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Chinese Physics B

Fine splits of photon emission spectrum of hydrogen atom caused by transitions between different dressed states in intense high frequency laser field

Zhou Zhao-Yan, Yuan Jian-Min

Published Dec 1, 2008• 5 citations
Publisher

Abstract

The photon emission spectrum of the hydrogen atoms in an intense high-frequency laser pulse is simulated by using one-dimensional soft Coulomb potential. Regular fine structures appear on the two sides of both the odd and even multiples of photon energy of the laser field besides the ordinary odd harmonic peaks. It is proved that the splits of the fine structures are responsible for hyper-Raman lines and the energy spacing between the odd harmonic lines is equal to the direrence in energy between the eigenstates with the same parity of the time averaged Krameters–Henneberger (KH) potential. By analysing the features of the fine structures, we also verify that the so-called even order harmonics under the stabilization condition are indeed hyper-Raman lines caused by the transitions between the dressed atomic states with different values of parity.

DOI
10.1088/1674-1056/17/12/032

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Journal of Physics B Atomic Molecular and Optical Physics•Oct 14, 1994•20 citations
The photon emission spectrum of the hydrogen atoms in an intense high-frequency laser pulse is simulated by using one-dimensional soft Coulomb potential. Regular fine structures appear on the two sides of both the odd and even multiples of photon energy of the laser field besides the ordinary odd harmonic peaks. It is proved that the splits of the fine structures are responsible for hyper-Raman lines and the energy spacing between the odd harmonic lines is equal to the direrence in energy between the eigenstates with the same parity of the time averaged Krameters–Henneberger (KH) potential. By analysing the features of the fine structures, we also verify that the so-called even order harmonics under the stabilization condition are indeed hyper-Raman lines caused by the transitions between the dressed atomic states with different values of parity.
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 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.
Abstract The spontaneous emission of a quantum system driven by a high-intensity, high-frequency classical laser field is analyzed. The study is based on the accurate consideration of the quantum system interacting with vacuum-quantized field modes in the first order of perturbation theory, while the intense laser field is considered classically beyond this theory. It is demonstrated that the spectrum of the spontaneous emission can be used for analyzing the strong-field dynamics and the structure of the energy spectrum of an atomic system. In particular, it is found that in high-frequency fields (where the energy of the laser quanta is greater than the ionization potential) atoms manifest the features of the Kramers–Henneberger atom. It is also found that in the stabilization regime, the atom emits both odd and even laser radiation harmonics.
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.
We present a theory of harmonic generation by a strongly driven atom within the framework of non-relativistic QED. The atom is assumed to possess a finite number N of levels and ionization is neglected. This atom is dressed by the driving field using a unitary time-dependent transformation. Within the quasistatic approximation this transformation is shown to lead from the bare to the Floquet atom. The interaction of the Floquet atom with the vacuum modes is derived and it is shown to give rise both to the high-order harmonic and to the hyper-Raman spectrum. In the case N=2 the spectrum of the light scattered into the vacuum modes can be evaluated analytically and it is shown to consist of two parts. Neglecting interference between these two parts, the first of them is the high-order harmonic spectrum displaying peaks at the odd harmonics of the driving field. The second part is the hyper-Raman spectrum which has finite bandwidth and which displays peaks at the even harmonics of the laser frequency, centred at the Stark-shifted natural atomic frequency. These two spectra partially overlap and they are discussed in various ranges of intensity of the driving field, both in the minimal coupling and in the multipolar scheme. The results support recent suggestions that the presence of the plateau is related to interference between the two spectra. The dependence of the high-order harmonic spectrum from the driving field intensity is found to be related to that of the hyper-Raman spectrum in such a way that when the former increases the latter decreases and vice versa. It is argued that this might help to explain the non-visibility of the hyper-Raman lines when the high-order harmonics are visible.