Decay quantum beats

Equation (9.1) documents that quadmpole splittings A q exhibit quantum-beat spectra with period H/IuAEq superimposed over the time dependence of the nuclear decay exp(—f/t) with mean decay time t = 141 ns for Fe. In Fig. 9.2, quadmpole splittings A q = 0 and 2 mm s in the energy domain (conventional MS) are compared with those in the time domain (MS using synchrotron radiation) [7]. The QBs in the time domain spectmm for A q = 2 mm s are the result of the interference between the radiation scattered by different nuclear resonances. Consequently, their frequencies correspond to the energetic differences between these resonances. 

The nature of the radiative decay in the resonance and in the statistical limits was considered by Berry and Jortner,7 who examined the interference effects in the radiative decay of coherently excited states. Quantum beat signals can be observed and used to analyze close-lying molecular... 

Fig. 23. The fluorescence decay of Cd vapor in a magnetic field, (a) Experimental data exhibiting the phenomenon of quantum beats, (b) The exponentially decaying component, (c) The decaying modulated component. This figure is reproduced from the work of Dodd, Kaul, and Warrington (158).

Consider now the resonance limit, when only a small number of eigenstates is involved. In this limit a true quantum beat spectrum is obtained. For simplicity of presentation we consider a three-level system in which the closely spaced coherently excited levels fa and fa decay into the ground state. The total number of photons counted is just... 

Level crossing spectroscopy has been used by Fredriksson and Svanberg44 to measure the fine structure intervals of several alkali atoms. Level crossing spectroscopy, the Hanle effect, and quantum beat spectroscopy are intimately related. In the above description of quantum beat spectroscopy we implicitly assumed the beat frequency to be high compared to the radiative decay rate T. We show schematically in Fig. 16.11(a) the fluorescent beat signals obtained by... 

Recombination fluorescence has been used to study the decay of radical ion pahs generated photolytically.288 Simulation of quantum beats caused by hyperfine interaction in the R and R+ enable the values of hfc to be determined for very short-lived species. In the case of one R excellent agreement with the value of hfc as determined by ESR is reported. The primary reaction in the photolysis of 1-arylalkyl radicals (128) is the heterolytic cleavage of the -halogen (X), generating the radical cation (129).289... 

In summary, the dynamics of the electronic decay of inner-shell vacancies in a charged environment, such as created by interaction of a cluster with a high intensity FEL radiation, can be qualitatively different from the one induced by a low-intensity source. If the emitted electrons are slow enough to be trapped by the neighboring charges, the familiar exponential decay will be suppressed by quantum beats between the initial state and the quasi-continuum of discrete final states. Physically, the predicted oscillations correspond to creation of the initial vacancy due to the reflections of the emitted electron by the charged cluster potential and the subsequent inverse Auger transition. 

Fig. 4.20. Experimental signals of ground state quantum beats in Kat E+.v" = 1, J" = 73) (a) field switched off, B = 0 (b) B = 0.816 T (c) differential signal with compensation of exponential decay (d) independence of (jJj .

Figure 2.26. Quantum beat-modulated fluorescence decay and its Fourier transform for the l W level of Sj thiophosgene. (Reprinted with permission from Ref. [42].)...

Fourth, the Si —> S0 fluorescence exhibits loss of emission at low Si excess vibrational energy and reappearance at very large excess energies, consistent with predissociation. A quantum beat-modulated Si fluorescence decay was observed at energies corresponding to the expected position of the T2 (71,71 ) state. 

The coincidence measurements discussed in the previous section were concerned with the total coincidence signal, i.e. the signal obtained when the decay of a particular ensemble of states is integrated over. These states are produced in a very short time ( 10 s) in electron impact excitation, and can sometimes evolve in a complicated way. In the absence of internal fields (e.g. the n P states of helium) each of the fm) states decays with the same exponential time dependence exp(—yt), and the coincidence technique can be used to yield the decay constant y of the excited state (see Imhof and Read, 1977, and references therein). However, if the excited state is perturbed by an internal (or external) field before decay, then the exponential decay is modulated sinusoidally giving rise to the phenomenon of quantum beats (Blum, 1981). 

Quantum beats have been observed in a variety of experiments, particularly in beam—foil measurements. Teubner et al. (1981) were the first to observe quantum beats in electron—photon coincidence measurements, using sodium as a target. The zero-field quantum beats observed by them are due to the hyperfine structure associated with the 3 Pii2 excited state (see fig. 2.20). The coincidence decay curve showed a beat pattern... 

Heck and Williams (1987) observed quantum beats in the decay of the n = 2 states of atomic hydrogen. In the presence of an external electric field the 2s and 2p states can be mixed and their correlation measured. With an applied field of 250 Vcm the modulation periods should be 0.1 ns and 0.6 ns. They were able to observe the second beat period corresponding to interference between the states which reduce to 2si/2 and 2pi/2 in the field-free limit. Williams and Heck (1988) were able to use the technique to determine many of the n = 2 state multipoles (section 8.2.4). 

While we have developed the theory of wave-packet scattering and resonances in the context of potential scattering of electrons it is easy to generalise. In particular there is no reason why the scattered particle should not be a photon. In this case the wave packet does not spread and the formalism is valid for general values of 3. Wave packets are known whose widths correspond to a lifetime of order lO s, which is easily resolved with nanosecond electronics. Such wave packets arise in the photon decay of many atomic states. The time spectrum of detected photons is given by (r,t)p for X < 0. We see from (4.166) that this involves an interference between a term whose lifetime is h/3 and one whose lifetime is Xr. The resulting time oscillations have been observed experimentally. They are called quantum beats. 

Using the former technique, the most significant result was the observation of quantum beats in the fluorescence decay of jet-cooled anthracene At low excess energies, the fluorescence and fluorescence excitation spectra of anthracene are very sharp, and the fluorescence decay of single vibronic levels is exponential. At an excess energy of 1400 cm however, clear quantum beats were seen, arising from the interference between the initially populated vibronic state, and a state produced... 

Guo and Yang [53] have analyzed spontaneous decay from two atoms initially prepared in an entangled state. They have shown that the time evolution of the population inversion, which is proportional to the intensity (87), depends on the degree of entanglement of the initial state of the system. Ficek et al. [10] have shown that in the case of two nonidentical atoms, the time evolution of the intensity 7(R, t) can exhibit quantum beats that result from the presence of correlations between the symmetric and antisymmetric states. In fact, quantum beats are present only if initially the system is in a nonmaximally entangled state, and no quantum beats are predicted for maximally entangled as well as unentangled states. 

In time space cs(t) 2 is now a perfect exponential with decay rate (r r + Tr), a clear signature of a large molecule with a dense k manifold. Conversely, the observation of quantum beats is a signature of a small molecule. For a relatively large molecule we will have an intermediately dense manifold,... 

Figure 7. Quantum beats observed in the decay after excitation of part of P(l).

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