Femtosecond Photo-Induced Multiphoton Analog Computation for Symmetry-Based Pattern Classification

Multiphoton femtosecond coherent control of is used for implementing innovative photo-induced analog coherent computation that generally might be a basis for future "smart hardware". The specific implemented computational task the classification of an unknown sequence into one of the three groups: (i) a constant sequence that is composed of identical numbers, (ii) a sequence that is antisymmetric around a given point, or (iii) neither. The input sequence is encoded into the spectral phases of a broadband femtosecond pulse and the computational task is being carried out by the multiphoton nonlinear response of the irradiated physical system. Here, it is the simultaneous coherent two- and three-photon absorption in atomic sodium (Na). The corresponding computational resources are the manifold of initial-to-final multiphoton excitation pathways photo-induced by the broad spectrum of the irradiating femtosecond pulse. The answer is obtained by measuring only two observables, which are two state-populations excited via the two- and three-photon absorption processes. Hence, the computational task is accomplished in a constant number of operations irrespective of the sequence length. As such, the presented scheme, where the femtosecond pulse serves as a query and the irradiated physical system serves as an oracle, provides a sufficient gain in the computational complexity.