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Journal of Physics B Atomic and Molecular Physics

The resonance fluorescence of a two-level system driven by a smooth pulse

Kazimierz Rza̧żewski, Mirosław Florjańczyk

Published Aug 14, 1984• 71 citations
Publisher

Abstract

The resonance fluorescence of a two-level atom irradiated by a smooth pulse of hyperbolic secant shape is investigated. The authors calculate explicitly the energy spectrum of photons at t to infinity in the limit of spontaneous linewidth much smaller than the Fourier width of the pulse. The spectrum is completely different from the Mollow spectrum. It is multi-peaked and the number of peaks increases with the area of the pulse.

DOI
10.1088/0022-3700/17/15/005

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Comment on 'The resonance fluorescence of a two-level system driven by a smooth pulse

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In a recent article, Rzazewski and Florjanczyk (1984) calculated the resonance fluorescence of a two-level atom driven by a smooth excitation pulse. The authors offer a different analysis of the problem which allows one to arrive at a physical interpretation of the results which differs from these authors. Moreover, they indicate that there is an additional contribution to the spectrum not considered in their work.

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The resonance fluorescence of a two-level atom irradiated by a smooth pulse of hyperbolic secant shape is investigated. The authors calculate explicitly the energy spectrum of photons at t to infinity in the limit of spontaneous linewidth much smaller than the Fourier width of the pulse. The spectrum is completely different from the Mollow spectrum. It is multi-peaked and the number of peaks increases with the area of the pulse.
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.
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.