Controlling four-wave mixing in a semiconductor quantum dot through coupling with a metal nanospheroid

We study the coherent interaction between a hybrid nanostructure and a strong pump electromagnetic field as well as a weak electromagnetic probe field, focusing on how various parameters influence the line shape of the four-wave-mixing (FWM) spectrum. More specifically, we examine the dependence of the FWM spectrum exhibited by a semiconductor quantum dot that is coupled with an ellipsoidal metal nanospheroid (MNS) on the interparticle distance and the depolarization factor. First, we derive the differential equations that determine the evolution of the density matrix elements in the rotating wave and dipole approximations and expand the density matrix elements, to first order with respect to the weak probe field. We then solve the equations of the density matrix, in steady state, and calculate the FWM spectrum. The investigation of the impact of the interparticle distance and the depolarization factor on the position and the width of the resonance follows. The derivation of analytical solutions of specific density matrix elements enables us to calculate the effective Rabi frequency that is introduced in the dressed-state description to predict the position of the effective resonances appearing in light-matter interaction. We demonstrate that the spectral line shape shifts from triple-peaked to single-peaked, while its amplitude is significantly suppressed, when the interparticle distance drops below a critical value that depends on the depolarization factor of the MNS. The highest critical distance occurs for a prolate MNS with high eccentricity, provided that the incident field's polarization direction is parallel with the nanostructure's symmetry axis, and the pump field detuning is positive and has a high absolute value. The spectral profile shows negligible dependence on the interparticle distance for an exactly resonant pump field with a polarization vector perpendicular to the MNS's polar axis, especially if the MNS is an oblate spheroid with high eccentricity.