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Physical Review A

Theory of time-delayed measurement: Subnatural linewidth and transient dip spectroscopy

Hai-Woong Lee, Pierre Meystre, Marlan O. Scully

Published Oct 1, 1981• 17 citations
Publisher

Abstract

Time-delayed measurement of naturally broadened transitions can lead to a narrowing of the linewidth. Moreover, under appropriate conditions, it may result in the appearance of a dip at the line center. An analysis of time-delayed measurement thus provides a theoretical basis for useful optical techniques yielding high spectral resolution. Such an analysis is presented in this work.

DOI
10.1103/physreva.24.1914

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Physical Review A•Oct 1, 1983•15 citations
Time-delayed measurement of naturally broadened transitions can lead to a narrowing of the linewidth. Moreover, under appropriate conditions, it may result in the appearance of a dip at the line center. An analysis of time-delayed measurement thus provides a theoretical basis for useful optical techniques yielding high spectral resolution. Such an analysis is presented in this work.
The resolution of a quantum-beat experiment, which is basically limited by the atomic natural linewidth, has been improved by observing the fluorescence only from those atoms which have survived in excited states after some time delay. The resulting narrowing enables one to resolve previously overlapping lines in beam-foil quantum-beats experiments using $\mathrm{H}\ensuremath{\alpha}$ and 4He^{4}\mathrm{He}4He ii (4\ensuremath{\rightarrow}3) deexcitation.
Spectra that are narrower than the natural width of decaying states can be achieved by beginning the observation of signals at a fixed delay time after excitation rather than immediately afterward. These signals are weaker (and noisier) than the full, time-unresolved signals. Applications of this line-narrowing technique to precision spectroscopy are discussed, and the properties of the resulting signals are studied. Numerical simulations demonstrate that time-resolved line narrowing is highly desirable in a large number of cases.
A single photon, emitted in a transition between two states, has a frequency distribution of intensity that is given by a Lorentzian if the transition is only naturally broadened and the period of observation TTT is long compared to the lifetime T1{T}_{1}T1​ of the excited state. However, when the observation time TTT is short or comparable to T1{T}_{1}T1​, the frequency spectrum is appreciably broadened. If only the delayed part of the emitted radiation field is detected, then the radiation spectrum does not change. However, if the radiation field is transmitted through a resonant absorber and then detected, the transmission spectrum of the delayed radiation field is narrowed. We show that this narrowing is due to the interference of the spectral components of the incident and coherently scattered fields. Experimental spectra of absorption of M\"ossbauer radiation, obtained by the coincidence technique, confirm this conclusion.
A method to obtain subnatural resolution in laser-induced fluorescence spectroscopy by phase switching is described. The subnatural linewidth is obtained by extracting a coherent transient response induced by the switching of the laser. The linewidth in this type of spectroscopy is determined by the time interval between the switching and observation, instead of the spontaneous lifetime. The result is compared with the experiment on the Na D1{D}_{1}D1​ line.