Time-Gated Coherent Spectroscopy

The first of these techniques is based on the selective detection of those excited atoms or molecules that have survived in the excited state for times t t, which are long compared to the natural lifetime t. 

If molecules are excited into an upper level with the spontaneous lifetime t = 1 /y by a light pulse ending at r = 0, the time-resolved fluorescence amplitude is given by 

If the observation time extends from r = 0 to r = oo, a Fourier transformation of the measured intensity I(t) ex A t) yields, for the line profile of the fluorescence emitted by atoms at rest, the Lorentzian profile (Vol. 1, Sect. 3.1) 

If the detection probability for I(t) is not constant, but follows the time dependence fit), the detected intensity 7g(r) is determined by the gate function fit) 

The Fourier transform of I git) now depends on the form of fit) and may no longer be a Lorentzian. Assume the detection is gated by a step function 

This is again a Lorentzian with a half width (FWHM) of 7 = 1 /t, that is independent of the gate time T Because of the delayed detection one loses the factor exp(-T/T) in intensity, since all fluorescence events occurring for times t T are missing. This shows that with incoherent techniques no narrowing of the natural linewidth can be achieved, even if only fluorescence photons from selected long-living atoms with t T r are selected [14.109]. 

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