Quantum beat

The method of quantum beats has found application in the measurement of fine structure intervals, polarizabilities, and hyperfine intervals in several species. The basis of the approach is to prepare a coherent superposition of at least two states by pulsed excitation and observe the subsequent 

Two different approaches have been used to observe quantum beats of the Na nd states using electric field ionization of Rydberg atoms in an atomic beam. These experiments rely on the fact that states of the same n and I but different m are ionized by different electric fields. In the experiments of Leuchs and Walther an ionizing field was applied at a variable time after the laser excitation. The ion signal versus delay time yields a signal similar to those observed by Haroche et and leys et 

The major limitations of the approach are two. First the excitation must coherently excite both levels. For laser excitation this usually means 

The example discussed considers the case of weak light excitation, where the first cycle J — J (see Fig. 3.14) does not produce ground state optical polarization via depopulation of the J level. If this is not so, then the signal is described, accounting for depopulation effects, and naturally assumes a more complex shape [30]. 

For a radical pair formed in a nonstationary state, the singlet probability will exhibit a characteristic time dependence at the frequency corresponding to the energy difference between the 5) 7o) states. The modulating pattern occurring at this 

Quantum beats can arise in a chemical system via the A or hyperflne mechanism which induce 5 — To mixing. For the Ag-mechanism the frequency of oscillation between the 5 — To states is given by the Larmor frequency (Eq. 3.4). In the case of an isotropic hyperflne interaction occurring on each radical as well, the frequency of oscillation is 

Molin [61] have shown that the parameters of quantum beats can usually be decomposed into (1) the frequency of the oscillation (2) the time taken for the oscillation to decay (3) the phase shift of oscillations and (4) the amplitude of the oscillation. The authors show that all these parameters can provide invaluable information of the spin-correlated radical pair. For example (1) gives information about the splitting in the ESR spectrum (2) contains information about the spin relaxation times (3) contains information about the time delay in forming the radical pair, and (4) can show the presence of spin-uncorrelated radical pairs (by comparing with theory). 

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Leonhardt R, Holzapfel W, Zinth W and Kaiser W 1987 Terahertz quantum beats in molecular liquids Chem. Phys. Lett. 133 373-7... 

Walmsiey I A, Wise F W and Tang C L 1989 On the difference between quantum beats in impulsive stimulated Raman scattering and resonance Raman scattering Chem. Phys. Lett. 154 315-20... 

The low MW power levels conuuonly employed in TREPR spectroscopy do not require any precautions to avoid detector overload and, therefore, the fiill time development of the transient magnetization is obtained undiminished by any MW detection deadtime. (3) Standard CW EPR equipment can be used for TREPR requiring only moderate efforts to adapt the MW detection part of the spectrometer for the observation of the transient response to a pulsed light excitation with high time resolution. (4) TREPR spectroscopy proved to be a suitable teclmique for observing a variety of spin coherence phenomena, such as transient nutations [16], quantum beats [17] and nuclear modulations [18], that have been usefi.il to interpret EPR data on light-mduced spm-correlated radical pairs. 

Kothe G, Weber S, BittI R, Ohmes E, Thurnauer M and Norris J 1991 Transient EPR of light-induced radical pairs in plant photosystem I observation of quantum beats Chem. Rhys. Lett. 186 474-80... 

Weber S, Ohmes E, Thurnauer M C, Norris J R and Kothe G 1995 Light-generated nuclear quantum beats a signature of photosynthesis Proc. Natl Acad. Sc/. USA 92 7789-93... 

BittI R, van der Est A, Kamlowski A, Lubitz W and Stehlik D 1994 Time-resolved EPR of the radical pair bacterial reaction centers. Observation of transient nutations, quantum beats and... 

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. 

Fig. 9.2 Mossbauer spectra in the energy domain and in the time domain. Non-zero quadrupole splitting shows up in the time domain as quantum beats. (Taken from [7])...

Fluctuations of the EFG cause a dephasing of the originally coherent waves which affects the quantum-beat pattern (as described for Mb02 in Sect. 9.4.3) and... 

