ladder. At intermediate intensities we observe oscillations in the population transfer to the upper level (5d), which can be attributed to interference between two routes of excitation: sequential transfer and direct two-photon excitation via a virtual intermediate state. We determine simultaneously the population transfer to the upper level (5d) and the direct three-photon ionization, the latter corresponding to a three-step ladder with the final state being in the continuum: 5s-5p-5d-\ensuremath{\varepsilon}p/\ensuremath{\varepsilon}f. Experiments were performed, using 100 fs pulses at \ensuremath{\sim}780 nm from a self-mode-locked Ti:

{\mathrm{Al}}_{2}

{\mathrm{O}}_{3}

oscillator amplified at 10 Hz.

The interplay between quantum-mechanical and classical evolutions in a chirped-driven Rydberg atom is discussed. It is shown that the system allows two continuing resonant excitation mechanisms, i.e., a successive two-level transitions (ladder climbing) and a continuing classicallike nonlinear phase locking (autoresonance). The persistent 1:1 and 2:1 resonances between the driving and the Keplerian frequencies are studied in detail and characterized in terms of two dimensionless parameters

{P}_{1,2}

representing the driving strength and the nonlinearity in the problem, respectively. The quantum-mechanical rotating wave and the classical single-resonance approximations are used to describe the regimes of efficient classical or quantum-mechanical excitation in this two-parameter space.

Two-photon excitation of a quantum ladder system by an ultrashort chirped pulse leads to interferences in the excited-state population, between direct and sequential paths. Experimental results have been obtained in atomic sodium vapor. The presence of several intermediate and final states leads to new phenomena. The interplay between the two sequential paths leads to strongly contrasted oscillations and a large enhancement of the transition probability for precise values of the chirp. A cubic spectral phase modifies significantly the behavior of the quantum interferences and can be used to enhance the two-photon absorption rate.