The study of nonlinear optical properties of quantum systems, like quantum dots and molecules, near plasmonic nanostructures has attracted significant interest in the past decade. Several nonlinear phenomena have been studied in quantum systems next to plasmonic nanostructures, like second and third harmonic generation, Kerr nonlinearity, four-wave mixing, optical bistability, and nonlinear optical rectification. The latter occurs in asymmetric quantum systems and it can be strongly influenced, enhanced or suppressed, depending on the particular plasmonic nanostructure used. In this work, we theoretically study the nonlinear optical rectification of a polar two-level quantum system, a specific molecule, the Zinc-phalocyanine molecular complex, interacting with an optical field near a gold nanoparticle. Initially, we use the steady-state solution of the density matrix equations for determining the correct form of the nonlinear optical rectification coefficient. We then use ab initio electronic structure calculations for determining the electronic structure of the molecule under study, i.e. the necessary energy differences and the induced and permanent electric dipole moments. We also use ab initio classical electromagnetic calculations for calculating the influence of the metallic nanoparticle on the decay rates of the molecule due to the Purcell effect and on the electric field applied in the molecule in the presence of the metallic nanoparticle. We then use the above to investigate the form of the corresponding nonlinear coefficient in the absence and the presence of the plasmonic nanoparticle for various parameters. We find that the nonlinear optical rectification coefficient can be quite enhanced for specific field polarization and for suitable distance between the molecule and the plasmonic nanoparticle. Also, we observe that high efficiency of this process is obtained for weak field intensity, zero pure dephasing rate and for small value of the transition dipole moment.
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