Beat phenomenon

Okamoto H and Yoshihara K 1991 Femtosecond time-resolved coherent Raman scattering from p-carotene in solution. Ultrahigh frequency (11 THz) beating phenomenon and sub-picosecond vibrational relaxation Chem. Phys. Lett. 177 568-71... 

Hanson (1978) studied this effect experimentally, by periodically flashing a light at a firefly and watching it try to synchronize. For a range of periods close to the firefly s natural period (about 0.9 sec), the firefly was able to match its frequency to the periodic stimulus. In this case, one says that the firefly had been entrained by the stimulus. However, if the stimulus was too fast or too slow, the firefly could not keep up and entrainment was lost—then a kind of beat phenomenon occurred. But in contrast to the simple beat phenomenon of Section 4.2, the phase difference between stimulus and firefly did not increase uniformly. The phase difference increased slowly during part of the beat cycle, as the firefly struggled in vain to synchronize, and then it increased rapidly through 2 r, after which... 

In the old days, this beat phenomenon was used to tune musical instruments. You would strike a tuning fork at the same time as you played the desired note on the instrument. The combined sound A, sin tOjZ + Aj sin fttj/ would get louder and softer as the two vibrations went in and out of phase. Each maximum of total amplitude is called a beat. When the time between beats is long, the instrument is nearly in tune.)... 

The situation changed, however, with two advances. The first advance was the discovery that in the S, - S0 spectrum of jet-cooled anthracene a second band exists (at S, + 1420 cm-1), the excitation of which gives rise to quantum beat-modulated fluorescence decays.40 Besides indicating a somewhat more global importance to the beat phenomenon in anthracene, the characteristics of these new beats provided very strong evidence that they arose as a manifestation of IVR. In particular, the beats were shown to have phases and modulation depths dependent on the fluorescence band detected. Such behavior, which... 

Figure 4 displays giant oscillations of the magnetoresistance, which exhibit a perfect (1/H) periodicity with the fundamental field = 3730 T, and a beating phenomenon characterized by the much smaller field = 36.8 T [15]. The large amplitude and the beating phenomenon can both be understood in terms of a tube-like Fermi surface (FS) in a 2-D conductor. For such an anisotropic FS, the amplitude of the oscillations is enhanced by the factor where m. and m are, respectively, the effective mass perpendicular and... 

Fig. 1. Calculated conversion signal C(to) of the transmitted pulse vs delay time for T2/tp = 16 and two values of absorption length, al — 0.2 and 1.0. (a) Single transition frequency, (b) Two transition frequencies leading to a beating phenomenon. Dotted curves Gaussian input pulse.

Similar results are presented in Fig. lb for two species with frequency difference Arnfg tp = 1.13. Equal dephasing time T2 and a ratio of uj/a2 3 are considered (a = aj + 02). Most important is the oscillatory time behaviour of the decaying pulse wing. A novel beating phenomenon occurs which is superimposed on an approximately exponential slope. The beating results from the coherent superposition of the adjacent molecular transitions. 

Recently Rothenberg and Grischkowsky [2] observed polarization beats also originating from the 3p fine structure splitting of Na. However, in their experiments the beat phenomenon has to be explained as an interference between the macroscopic polarizations simultaneously excited in the sodium vapor on the D- - and D2-resonance line. 

We have already discussed quantum-beat spectroscopy (QBS) in connection with beam-foil excitation (Fig.6.6). There the case of abrupt excitation upon passage through a foil was discussed. Here we will consider the much more well-defined case of a pulsed optical excitation. If two close-lying levels are populated simultaneously by a short laser pulse, the time-resolved fluorescence intensity will decay exponentially with a superimposed modulation, as illustrated in Fig. 6.6. The modulation, or the quantum beat phenomenon, is due to interference between the transition amplitudes from these coherently excited states. Consider the simultaneous excitation, by a laser pulse, of two eigenstates, 1 and 2, from a common initial state i. In order to achieve coherent excitation of both states by a pulse of duration At, the Fourier-limited spectral bandwidth Au 1/At must be larger than the frequency separation ( - 2)/ = the pulsed excitation occurs at... 

