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Applied Spectroscopy

Lifetime Measurement by Using the Laplace Transform in Single-Photon-Decay Spectroscopy

Fernando G. Moreno, Rafael J. López

Published Nov 1, 1987• 9 citations
Publisher

Abstract

In this paper we present a method for processing the time-interval data obtained in a single-photon-decay spectroscopy experiment. This method is based on the measurement of the Laplace transform of P ƒ ( t) [the probability distribution function of the time of arrival of the first photon (PDFP) after the excitation pulse] instead of the direct measurement of P ƒ ( t) by means of a multichannel analyzer. With the use of this method, a good estimation of the lifetime of the signal can be obtained with a shorter measurement time than that used in the conventional method, in which the recorded time intervals are used to construct P ƒ ( t). A theoretical model of the error involved in determining the lifetime is obtained for the Laplace method, and it is compared with that corresponding to the measurement of P ƒ ( t) by means of a multichannel analyzer. Finally, a computer simulation of the experiment is performed to corroborate the theoretical predictions.

DOI
10.1366/0003702874447103

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In this paper we present a method for processing the time-interval data obtained in a single-photon-decay spectroscopy experiment. This method is based on the measurement of the Laplace transform of P ƒ ( t) [the probability distribution function of the time of arrival of the first photon (PDFP) after the excitation pulse] instead of the direct measurement of P ƒ ( t) by means of a multichannel analyzer. With the use of this method, a good estimation of the lifetime of the signal can be obtained with a shorter measurement time than that used in the conventional method, in which the recorded time intervals are used to construct P ƒ ( t). A theoretical model of the error involved in determining the lifetime is obtained for the Laplace method, and it is compared with that corresponding to the measurement of P ƒ ( t) by means of a multichannel analyzer. Finally, a computer simulation of the experiment is performed to corroborate the theoretical predictions.
A Poisson point process (PPP) presents a series of characteristics which may be used to define functions with an optimal signal-to-noise ratio. This work describes a statistical function, obtained by measuring time intervals in a PPP, which contains the same information about the signal to be analysed as the autocorrelation function. The advantage of this function is that it can be applied to cases of low light level in which the autocorrelation function gives a low SNR. As a particular case of low light level signals, the authors have used this method in a real experiment of single photon decay spectroscopy and measured the lifetime of the 4 T 1 state of Mn 2+ in an undoped TMMC crystal at room temperature.
We report a measurement of the 5P3/2 excited-state lifetime using two-pulse photon echoes in Rb vapor. The measurement is precise to ∼1% and agrees with the best measurement of atomic lifetime in Rb. The results suggest that a measurement precise to ∼0.25% is possible through additional data acquisition and study of systematic effects. The experiment relies on short optical pulses generated from a cw laser using acousto-optic modulators. The excitation pulses are on resonance with the F=3-->F′=4 transition in Rb85 or the F=2-->F′=3 transition in Rb87. The resulting photon echo signal is detected using a heterodyne detection technique. The excited-state lifetime is determined by measuring the exponential decay of the echo intensity as a function of the time between the excitation pulses. We also present a study of the echo intensity as a function of excitation pulse area and compare the results to simulations based on optical Bloch equations. The simulations include the effects of spontaneous emission as well as spatial and temporal variations of the intensities of excitation pulses.
In this work we expose a recently developed theoretical model for the analysis of the measurements obtained with the so-called pinhole method, for the determination of the upper level lifetime in materials where the superimposition between fluorescence and absorption spectra determines significant radiation trapping effect. Under fairly general conditions the fluorescence decay curve after a pulsed excitation of the sample obtained with this experimental set-up can be conveniently described by a double exponential functional form. The faster of the two decay times is close to the intrinsic fluorescence lifetime, with a difference that can be calculated with geometrical considerations. The theoretical results were tested with a suitably designed experiment, where the upper level lifetime of the laser transition of some Yb doped samples were investigated, obtaining results that are consistent with literature data and in good agreement with the theoretical results as for the temporal dependence of the fluorescence decay.
Classical time-resolved optical spectroscopy experiments are performed using sequences of ultrashort light pulses, with photon fluxes incident on the sample which are many orders of magnitude higher than real-world conditions corresponding to sunlight illumination. Spectroscopy and microscopy schemes that use quantum states of light have been widely described theoretically with fewer experimental demonstrations that typically require very long measurements that can extend for hours or more. Here, we show that time-resolved spectroscopy with quantum light can be performed without compromising measurement time or wavelength tunability, recording a fluorescence lifetime trace in biological samples in less than a second with acceptable signal-to-noise ratio. Starting from spontaneous parametric down-conversion driven by a continuous-wave laser, we exploit the temporal correlation between randomly generated signal/idler pairs to obtain temporal resolution, and their spectral correlation to select the excitation frequency. We also add spectral resolution in detection, using a 'photon-efficient' Fourier transform approach which employs a common-path interferometer. We demonstrate the potential of this approach by resolving, at the single-photon level, excitation energy transfer cascades from LH2 to LH1 in the photosynthetic membrane and disentangling the lifetimes of two dyes in a mixture. Our results provide a new approach to ultrafast optical spectroscopy, where experiments are performed under illumination intensity conditions comparable to real-world sunlight illumination.
We present a methodology that allows recording the coherence length of photons emitted by a single quantum system in a solid. The feasibility of this approach is experimentally demonstrated by measuring the self-interference of photons from the zero-phonon line emission of a single nitrogen-vacancy defect in diamond at 1.6 K. The first-order correlation function has been recorded and analyzed in terms of a single exponential decay time. A coherence time of $\ensuremath{\sim}5\mathrm{ps}$ has been obtained, which is in good agreement with the corresponding spectral line width and demonstrates the feasibility of the Fourier-transform spectroscopy with single photons.