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AIP conference proceedings

Two-level atom in an intense low-frequency field: Effects of damping and ellipticity of the field

L. Lo Cascio

Published Jan 1, 2000• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.1291976

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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.
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.
An ansatz is proposed for the analytic solution of the Heisenberg equations of a two-level atom in a classical, linearly polarized and intense low-frequency field. According to this ansatz, the motion of the vector representing the state of the atom on the Bloch sphere consists of a fast precession around a direction, which in turn basculates slowly around an axis perpendicular to the field. The time evolution of the atomic state, which is obtained analytically by this vectorial model, is shown to compare quite satisfactorily with the exact numerical solution of the Heisenberg equations. The limits of validity of the ansatz are discussed. The spectrum of the light scattered by the two-level atom is evaluated analytically using the ansatz and it is shown to reproduce very precisely the exact spectrum evaluated numerically. It is shown that the slow component of the motion of the atomic Bloch vector yields the high-order harmonic part of the spectrum, whereas the fast precession gives rise to the hyper-Raman part. The appearance of the overall spectrum is discussed as a function of the various physical parameters of the model. The insight provided by the vectorial model is exploited to investigate the manifest universality of the main features of the overall spectrum and to suggest experiments to test the validity of the vectorial model.
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.
In a previous paper, we have already considered the system composed by a two level atom interacting with a coherent external electromagnetic field. No application whatsoever has been made of the rotating wave approximation. Being specially interested in the problem of higher harmonic generations for the case of very intense laser fields, we have developed in this letter a much more efficient way to obtain these solutions as well as to carry out some calculations in a range in which the parameters take extreme values. Also the formalism allows us now to provide analytic expressions in the WKB regime for the electric dipole moment and the population inversion. The spectrum can be decomposed in periodic and non-periodic contributions. Only the latter depends upon the Floquet exponent and can be responsible of the main complexities of the observed Rabi revivals and the hyper-Raman shift.
We present the most prominent features in two-colour coherent control of high-order harmonic generation using a strongly driven two-level atom model, which are known to generate high harmonics as well as hyper-Raman lines with a plateau and a cut-off. Furthermore, for one laser field case, we find, when the hyper-Raman lines are located at the position of the high harmonics, that the high harmonics are strongly enhanced due to the interference effect between the high harmonics and the hyper-Raman lines. Within these conditions, by combining the laser field with another much weaker laser field, we show plentiful and strong high harmonics in the light spectrum of the driven atomic system.
We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.