Although the general features of the quantum-beat phenomenon can be understood in a simple semi-classical model, a full quantum-mechanical description is required for calculating the correct relation between B and A in (9.23) to determine the beat contrast in the decay curve. Quantum-beat spectroscopy has been discussed in detail in [9.127,128]. 

Although the general features of the quantum-beat phenomenon can be. understood in a simple semiclassical model, a full quantum-mechanical de-... 

Under even more intense photoexcitation ( 10mJ/cm2), the coherent A g and Eg phonons of Bi and Sb exhibit a collapse-revival in their amplitudes (Fig. 2.10) [42,43], This phenomenon has a clear threshold in the pump density, which is common for the two phonon modes but depends on temperature and the crystal (Bi or Sb). At first glance, the amplitude collapse-revival appears to be analogous to the fractional revival in nuclear wavepackets in molecules [44,45]. However, the pump power dependence may be an indication of a polarization, not quantum, beating between different spatial components of the coherent response within the laser spot [46],... 

The analysis of the EXAFS of alloy catalyst particles is inherently more complicated than that of single metals. In the case of PtRu catalysts there is an added complication that the backscattering from Pt and Ru neighbors at similar distances interfere with one another, giving rise to beats in the EXAFS data. This phenomenon was first described by McBreen and Mukerjee ° for a poorly alloyed 1 1 atomic ratio PtRu/C catalyst. The presence of beats in the EXAFS data is more apparent in the EXAFS obtained at the Pt L3 edge for a well mixed 1 1 PtRu/C catalyst than in that of a poorly mixed catalyst of the same composition, as shown in Figure 27 compare panels a and c. Pandya et al. showed that the beats occur because the difference in the backscattering phase shifts from Pt and Ru is... 

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).

It is shown in Fig. 2.9, for a case where p and p2 are fairly similar. The periodic variations of amplitude are known as beats . They come from the interference of two sinusoidal waves which make up yf in eqn 2.37 at some points these are in phase, and at other points out of phase. This phenomenon... 

The next phenomenon to be discussed here is the energy gap dependence. To demonstrate this effect, the probing frequency is fixed at the peak positions of the induced absorptions to reduce complications from the stronger quantum beats. Shown in Figure 5.14 is the case when the energy gap is increased to 200 cm-1. The ET dynamics is less efficient than the case of 20 cm-1 gap. This is reasonable because in the case of single displaced mode, the smaller the energy gap, the better the resonance between the... 

In spite of the apparent obviousness of the beat effect in optical radiation at pulsed excitation, it was only registered and studied comparatively recently. At the beginning of the 1960s Aleksandrov [3] and, independently, Dodd and coworkers [119] discovered beats in atomic emission. It may be pointed out that this, and the related phenomenon of beat resonance, was predicted by Podgoretskii [313], as well as by Dodd and Series [118]. The phenomenon was treated on the basis of well-known fundamental concepts on coherent superposition of states, and was named accordingly quantum beats. These ideas are amply expounded in reviews and monographs [4, 5, 6, 71, 96, 120, 146, 182, 188, 343, 348, 388]. 

Let us mention the rotational beats which have recently been observed (with a trans-stilbene molecule in a gasodynamic jet) and interpreted by Felker and Zewail [54, 145]. The essence of this interesting phenomenon may be described in a simplified way as follows. Let a picosecond laser pulse be capable of coherently exciting from some rotational state J f of a... 

There are approximately 200 cilia on each ciliated cell. They are packed at a density of 6-8 cilia per m2 and cannot move without affecting neighbouring cilia. In order to perform an unhindered beat cycle the movement of each cilium is slightly out of phase with that of its neighbor, leading to a phenomenon termed ciliary metachrony . Metachrony results solely from hydrodynamic coupling between adjacent cilia and provides the necessary cooperation within a field of cilia to permit them to transport mucus. 

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