Linewidth lifetime-limited

Figure 8. Fluorescence excitation spectra for pentacene in/j-terphenyl at 1.5 K measured with a tunable dye laser of linewidth 3 MHz. The laser detuning frequency is referenced to the line center at 592.321 nm. (a) Broad scan of the inhomogeneously broadened line all the sharp features are repeatable structure, (b) Expansion of 2 GHz spectral range showing several single molecules, (c) Low-power scan of a single molecule at 592.407 nm showing the lifetime-limited width of 7.8 MHz and a Lorentzian fit. After Ref. 7.

Upon close examination of an individual single-molecule peak at lower intensity (Fig. 8(c)), the lifetime-limited homogeneous linewidth of 7.8 0.2 MHz can be observed [73]. This linewidth is also termed quantum-limited , since the optical linewidth has reached the minimum value allowed by the lifetime of the optical excited state. This value is in excellent agreement with previous photon echo mea-... 

The first temperature dependent study of the optical linewidth of individual molecules was performed on single pentacene molecules doped into p-terphenyl [10]. As can be seen in Fig. 4, below 4 K the optical linewidth remains essentially constant at the lifetime-limited value of 7.8 MHz. Above 4 K, temperature dependent dephasing processes contribute to the linewidth. In previous photon echo experiments, the... 

At low exciting intensities the linewidths (Fig. 7(a)) reach a value of 7.3 + 0.8 MHz in agreement with the lifetime-limited value, and the fluorescence emission rate increases almost linearly. In the high-intensity limit, the peak fluorescence emission rate saturates at 7.2 + 0.7 x 10 photons/s (Fig. 7(b)). As the peak emission rate saturates, the emission rate in the wings of the excitation spectrum continues to increase with intensity, and the linewidth broadens as shown in Fig. 7(a). Actually,... 

Figure 13. Stochastic simulation of the fluorescence intensity (top) and frequency (middle) correlation functions for a model of spectral diffusion in a glass. The molecule is coupled to a three dimensional distribution of tunneling systems with distributed microscopic parameters. The bottom panel shows the timescale (horizontal) and amplitude of the frequency jumps (relative to the lifetime limited linewidth, vertical scale). The inset in the top panel shows the line-shape and the lifetime limited linewidth as a small bar (from Ref. 77).

The natural linewidth is the smallest contribution to the line profile of a transition and is only rarely seen as limiting within the laboratory. For an electronic transition with a lifetime of 10000 ps the linewidth is of order 0.00053 cm-1 but for a rotational transition the lifetime linewidth 5.3 x 10-15 cm-1. The best microwave spectra recorded in the laboratory have a linewidth of a few Hz or 10-12 cm-1, which is close (but not very) to the natural linewidth limit. 

It is clear that a number of questions need to be answered. Why, in the condensed phase, is the intersystem crossing between two nn states so efficient What is the explanation of the conflict between the linewidth studies of Dym and Hochstrasser and the lifetime studies of Rentzepis and Busch, with respect to the vibrationally excited levels It was in an attempt to provide some answers to these questions that Hochstrasser, Lutz and Scott 43 carried out picosecond experiments on the dynamics of triplet state formation. In benzene solution the build up of the triplet state had a lifetime of 30 5 psec, but this could only be considered as a lower limit of the intersystem crossing rate since vibrational relaxation also contributed to the radiationless transition to the triplet state. The rate of triplet state build-up was found to be solvent-dependent. 

Figure 1 Schematic showing a chromophore with a radiative lifetime of 10 ns with its linewidth passing from the radiatively limited value of 5.3 x 10 cm at cryogenic temperatures to the situation at higher temperatures where rapid dephasing induces a strong additional broadening, yet leaves the emission lifetime unaffected...

Figure 2 Schematic of the electronic absorption spectrum of a single chromophoric site in a condensed phase host environment at low temperatures. An extremely sharp electronic origin, exhibiting a radiatively limited linewidth is accompanied by a phonon sideband with vibrational sidelines. A second electronic excited state lies at higher energies. Vibrational sidelines and the second electronic excited state are lifetime broadened by rapid radiationless deactivation processes...

Time-independent picture. The opposite extreme from short-pulse excitation involves the use of nearly monochromatic radiation. Practically, this means that the interaction between molecule and radiation field is of longer duration than Tnr. In this limit, the quantity measured is the absorption lineshape. It will be shown below that the linewidth observed in an energy-resolved experiment is related in a very simple way to the predissociation lifetime in the time-resolved experiment. 

The 79-3-keV resonance in Er was the last to be reported [149]. Coulomb excitation of an ErjOa target by 3-meV protons populates the first excited level, and the spectrum of an EraOa absorber at 30 K is a single line. The linewidth of 33-4 mm s corresponds to a lower limit to the excited-state lifetime of 0-103 ns. No hyperfine effects have been reported. 

The important point to note here is that the photon echo does not suffer from the triplet state bottleneck in the same sense as hole-burning or optical free induction decay. It is only the repetition rate in the photon-echo experiment that is limited by the triplet state decay rate. Morsink et al. showed that at low temperature ( 2 K) the photon-echo hfetime of dilute PTC-A,4 and PTC-d,4 in p-terphenyl crystals is identical to the fluorescence lifetime. This implies that at this temperature pure dephasing processes are absent. The homogeneous linewidths are therefore 5.9 MHz (PTC-rf,4) and... 

Due to the contribution of various broadening mechanisms, the linewidths typically observed in atomic spectrometry are significantly broader than the natural width of a spectroscopic line which can be theoretically derived. The natural width of a spectral line is a consequence of the limited lifetime r of an excited state. Using Heisenberg s uncertainty relation, the corresponding half-width expressed as frequency is ... 

For transitions between sublevels in the ground state, the radiative lifetimes may be extremely long and the linewidth is only limited by the transit time of the molecules through the RF field. Sub-kilohertz resonances have been observed in the RF-optical double resonance spectroscopy of rare-earth ions [519]. 

This is a very narrow signal because the lifetime of the level is r = 00 and the linewidth is solely limited by the transit time T, which can be prolonged by enlarging the laser beam or by adding a buffer gas. 

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