Fig. 9.12 (a) NFS spectra of FC/DBP with quantum beat and dynamical beat pattern, (b) Temperature-dependent /-factor. The solid line is a fit using the Debye model with 0D = 41 K below 150 K. Above, a square-root term / - V(Tc - T)/Tc was added to account for the drastic decrease of /. At Tc = 202 K the glass-to-liquid transition occurs. (Taken Ifom [31])... 

A series of NFS spectra of the spin-crossover complex [Fe(tpa)(NCS)2] were recorded over a wide temperature range [45]. A selection of spectra around the spin-crossover transition temperature is shown in Fig. 9.13. At 133 K, the regular quantum-beat structure reflects the quadrupole splitting from the pure high-spin (HS) phase, and the envelope of the spectrum represents the dynamical beating with a minimum around 200 ns. Below the transition, at 83 K, the QBs appear with lower frequency because of smaller AEq of the low-spin (LS) phase. Here the minima of... 

Fig. 9.16 Time-dependent NFS of [Fe(tpa)(NCS)2] recorded at 108 K. The two curves represent comparison of a coherent vs incoherent superposition of the scattering from 50 % LS and 50 % HS iron(II) characterized by their corresponding quantum beat pattern. The effective thickness of the sample was =18. (Taken from [42])...

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

In conventional theories of rate processes, the temperature T is usually involved. The involvement of T implicitly assumes that vibrational relaxation is much faster than the process under consideration so that vibrational equilibrium is established before the system undergoes the rate process. For example, let us consider the photoinduced ET (see Fig. 5). From Fig. 5 we can see that for the case in which vibrational relaxation is much faster than the ET, vibrational equilibrium is established before the rate process takes place in this case the ET rate is independent of the excitation wavelength and a thermal average ET constant can be used. On the other hand, for the case in which the ET is much faster than vibrational relaxation, the ET takes place from the pumped vibronic level (or levels) and thus the ET rate depends on the excitation wavelength and often quantum beat will be observed. 

The events taking place in the RCs within the timescale of ps and sub-ps ranges usually involve vibrational relaxation, internal conversion, and photo-induced electron and energy transfers. It is important to note that in order to observe such ultrafast processes, ultrashort pulse laser spectroscopic techniques are often employed. In such cases, from the uncertainty principle AEAt Ti/2, one can see that a number of states can be coherently (or simultaneously) excited. In this case, the observed time-resolved spectra contain the information of the dynamics of both populations and coherences (or phases) of the system. Due to the dynamical contribution of coherences, the quantum beat is often observed in the fs time-resolved experiments. 

Recently, Scherer et al. have used the 10-fs laser pulse with A,excitation = 860 nm to study the dynamical behavior of Rb. Sphaeroides R26 at room temperatures. In this case, due to the use of the 10-fs pulse both P band and B band are coherently excited. Thus the quantum beat behaviors are much more complicated. We have used the data given in Table I and Fig. 19 to simulate the quantum beat behaviors (see also Fig. 22). Without including the electronic coherence, the agreement between experiment and theory can not be accomplished. 

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],... 

Bitto, H., and Huber, J. R. (1992), Molecular Quantum Beats. High-Resolution Spectroscopy in the Time Domain, Acc. Chem. Res. 25, 65. 

Figure 7.8 Pump-control-probe quantum beat signal obtained at various probe wavelengths from 378 (bottom) to 390 (top) nm. The delay between the pump and control pulses was set around timing. Each panel shows the different relative phase condition between the pump and control pulses. Reproduced with permission from the supplement of Ref. [39]. Copyright 2009 by the American Physical Society. (See color plate section for the color representation of this figure)...

Figure 7.12 Strong-laser-induced quantum interference. Quantum beats observed in the populations of the eigenstates v = 25, 27, and 29 as functions of the pump-NlR delay Tfjjjj. Each trace is an average of three repeated scans. The vertical scahngs of the traces for v = 25, 27, and 29 have been normahzed by their intensities averaged over Tpjjjj = —536 —283, —531 —278, and —535 —281 fs, respectively. Reproduced from Ref. [40] with permission from Nature Publishing Group.

Quantum Beats and Dephasing in Isolated Large Molecules Cooled by Supersonic Jet Expansion and Excited by Picosecond Pulses Anthracene, W. R. Lambert, P. M. Felker, and A. H. Zewail, J. Chem. Phys. 75, 5958 (1981). 

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