Fluorescence wavepackets

CN] —> I + CN. Wavepacket moves and spreads in time, with its centre evolving about 5 A in 200 fs. Wavepacket dynamics refers to motion on the intennediate potential energy surface B. Reprinted from Williams S O and lime D G 1988 J. Phys. Chem.. 92 6648. (c) Calculated FTS signal (total fluorescence from state C) as a fiinction of the time delay between the first excitation pulse (A B) and the second excitation pulse (B -> C). Reprinted from Williams S O and Imre D G, as above. 

Appendix C Four-Point Correlation Function Expression for Fluorescence Spectra Appendix D Phase-Space Doorway-Window Wavepackets for Fluorescence Appendix E Doorway-Window Phase-Space Wavepackets for Pump-Probe Signals References... 

The first term in Eq. (4.3) is reminiscent of Eq. (3.2) for the spontaneous emission spectrum. It represents a doorway wavepacket created by the pump in the excited state, which is then detected by its overlap with a window. The only difference is that the role of the gate in determining the window in SLE is now played by the probe Wigner function W2. In addition, the pump-probe signal contains a second term that does not show up in fluorescence. This term represents a wavepacket created in the ground state (a hole ) that evolves in time as well and is finally determined by a different window Wg [24]. In the snapshot limit, defined in the preceding section, we have... 

APPENDIX D PHASE-SPACE DOORWAY-WINDOW WAVEPACKETS FOR FLUORESCENCE... 

We now derive the expression for the fluorescence signal in terms of the doorway and window wavepackets instead of the four-point correlation function. We start with Eq. (3.1) and write the four-point correlation function F(4) explicitly as the trace with respect to the equilibrium density matrix. We then use the cyclic invariance of the trace and obtain... 

We show how one can image the amplitude and phase of bound, quasibound and continuum wavefunctions, using time-resolved and frequency-resolved fluorescence. The case of unpolarized rotating molecules is considered. Explicit formulae for the extraction of the angular and radial dependence of the excited-state wavepackets are developed. The procedure is demonstrated in Na2 for excited-state wavepackets created by ultra-short pulse excitations. 

Consider the fluorescence from a molecular wavepacket excited from the ground electronic state by a short pulse of light. We assume that the initial eneigy of the molecule is EVgjg, where v, j denote, respectively, vibrational and rotational quantum numbers, with well defined magnetic quantum m,... 

The ( non-dispersed ) rate of fluorescence, Fm(t)> from the entire wavepacket is given [10, 11] as a coherent (double) sum of amplitudes from the excited states comprising the wavepacket, summed over all the possible final states. It can be expressed, in matrix notation, by treating s, s as a single index k, as... 

In order to check our imaging procedure we have to first stimulate the fluorescence emitted by excited polarized (and unpolarized) Na2 wavepackets. In these simulation we assume that the molecule, which exists initially in a (Xvg,jg) Na2 (X1 5 ) vib-rotational state, is excited by a pulse to a superposition of (xs) vib-rotational states belonging to the Na2(B IIu) electronic-states. 

The cross-correlation functions Cj/ are the links between the motion of the wavepacket in the upper state, on one hand, and the Raman spectrum on the other hand. Its behavior in time controls the fluorescence intensities into the vibrational states of the electronic ground state. 

In the photochemistry of benzene, the so-called channel 3 represents a well-known decay route along which fluorescence is quenched above a vibrational excess of 3000 cm [57], The decay takes place through a prefulvenic conical intersection characterized by an out of plane bending [52,58] and results in the formation of benzvalene and fulvene. The purpose of this study is to find distinct radiationless decay pathways that could be selected by exciting specific combinations of photoactive modes in the initial wavepacket created by a laser pulse. For this, we carry out quantum dynamics simulations on potential energy surfaces of reduced dimension, using the analysis outlined above for the choice of the coordinates. 

The fundamental idea is that the pump and probe pulses create wavepackets, which evolve on the excited state potential surface. Interference between the excited state wavefunction amplitudes created by the two pulses affects the population transferred to the excited state. The population that is measureable in a typical incoherent experiment (spontaneous fluorescence, field ionization, excitation to a different excited state by a nanosecond pulsed laser) is proportional... 

There are many schemes for detecting the arrival of the vibrational wavepacket at a specifiable position on the excited state potential energy curve. These include one-color and two-color schemes, with detection by absorption, fluorescence, ionization, four-wave mixing, and many other methods. Two simple schemes are discussed here. 

In the phase-coherent, one-color pump/probe scheme (see Section 9.1.9) the wavepacket is detected when the center of the wavepacket returns to its to position, (x)to+nT — (x)to, after an integer number of vibrational periods. The pump pulse creates the wavepacket. The probe pulse creates another identical wavepacket, which may add constructively or destructively to all or part of the original pump-produced wavepacket. If the envelope delay and optical phase of the probe pulse (Albrecht, et al, 1999) are both chosen correctly, near perfect constructive or destructive interference occurs and the total spontaneous fluorescence intensity (detected after the pump and probe pulses have traversed the sample) is either quadrupled (relative to that produced by the pump pulse alone) or nulled. As discussed in Section 9.1.9, the probe pulse is delayed, relative to the pump pulse, in discrete steps of At = x/ojl- 10l is selected by the experimentalist from within the range (ljl) 1/At (At is the temporal FWHM of the pulse) to define the optical phase of the probe pulse relative to that of the pump pulse and the average excitation frequency. However, [(E) — Ev ]/K is selected by the molecule in accord with the classical Franck-Condon principle (Tellinghuisen, 1984), also within the (ojl) 1/At range. When the envelope delay is chosen so that the probe pulse arrives simultaneously with the return of the center of the vibrational wavepacket to its position at to, a relative maximum (optical phase at ojl delayed by 2mr) or minimum (optical phase at u>l delayed by (2n + l)7r) in the fluorescence intensity is observed. 

Figure Al.6.8. Wavepacket interferometry. The interference contribution to the excited-state fluorescence of Ij as a function of the time delay between a pair of ultrashort pulses. The interference contribution is isolated by heterodyne detection. Note that the structure in the interferogram occurs only at multiples of 300 fs, the excited-state vibrational period of f it is only at these times that the wavepacket promoted by the first pulse is back in the Franck-Condon region. For a phase shift of 0 between the pulses the returning wavepacket and the newly promoted wavepacket are in phase, leading to constructive interference (upper trace), while for a phase shift of n the two wavepackets are out of phase, and interfere destructively (lower trace). Reprinted from SchererN Feta/1991 J. Chem. Phys. 95 1487. 

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