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Journal of Physics B Atomic and Molecular Physics

Resonant interaction of smooth laser pulses with two-level atoms

Stefano Cavalieri, Roberto Buffa, M. Matera, Massimo Mazzoni

Published Oct 28, 1987• 11 citations
Publisher

Abstract

The authors have studied the fluorescence spectrum of a two-level atom interacting with a resonant smooth laser pulse. Assuming a filter width larger than the Fourier width of the pulse, an approximate analytic closed form for the power spectrum valid for any pulse shape is obtained. In these conditions the power spectrum exhibits a time-developing three-peak structure, while the energy spectrum presents a single line, unless the pulse is near rectangular. Theoretical energy spectra are in qualitative agreement with measurements of the resonance fluorescence emitted by strontium atoms irradiated by short laser pulses.

DOI
10.1088/0022-3700/20/20/014

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Physical Review A•Mar 1, 1988•17 citations
The authors have studied the fluorescence spectrum of a two-level atom interacting with a resonant smooth laser pulse. Assuming a filter width larger than the Fourier width of the pulse, an approximate analytic closed form for the power spectrum valid for any pulse shape is obtained. In these conditions the power spectrum exhibits a time-developing three-peak structure, while the energy spectrum presents a single line, unless the pulse is near rectangular. Theoretical energy spectra are in qualitative agreement with measurements of the resonance fluorescence emitted by strontium atoms irradiated by short laser pulses.
The resonance fluorescence of a two-level atom interacting with a laser pulse is studied, following the short-pulse approximation. The authors demonstrate that an explicit expression of the energy spectrum in terms of atomic-state amplitudes holds also for an off-resonance excitation. Some analytically solvable cases are studied in detail, showing that the main spectral properties of the fluorescence emitted under adiabatic and non-adiabatic pulsed excitation can be easily described. For the first time the continuous dependence of the fluorescence spectrum on laser detuning is reported for a smooth pulse.
We examine the transient resonance fluorescence (RF) spectrum from a two-level atom excited by a rectangular laser pulse containing many frequency modes. We predict exactly the qualitative features of the spectra in which the number of components and their locations in the spectra are precisely specified. The extreme case of the infinite-mode limit is also analysed. The RF spectra (with and without the rotating wave approximation) of a harmonic oscillator excited by a similar pulse have been calculated.
The responses of the time-dependent resonance fluorescence spectra of two-level atoms in the presence of (a) strong cw laser fields and (b) short pulsed laser fields to functional disturbances in these fields have been studied by the use of functional-sensitivity-analysis techniques. For the cw case, the transient and steady-state response regions are explored separately. It is found that the response to the field disturbance occurring during the earlier transient period is most prominent at the positions of the well-known three peaks of the corresponding spectrum. In contrast, the response to a disturbance taking place in or near the steady-state region tends to increase the separation between the peaks and lower the intensity of the line center, in exact agreement with the direct calculation of the perturbed spectrum. For the pulsed case, the response to the disturbance is most visible at the line center and at the accompanying multiple peaks caused by the population oscillation of the upper atomic level. The response strongly depends on the magnitude of the pulse area, thus giving rise to distinct asymptotic behavior for (2n+1)\ensuremath{\pi} and 2n\ensuremath{\pi} pulses. As the pulse area becomes large enough to cause significant population oscillation of the upper atomic level, the response of the spectrum shows a resemblance to that of the cw case.
A study is presented for the time-dependent resonance-fluorescence spectrum of two-level atoms irradiated by hyperbolic-secant pulsed lasers, allowing for an arbitrary spontaneous-emission rate from the excited level to the ground level. Novel features of the temporally transient spectrum have been observed. The spectrum is dominated by a central peak which oscillates in time and is accompanied by multiple side peaks. Asymptotically (i.e., after the pulse has passed) the side peaks disappear, leaving a tail at the line center which displays a Lorentzian shape of width equal to the sum of the spontaneous-emission rate and the width of the spectrometer considered and of magnitude proportional to the instantaneous intensity of the pulse. The exact behavior of the spectrum is dictated by the area of the engaged pulse and by how the atom is prepared initially. In particular, it is found that the spectrum can be asymmetric even when the laser is tuned to exact resonance if the atoms are initially prepared in a certain class of proper coherent states, irrespective of how the field amplitude may vary in time. An analysis of the spectral symmetry without resorting to any explicit evaluation of the spectrum itself is also presented. Furthermore, the associated optical Bloch equations are solved analytically in terms of hypergeometric functions in a similar manner to that done previously for the undamped two-level Schr\"odinger equation. Specific numerical results are presented for pulses of area equal to \ensuremath{\pi}, 2\ensuremath{\pi}, 3\ensuremath{\pi}, 4\ensuremath{\pi}, and 5\ensuremath{\pi} for both symmetric and asymmetric cases.