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Physical Review A

Resonant pulse excitation leading to ionization

Jay R. Ackerhalt

Published Jan 1, 1978• 19 citations
Publisher

Abstract

Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time $t$, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the $N$-level atom is discussed.

DOI
10.1103/physreva.17.293

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Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width \ensuremathγ\ensuremath{\gamma}\ensuremathγ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time ttt, \ensuremathΦ(t)\ensuremath{\Phi}(t)\ensuremathΦ(t). Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: \ensuremathΦ(t)\ensuremath≈sin\ensuremathΦ(t)\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)\ensuremathΦ(t)\ensuremath≈sin\ensuremathΦ(t) and \ensuremathΩ(t)>\ensuremathγ\ensuremath{\Omega}(t)>\ensuremath{\gamma}\ensuremathΩ(t)>\ensuremathγ, where \ensuremathΩ(t)\ensuremath{\Omega}(t)\ensuremathΩ(t) is the resonance Rabi frequency. The generalization of the two-level atom results to the NNN-level atom is discussed.
We present a comprehensive analytical study of the optical Bloch equations for a closed two-level atom. We obtain a map in phase space of the Rabi frequency and the laser frequency detuning, discriminating the characteristics of solutions to the optical Bloch equations separated by a boundary in phase space. Outside the boundary, oscillatory behavior is shown, while simple decaying behavior is shown inside the boundary. The behavior of the solutions is also found to be dependent on the relative magnitude of the decay rates of the optical coherence and the excited state population.
We present an exactly solvable two-level model with smoothly varying coupling, detuning, and loss functions. Whenever the common temporal profile of these parameter functions is analytically integrable, the complex population amplitudes are found for all times in simple analytic forms. This makes the model suitable for studying the population and phase dynamics of resonance-enhanced ionization processes. Incorporating two-photon Rabi frequency, dynamical Stark shifts, and one-photon ionization rate into this model, the 2 + 1 photon ionization of atomic lithium is studied as a showcase example. Finally, when the intensity profile of the laser pulse has the sine-squared shape, we find the exact analytic expression of the photoelectron spectrum, allowing additional insight into the structure of the Autler-Townes doublet.
It has been widely believed that short-pulse multiphoton ionization is dominated by a resonance process: excited states of the atom are shifted by the radiation field into multiphoton resonance with the ground state, are populated, and then rapidly ionized. A recent experiment, shows significant population remaining in excited states at the end of the laser pulse, and this result has been interpreted as indicating that ionization proceeds slowly out of these states. We investigate this issue in the framework of Floquet theory, supplemented by direct numerical solution of the time-dependent Schrodinger equation. In this framework, the standard picture is portrayed as an adiabatic transition between Floquet eigenstates, which occurs as the amplitude of the laser field is ramped through the resonance value (i.e. through an avoided crossing of Floquet quasienergies). Thus it follows that the same type of transition must occur as the field is turned off. This mechanism can yield significant populations of excited states that do not suffer appreciable ionization. We exhibit this effect by numerical studies of a model atom with two bound states and two continua.
We have found new analytic results for a wide variety of atomic excitation processes which involve the use of amplitude-and frequency-modulated laser pulses: (1) We have unified all the previously known solutions including those of Rosen and Zener,1 Landau2 and Zener,3 Rabi,4 Bambini and Berman,5 Demkov,6 McCall and Hahn,7 Allen and Eberly,8 and Hioe,9 among others, and have significantly extended it with expressions involving three free parameters and an arbitrary function to an infinite variety of amplitude-and frequency-modulated laser pulses.10 We have found a simple condition which the three essential parameters in the amplitude-and frequency-modulation functions must satisfy in order to achieve a complete population inversion, or to achieve a complete population restoration as in the case of self-induced transparency7 or soliton propagation.