Beat period

In this case the pulse sequence favours the generation of population and coherence ensembles in the excited state of the molecule according to the Feynman diagrams (a) and (b). The time evolution of the spectrum reflects the relaxation of those ensembles and can be used to determine the dynamics of molecules in the excited state. Some oscillations in the intensity of the echo spectrum versus population time are observed with several beat periods corresponding to the splitting of vibrational levels... 

Figure 1. Shows the resulting ion yield, as measured by the norm (i.e., the integrated density) of the wavepacket in the ion ground state, depending on the delay time At of the bum-and-probe laser pulses. The oscillatory pattern of the norm reflects the motion of the hole in the wavepacket of K fX). The beat period of approximately 190 fs corresponds to half of the vibrational period in the X state. Large and small maxima correspond to large and small lobes entering the FC regions, respectively.

Equation 3.24 specifies the minimum amount of total delay required. In practice, low modal density can lead to audible beating in response to narrowband signals. A narrowband signal may excite two neighboring modes which will beat at their difference frequency. To alleviate this, the mean spacing of modes can be chosen so that the average beat period is at least equal to the reverberation time [Stautner and Puckette, 1982], This leads to the following relationship ... 

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). 

Abassi YA, Xi BA, Li N et al (2012) Dynamic monitoring of beating periodicity of stem cell-derived cardiomyocytes as a predictive tool for preclinical safety assessment. Br J Pharmacol 165(5) 1424-1441... 

Figure 7a shows that there exists a longer time modulation (about 2 ps) in the chromophore population. The origin of this modulation can be directly traced to the i3 mode, the population of which displays the same evolution pattern as shown in Figure 7c. In this figure, we have compared the Aj and N3 average quantum numbers. It can be seen that these populations vary out of phase, indicating a resonance between the v, and v3 modes. From the quantum beat period, we expect a resonance between two states separated by 15 cm 1 as we noticed previously, the states with energies 16,169 cm 1 and 16,152 cm-1 have an important contribution from the 3 mode. Finally the N2, N4, and N6 populations, shown in Figure 7d, display a monotonic increase over the 15-ps interval, apart from modulations due to the N -N5 and Nt-N2 resonances. The overall relaxation from the 6v,)° mode is displayed in Figure 8.

The two Zeeman components of an atomic level (L = 1, 5 = 1/2, / = 1/2) are coherently excited by a short laser pulse. Calculate the quantum-beat period of the... 

The time-dependent fluorescence from these coherently excited states shows, besides the exponential decay exp(—t/tsp), a beat period ATqb = fi/( a — Eb) due to the different frequencies coj and... 

Time spectra of nuclear resonant scattering for selected orientations of the principal axis /zz of the electric field gradient relative to the incident wave vector /cq. Calculations were performed for the same sample as in Fig. 1.14. The beat period in the time spectra corresponds to a quad-rupole splitting as observed in the ferrocene molecule [4]. (Reproduced from Ref. 22 with permission of Springer.)... 

In the inset of Fig. 3.22 b the corresponding plot is presented for 642 nm. Here, the RKR-based frequencies are not in agreement with the frequencies obtained from the 3PI real-time spectra. In the center of the frequency group the deviations are especially pronounced. In the Fourier spectrum, two main frequencies, both located slightly away from the center of the Av = 1 frequency group, dominate the pattern. These frequencies lie at uji = 112.4 cm and UJ2 — 110.2cm . The classical beat period from the two frequencies... 

Two tuning forks sound simultaneously. Their frequencies are Vj = 440 Hz and V2 = 440.5 Hz. Detennine the resulting beatings period T. 

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