Quantum coherent vibrational dynamics

Figure 14. (a) Potential-energy surfaces, with a trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snapshots of the wavepacket motion (quantum molecular dynamics calculations) are shown for the same reaction at / = 0 and t = 600 fs. (b) Femtosecond dynamics of barrier reactions, IHgl system. Experimental observations of the vibrational (femtosecond) and rotational (picosecond) motions for the barrier (saddle-point transition state) descent, [IHgl] - Hgl(vib, rot) + I, are shown. The vibrational coherence in the reaction trajectories (oscillations) is observed in both polarizations of FTS. The rotational orientation can be seen in the decay of FTS spectra (parallel) and buildup of FTS (perpendicular) as the Hgl rotates during bond breakage (bottom). 

It is interesting that both dynamical methods give the same gross mechanistic explanation (with very good matches for the coherent vibrational timescale), but crucially they differ in the precise nature of the coherent vibration observed. Both dynamics methods have their own deficiencies, and further quantum dynamical simulation with better potentials, more coupled vibrational modes, and longer simulation times are therefore desirable for this important system. Another possible fruitful method is using time-independent vibrational structure approaches, with similar potentials expanded around the unsaturated minima in the Jahn-Teller moat . Recent advances in such methodology should see this approach utilized in the near future [110, 111]. 

The examples collected for this survey of femtosecond nonadiabatic dynamics at conical intersections illustrate the interesting interplay of coherent vibrational motion, vibrational energy relaxation and electronic transitions within a fully microscopic quantum mechanical description. It is remarkable that irreversible population and phase relaxation processes are so clearly developed in systems with just three or four nuclear degrees of freedom. 

Since the very beginning, almost a century ago, spectroscopy has revealed that vibrational dynamics are quantal in nature the energy is quantized and dynamics are described in terms of eigenstates. The quantum theory has developed predominantly within the harmonic approximation, that is the simplest expansion, to quadratic terms, of the potential hypersurface around the equilibrium position. Vibrational dynamics can be thus represented with harmonic oscillators (normal modes) corresponding to coherent oscillations of all degrees... 

Recently, the femtosecond time-resolved spectroscopy has been developed and many interesting publications can now be found in the literature. On the other hand, reports on time-resolved vibrational spectroscopy on semiconductor nanostructures, especially on quantum wires and quantum dots, are rather rare until now. This is mainly caused by the poor signal-to-noise ratio in these systems as well as by the fast decay rates of the optical phonons, which afford very fast and sensitive detection systems. Because of these difficulties, the direct detection of the temporal evolution of Raman signals by Raman spectroscopy or CARS (coherent anti-Stokes Raman scattering) [266,268,271-273] is often not used, but indirect methods, in which the vibrational dynamics can be observed as a decaying modulation of the differential transmission in pump/probe experiments or of the transient four-wave mixing (TFWM) signal are used. 

The generalized Prony analysis can extract a great variety of information from the ENDyne dynamics, such as the vibrational energy vib arrd the frequency for each normal mode. The classical quantum connection is then made via coherent states, such that, say, each nomral vibrational mode is represented by an evolving state... 

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. 

The last mentioned dynamical capability of lasers is in its infancy. It is possible in principle to make optical measurements which are analogous to coherent NMR measurements, and thereby to observe homogeneous linewidths in inhomogeneously broadened systems, to measure optical or vibrational Ti and T2 relaxation times directly, and to observe quantum recurrences. 

B. Kohler Prof. Fleming, your experimental results clearly indicate that in the case of I2 in hexane the vibrational coherence of an initially prepared wavepacket persists for unexpectedly long times. However, quantum dynamical calculations show that wavepacket spreading due to anharmonicity can be very substantial even for isolated molecules... 

Figure 5.4, one can easily understand why the interfacial electron transfer should take place in the 10-100 fsec range because this ET process should be faster than the photo-luminescence of the dye molecules and energy transfer between the molecules. Recently Zimmermann et al. [58] have employed the 20 fsec laser pulses to study the ET dynamics in the DTB-Pe/TiC>2 system and for comparison, they have also studied the excited-state dynamics of free perylene in toluene solution. Limited by the 20 fsec pulse-duration, from the uncertainty principle, they can only observe the vibrational coherences (i.e., vibrational wave packets) of low-frequency modes (see Figure 5.5). Six significant modes, 275, 360, 420, 460, 500 and 625 cm-1, have been resolved from the Fourier transform spectra of ultrashort pulse measurements. The Fourier transform spectrum has also been compared with the Raman spectrum. A good agreement can be seen (Figure 5.5). For detail of the analysis of the quantum beat, refer to Figures 5.5-5.7 of Zimmermann et al. s paper [58], These modes should play an important role not only in ET dynamics or excited-state dynamics, but also in absorption spectra. Therefore, the steady state absorption spectra of DTB-Pe, both in...

The relaxation and coherence dynamics contributions to Eq. (128) within the BOA approximation are considered. For this purpose, g = (a, ), m — (b, a ), and n — (c, w ) are defined, where, for example, u represents the vibrational quantum numbers of the vibrational modes of the electronic ground state. For the electronic coupling between the two excited states, it is assumed that the interaction Hamiltonian is given by H — c)Jcb(Q)(b + h.c. where Q denotes the normal coordinate. The coupled GMEs, for example, for pbv,cw can be written as [67]... 

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