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Physical Review A

Analytical study of the spectrum emitted by a two-level atom driven by a strong laser pulse

ANTONINO DI PIAZZA, Emilio Fiordilino, Marvin H. Mittleman

Published Jun 11, 2001• 28 citations
Publisher

Abstract

The wave function of a two-level atom driven by a low-frequency laser pulse is obtained in analytical form and is used to determine the power spectrum of the dipole moment of the atom for different initial atomic states. The solution goes over some known approximate solutions and gives the energy of the two dressed states, the position of the hyper-Raman lines, the amplitudes both of the hyper-Raman lines and of the odd harmonics, and the position of the cutoff. The form of the hyper-Raman spectrum results independently of the initial atomic state and shows an onset and a cutoff of the emission.

DOI
10.1103/physreva.64.013414

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The wave function of a two-level atom driven by a low-frequency laser pulse is obtained in analytical form and is used to determine the power spectrum of the dipole moment of the atom for different initial atomic states. The solution goes over some known approximate solutions and gives the energy of the two dressed states, the position of the hyper-Raman lines, the amplitudes both of the hyper-Raman lines and of the odd harmonics, and the position of the cutoff. The form of the hyper-Raman spectrum results independently of the initial atomic state and shows an onset and a cutoff of the emission.
Numerical results are presented on the spectrum of the light scattered into the vacuum modes by a two-level atom driven by a strong ramped field of frequency smaller than the natural atomic frequency. The attention is focused on the role of the hyper-Raman part of the spectrum, which is shown to decrease dramatically with increasing ramp time. It is suggested that this may explain lack of experimental observation of the hyper-Raman lines. For zero ramp time, the numerical intensity of both high-order harmonics and hyper-Raman peaks is shown to agree satisfactorily with previous analytical predictions except in the region of overlap of the two series of peaks. This lends support for the suggestion that the plateau in the spectrum is related to quantum-mechanical interference between high-order harmonics and hyper-Raman processes. There is also good agreement between the numerical amplitude of the plateau and previous analytical predictions. A physical mechanism for the cut-off frequency which terminates the plateau, based on approximate energy conservation in hyper-Raman transitions, is presented and is shown to be in agreement with present numerical and previous analytical results.
The photon emission spectrum of the hydrogen atom in an intense high-frequency laser pulse is simulated to show that regular fine structures appear in the two sides of both the odd and even order harmonics. The splitting of the fine structures around the normal harmonic line are determined by the energy differences of the eigenstates of the time averaged Kramers-Henneberger potential with the same parity. The lines around the even order harmonic positions are produced by the hyper-Raman transitions between the dressed atomic states with different parities. The hyper-Raman lines are predicted as long as stabilization occurs and are not so sensitive to the initial state of the atom as those appearing with the low-frequency and less strong laser field. The hyper-Raman lines can be strongly reduced with longer turn-on and turn-off times.
The acceleration of the electron in a two-level atom driven by a short laser pulse of intermediate strength is calculated and therefore analysed through two wavelet transforms in order to obtain the temporal evolution of the spectrum of the emitted radiation. We show (i) the full spectrum at different instants and (ii) the time profile of some representative harmonics. The growth of the harmonics as well as the appearance and erratic behaviour of the hyper-Raman can be followed with the laser intensity.
We have deduced analytical solutions of an energy level diagram of the doubly driven/dressed atom for a two-level atom exposed to a strong near-resonant bichromatic laser field in a special case, i.e., the bichromatic field with frequencies ω 1 and ω 2 , and Rabi frequencies Ω 1 and Ω 2 , in which the first coupling field of Ω 1 acts on the bare atomic levels, and then the resulting singly dressed states are driven by the second coupling field of Ω 2 , thus resulting in the doubly dressed atom. We have measured the probe absorption spectra of a doubly driven two-level atom. The system consists of 5 2 S 1 / 2 , F = 2 and 5 2 P 3 / 2 , F ′ = 3 states of 87 Rb atoms in a magneto-optical trap (MOT) as well as the cooling/trapping beams and an additional coupling field. As for the spectroscopic properties of the doubly driven two-level atom, theoretical analytical solutions are in general agreement with the experimental spectrum as a whole.
We propose an extension of the vectorial model for a linearly polarized field to the more general elliptically polarized field. In particular, we will show how the emitted spectra depend on the ellipticity of the laser, using both an analytic and a numerical approach. A further result deals with the introduction of damping terms into the system. In this case, we show that the main effects of the damping terms are the disappearance of the hyper-Raman lines and the independence of the dynamics from the initial conditions.