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Journal of Modern Optics

Resonance fluorescence in intense laser fields

Dan E. Browne, Christoph H. Keitel

Published Jul 1, 2000• 21 citations
Publisher

Abstract

We consider the resonance fluorescence of a two-level atom in a vacuum with a high intensity driving field, such that the Rabi frequency of the field is non-negligible up to frequencies comparable to the transition frequency of the atom. At these high intensities, the conventional rotating wave approximation cannot be applied to the atom-laser Hamiltonian and the modal densities of the vacuum at the dressed transition frequencies differ significantly from each other. On treating the counter-rotating part of the Hamiltonian as a perturbation and carrying out the Weisskopf-Wigner approximation in the dressed states basis, we find that the high driving intensity leads to significant deviations from the traditional Mollow resonance fluorescence spectrum. In particular we find unequally intense Mollow side-bands and that the generation of higher order triplets and harmonics is substantially enhanced by the high vacuum modal density at the corresponding high resonance frequencies.

DOI
10.1080/09500340008235106

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Physical Review A•Jul 1, 1986•22 citations
We consider the resonance fluorescence of a two-level atom in a vacuum with a high intensity driving field, such that the Rabi frequency of the field is non-negligible up to frequencies comparable to the transition frequency of the atom. At these high intensities, the conventional rotating wave approximation cannot be applied to the atom-laser Hamiltonian and the modal densities of the vacuum at the dressed transition frequencies differ significantly from each other. On treating the counter-rotating part of the Hamiltonian as a perturbation and carrying out the Weisskopf-Wigner approximation in the dressed states basis, we find that the high driving intensity leads to significant deviations from the traditional Mollow resonance fluorescence spectrum. In particular we find unequally intense Mollow side-bands and that the generation of higher order triplets and harmonics is substantially enhanced by the high vacuum modal density at the corresponding high resonance frequencies.
We investigate the fluorescence spectrum of a two-level system driven by a monochromatic classical field by the Born-Markovian master equation based on a unitary transformation. The main purpose is to understand the effects of counter-rotating-wave terms of the driving on spectral features of the fluorescence. We have derived an analytical expression for the fluorescence spectrum, which is different from Mollow's theory, while Mollow's result on resonance is the limiting case of ours in moderately weak driving regimes. Our results demonstrate precisely that the counter-rotating-wave terms of the driving play an important role in the fluorescence spectrum for intense driving: (i) the counter-rotating coupling suppresses the red sideband in the Mollow triplet and it enhances the blue one in explicitly contrast to the well-known equal intensity of the sideband in Mollow's theory, (ii) the higher-order Mollow triplets appear as a characteristic spectral feature arising from counter-rotating-wave terms of the driving, and (iii) a significant frequency shift of the sidebands is observed, which depends on both the detuning and driving strength.
An experiment was performed recently [Y. Zhu, A. Lezama, Q. Wu, and T. W. Mossberg (unpublished)] in which a two-level atom of transition frequency \ensuremath{\Omega} was placed in a bichromatic laser field with frequencies \ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}, of sufficient intensity to produce dynamic Stark splitting. The observed fluorescence spectrum differed qualitatively in almost all its details from the well-known Mollow triplet [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. In this article, we use a dressed-atom model to explain the observed results.
The authors present analytical and numerical results for resonance fluorescence produced by a two-level atom damped by a broad-band squeezed vacuum. Previous theoretical analyses of this model have assumed that the laser frequency and the carrier frequency of the squeezed vacuum are equal. The authors introduce a non-zero detuning between the laser frequency and the carrier frequency while maintaining resonance between the laser frequency and atomic resonance. In the absence of the driving field there is a squeezing threshold: above threshold the decay rate of the atomic polarization can be reduced, and below threshold a squeezing-induced two peak spectrum and frequency shift, which is analogous to the Bloch-Siegert shift, are predicted. In the presence of the driving field, the spectrum is asymmetric for Rabi frequencies smaller or comparable to the detuning of the squeezed vacuum. A symmetric spectrum is obtained for large Rabi frequencies. An interpretation is predicted by means of a dressed-state analysis. The authors find that for not too large Rabi frequencies a remarkably large population inversion can be induced in the dressed states, even at exact resonance of the driving field, provided that the laser frequency and carrier frequency are detuned. Moreover, for detection times larger than the inverse detuning, the spectrum is insensitive to the phase between the driving field and the squeezed vacuum, in marked contrast to the case of no detuning.
We study the effects of driving a two-level atom by two intense field modes that have equal frequencies but are otherwise distinguishable; the intensity of one mode is also assumed to be greater than that of the other. We calculate first the dressed states of the system, and then its resonance fluorescence and Autler-Townes absorption spectra. We find that the energy spectrum of the doubly dressed atom consists of a ladder of doublet continua. These continua manifest themselves in the fluorescence spectrum, where they produce continua at the positions of the Mollow sideband frequencies ${\mathrm{\ensuremath{\omega}}}_{\mathrm{L}}$ \ifmmode\pm\else\textpm\fi{}2\ensuremath{\Omega} of the strong field, and in the Autler-Townes absorption spectrum, which becomes a two-continuum doublet.
We study the transient fluorescence spectra of two-level atoms driven by a strong optical field when the atoms are initially prepared in pure dressed states of the atom-field Hamiltonian. Spectra obtained here differ qualitatively from those observed in the steady state. In the case of steady-state resonant excitation, a three-peaked spectrum symmetric about the laser frequency is obtained; with pure-dressed-state preparation, the symmetry of the spectrum about the driving field is broken---one side peak is initially enhanced and the other is initially suppressed. Furthermore, the temporal oscillations of fluorescence intensity observed in previous calculations of transient fluorescence spectra appropriate to atoms prepared in a superposition of dressed states [J. H. Eberly et al., J. Phys. B 13, 217 (1980)] are suppressed when pure-dressed-state preparation is considered.