Vibrational energy flow is of fundamental importance as the initial step in polyatomic molecule chemical reactions. In essence, molecules roughly behave like a set of balls connected by anharmonic springs: tweaking one of these springs and letting go will soon cause the whole contraption to vibrate in an apparently random fashion. Or is it as random as it seems? Basic theories of reaction dynamics (e.g. the celebrated RRKM theory) assume that energy redistribution is complete long before interesting chemical reactions happen. Yet there are signs that the energy flow and reaction timescales are not separated by orders of magnitude in time. Our goal is to slow down energy flow further, until chemical reactions are no longer "statistical." We investigate this problem theorectically by developing tools to do computations on large and highly excited molecules. This high energy regime offers two challenges: 1) the potential surface of molecules is difficult to obtain; 2) even with a potential surface or matrix elements in hand, it is difficult to calculate molecular spectra or the time evolution of a molecule's wavefunction because very large (10,000's to 1,000,000's) of molecular energy levels are involved. We have developed multidimensional quantum dynamics algorithms and realistic anharmonic Hamiltonians. In particular, we developed a scaling model for vibrational couplings based on the Born-Oppenheimer approximation. We also study the problem experimentally by frequency- and time-resolved stimulated emission pumping experiments on organic molecules. The key in our experiments is that we study "skeletal vibration" involving carbon, oxygen, sulfur, etc. atoms, not hydrogen stretching or bending modes, which are not typical of the "bath" of vibrations into which energy flows in large organic molecules. The calculations agree with ours and other groups' experiments: vibrational energy redistribution slows dramatically as the molecule explores more of the available quantum states. At short times, the vibrational wavepacket decays exponentially fast as predicted by the Golden Rule of time-dependent perturbation theory. At longer times, the decay slows down and becomes a polynomial in time. Another way of looking at this problem is in terms of the dimensionality of the vibrational wavepacket as it explores "state space." State space is a 3N-6 dimensional lattice of coordinates, one coordinate for each vibrational mode of a molecule with N atoms. A laser initially excites a single point or small group of states in this lattice. This group or "vibrational wavepacket" then expands, until all states compatible with energy conservation are covered in the statistical limit at long times. Where our model differs from the Golden Rule is how the wavepacket gets to the statistical limit: in the Golden Rule approximation, the wavepacket uniformly expands in 3N-6 dimensions, leading to a nearly exponential decay (in the limit where 3N-6 becomes very large). In our model, and in the experiments, the wavepacket expands in only 1-4 dimensions, so it has a fractal dimension much smaller than 3N-6. The nature of the coordinates along which the wavepacket expands changes with time, so eventually the wavepacket does cover all eigenstates allowed by energy conservation, but it takes much longer to do so.
As a result, the number of parameters to control the evolution of the molecular wavepacket via coherent laser excitation grows more slowly in time than expected. This can be exploited to allow coherent control of the vibrational energy flow. Once the energy flow is controlled, subsequent chemical reactions are no longer statistical. The phenomenon of vibrational energy flow also provides a model laboratory for molecular quantum computing. Because an isolated molecule obeys energy conservation, energy flow is a pure dephasing process in terms of the molecular eigenstates. Different vibrational modes, or different combinations of energy levels, can have their populations and phases switched around by laser pulses, in effect performing quantum computations. For example, a set of 4 vibrational states arbitrarily coupled by laser pulses can perform any 2-qubit calculation. These computations occur on a femtosecond time scale, long before nanosecond dephasing processes set in.
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