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

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.

Pair production at the focus of two equal and oppositely directed laser beams: The effect of the pulse shape

“…Now, the coefficients given in Eqs. (21) and (22) in [25] correspond exactly to the coefficients c ÿm;# t and c m;# t [or, equivalently, c ÿm;" t and c m;" t] calculated up to first order in the time derivative of t. By using those coefficients and by adapting the notation, it can easily be shown that up to first order where the change of variable !t has been performed. Now, despite that the previous integral cannot be evaluated exactly, we have said that in our hypotheses m=!…”

“…2m in such a way the external perturbation can be considered adiabatic. In this respect, the adiabatic treatment used in [25] in the different context of high order harmonic generation can also be used here to calculate the probability PT=2 that a pair is created at the end of the laser pulse. In fact, by assuming, for example, that c ÿm;# ÿT=2 1 and c ÿm;" ÿT=2 0, this probability is given by 1…”

“…decoupled two-level (both with energies ÿm and m) systems subject to an external adiabatic perturbation (the laser periods we have in mind are much larger than the typical times during which a pair is created). By using a technique already applied in [25], we have been able to calculate the production probability at the end of the pulse by including perturbatively the effect of the pulse shape. The final result Eq.…”

“…This system has been largely used in the study of high order harmonic generation by atoms [20 -25]. In particular, some results we have already obtained in [25] will be used here also. Finally, the production probability so calculated has been compared with the analogous quantity obtained in the presence of an infinite laser pulse with a constant pulse shape and, as we will remark in the conclusion [see Sec.…”

Algebraic solution for a two-level atom in radiation fields and the Freeman resonances

“…And Cohen-Tannoudji et al [5] used perturbation methods to solve a quantumfield two-level system. Mittleman et al [6] have recently derived the wave functions and quasi energies for a two-level atom driven by a low-frequency strong laser pulse and applied their result to emission spectra and high harmonic generation (HHG). The low-frequency approximation adopted by Mittleman et al skips all higher resonances and can be thought of as a limiting case opposite to the near-resonance approximation.…”