Molecular decision trees realized by ultrafast electronic spectroscopy

Abstract

The outcome of a light-matter interaction depends on both the state of matter and the state of light. It is thus a natural setting for implementing bilinear classical logic. A description of the state of a time-varying system requires measuring an (ideally complete) set of time-dependent observables. Typically, this is prohibitive, but in weak-field spectroscopy we can move toward this goal because only a finite number of levels are accessible. Recent progress in nonlinear spectroscopies means that nontrivial measurements can be implemented and thereby give rise to interesting logic schemes where the outputs are functions of the observables. Lie algebra offers a natural tool for generating the outcome of the bilinear light-matter interaction. We show how to synthesize these ideas by explicitly discussing three-photon spectroscopy of a bichromophoric molecule for which there are four accessible states. Switching logic would use the on-off occupancies of these four states as outcomes. Here, we explore the use of all 16 observables that define the timeevolving state of the bichromophoric system. The bilinear lasersystem interaction with the three pulses of the setup of a 2D photon echo spectroscopy experiment can be used to generate a rich parallel logic that corresponds to the implementation of a molecular decision tree. Our simulations allow relaxation by weak coupling to the environment, which adds to the complexity of the logic operations.finite-state machines | Shannon decomposition | parallel multivalued logic | quaternary logic T he need to further reduce the physical dimensions of a computing node is well recognized (1-4). A direct way to go below a nanometer scale is to use a molecule or an artificial atom-a quantum dot-as a switch (5-11). Molecules can also respond in more interesting ways than switching. So for some time we have followed a program of seeking to implement an entire logic circuit on an atom or molecule and to concatenating such units. To do so, we used intramolecular dynamics resulting from the response of a molecule to a perturbation-the inputs to the computationthat can be electrical (12) or optical (13) or chemical (14), etc. In principle, such an approach can implement finite-state logic (15) because typically the response of a molecule depends on its initial state as well as on the applied perturbation.In finite-state machines, the execution of the logic relies on transitions between states. The operation is inherently parallel (15). A simple situation is when a molecule relaxes after being perturbed by an optical (16,17) or an electrical pulse (18,19). In optical molecular implementations, several states can be simultaneously addressed, which leads to massively parallel linear finitestate machines (16,17). The other mode of operation is to provide inputs at each machine cycle. If the molecule is switched between two states, the ability to encode a dependence on the initial state means that one can implement memristor logic (20). More elaborated memory integrated units like set-reset ...

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