Quantum beat pump/probe

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)...

Although the presented numerical approach to the coupled master equations has shown that a turnover feature can be seen in vibronic dynamics appearing in the calculated pump-probe stimulated emission spectra as a function of the energy gap between the two relevant vibronic states. It is found that vibronic quantum beats cannot be observed when the energy gap becomes larger in which situation it leads to smaller Franck-Condon overlaps between the energy conserved levels. 

Walther, Th., Bitto, H. and Huber, J.R. (1993). High-resolution quantum beat spectroscopy in the electronic ground state of a polyatomic molecule by IR-UV pump-probe method, Chem. Phys. 

The second major section (Section III), comprising the bulk of the chapter, pertains to the studies of IVR from this laboratory, studies utilizing either time- and frequency-resolved fluorescence or picosecond pump-probe methods. Specifically, the interest is to review (1) the theoretical picture of IVR as a quantum coherence effect that can be manifest in time-resolved fluorescence as quantum beat modulated decays, (2) the principal picosecond-beam experimental results on IVR and how they fit (or do not fit) the theoretical picture, (3) conclusions that emerge from the experimental results pertaining to the characteristics of IVR (e.g., time scales, coupling matrix elements, coupling selectivity), in a number of systems, and (4) experimental and theoretical work on the influence of molecular rotations in time-resolved studies of IVR. Finally, in Section IV we provide some concluding remarks. 

Now, the argument just presented relies on the unproven assumption that rotational quantum beats arising from a thermal sample of isolated molecules will wash each other out. Recently, we examined this assumption by directly simulating the decays associated with thermally averaged rotational beats.47 (Our initial motivation for this work was to try to explain the picosecond pump-probe results of Refs. 51 and 52, which results showed the existence of polarization-dependent early time transients in the decays of t-stilbene.) These theoretical simulations and subsequent picosecond-beam experiments47-50 have revealed that the manifestations of rotational coherence in thermally averaged decays can, in fact, be observed. In this section, we briefly review these results and examine some of their implications with regard to time-resolved studies of IVR. 

The earliest pulsed laser quantum beat experiments were performed with nanosecond pulses (Haroche, et al., 1973 Wallenstein, et al., 1974 see review by Hack and Huber, 1991). Since the coherence width of a temporally smooth Gaussian 5 ns pulse is only 0.003 cm-1, (121/s <-> 121 cm"1 for a Gaussian pulse) nanosecond quantum beat experiments could only be used to measure very small level splittings [e.g. Stark (Vaccaro, et al., 1989) and Zeeman effects (Dupre, et al., 1991), hyperfine, and extremely weak perturbations between accidentally near degenerate levels (Abramson, et al., 1982 Wallenstein, et al., 1974)]. The advent of sub-picosecond lasers has expanded profoundly the scope of quantum beat spectroscopy. In fact, most pump/probe wavepacket dynamics experiments are actually quantum beat experiments cloaked in a different, more pictorial, interpretive framework,... 

From the discussion of the fs pump-probe experiments, when the fs laser pulse is used for pumping, from the uncertainty principle AmAf 1, one can expect that when the pulse duration of At is employed, the coherence corresponding to Aco 1 /At will be created, and the corresponding quantum beat will be observed. This can indeed be seen from Fig. 4.5 for the pyrazine case. In this case, Aco 560cm is corresponding to the mode vea, which has the largest Huang-Rhys factor and can be most effectively pumped. 

Quantum beats can be observed not only in emission but also in the transmitted intensity of a laser beam passing through a coherently prepared absorbing sample. This has first been demonstrated by Lange et al. [872, 873]. The method is based on time-resolved polarization spectroscopy (Sect. 2.4) and uses the pump-and-probe technique discussed in Sect. 6.4. A polarized pump pulse orientates atoms in a cell placed between two crossed polarizers (Fig. 7.12) and generates a coherent superposition of levels involved in the pump transition. This results in an oscillatory time dependence of the transition dipole moment with an oscillation period AF = 1/Av... 

A theory for the ultrafast pump-probe spectroscopy of large polyatomic molecules in condensed phases was developed in the work [15]. A multimode Brownian oscillator model was used to account for high-frequency molecular vibrations and local intermolecular modes as well as collective solvent motions. A semiclassical picture was provided using the density matrix in Liouville space. Conditions for the observation of quantum beats, spectral diffusion, and solvation dynamics (dynamic Stokes shift) are specified. 

Quantum dynamical calculations of the pump probe spectra for the two isotopes were performed for delay times up to 40 ps. A comparison of the experimental and theoretical ionization signals as a function of the delay time is presented in Fig. 3.15. In agreement with the experimental data, the short-time dynamics of the theoretical signal show the 500 fs oscillation period of the wave packet prepared in the A state (centered around v = 11) and the long time dynamics reflect the totally different beat structures of the two isotopes. However, the oscillation periods of the pronounced regular beat structure of the isotope (Fig. 3.15 a) and of the weak, irregular... 

A short pump pulse excites coherently different upper levels. The time evolution of the superposition of states following the coherent excitation causes time-dependent changes of the complex susceptibility x of the sample. Similar to the quantum beats in the fluorescence intensity the susceptibility x(t) is found to contain oscillating nonisotropic contributions which can be readily detected by placing the sample between crossed polarizers and transmitting a probe pulse with variable delay (see also Sect.10.3 on polarization spectroscopy). Even a cw broadband dye laser can be used for probing if the probe intensity transmitted by the polarizer is monitored with sufficient time resolution. 

FIGURE 5 (a) Quantum beats observed in pump-probe signals of ARC trimer at room temperature. Signals were obtained as a function of deiay time between the pump and probe puises as well as the probe wavelength. Insets are oscillatory components extracted from the observed signals, (b) Fourier transform analysis of the oscillatory components. 

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