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Journal of the Optical Society of America B

Collective spectral properties in time-dependent resonance fluorescence

Tran Quang, L. H. Lan, A.S. Shumovsky

Published Jun 1, 1990• 2 citations
Publisher

Abstract

The dynamic evolution of the collective resonance-fluorescence spectrum from N two-level atoms in a strong laser field is investigated. The analytical formulas for the transient spectrum are given. The essential differences between the transient spectrum and the steady-state spectrum are shown.
DOI
10.1364/josab.7.000908

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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.
An S-conserving theory of collective resonance fluorescence by NNN two-level atoms driven by a uniform strong field is presented. The detuning between field and atoms can be varied. A canonical transformation to dress the atoms by the driving field and Langevin equations for dressed operators are used to investigate the behavior of the system. For sufficiently large detuning the dressed atoms are shown to reach a steady state after a transient super-radiant-like decay in times short, compared with the long decay time which is attained on resonance and which is the same as the single-atom spontaneous-decay time. In the transient regime the parameters of the quasi-super-radiant decay are shown to vary with detuning and with the driving-field amplitude. Both the amplitude spectrum and the integrated intensity of the fluorescence field, emitted off resonance by the dressed atoms during the transient, are shown to bear pulselike traces of the quasi-super-radiant decay. The elastic components of the off-resonance amplitude spectrum at the end of the super-radiant-like transient are broadened with respect to resonance, and the integrated intensity exhibits a sudden transient decrease in an appropriate range of detuning, which has been given the name "superdarkening" and which disappears on resonance. After the steady-state regime is attained, the resonance intensity spectrum is shown to coincide with that obtained by other authors, while off resonance the inelastic lines are broadened in a super-radiant-like fashion.