Absorptive and dispersive nonlinear optical properties have been studied considering a two-level molecular system with permanent dipole moments immersed in a thermal reservoir interacting with a classical electromagnetic field. Our model is based in a stochastic description, where the system–solvent interaction induces random shifts in the Bohr frequency (ω0) that transforms ω0 into a stochastic variable ξ(t). Our results show that it is necessary to neglect the rotating-wave approximation in order to measure the effect of the permanent dipole moments. The two-photon transitions over those with one-photon are favored when the permanent dipole moments are considered.
We have considered the stochastic effect of a thermal reservoir on a two-level system interacting with a classical electromagnetic field. The collective effect of the bath is modelled in this work as a random Bohr frequency whose manifestation is the broadening of the upper level according to a prescribed random function. This assumption transforms the optical Bloch equations to a system of multiplicative stochastic differential equations whose solution is found. After obtaining analytical expressions for the linear absorption coefficient and linear refraction index, numerical results are presented. This is done in the form of tridimensional plots of the optical properties as a function of the pump-frequency detuning factor and the strength or relaxation time of the noise source.
We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular, we obtain the Green's functions for a waveguide with an embedded two-level system in the single- and two-excitation sector for arbitrary dispersion relations both in the time and the frequency domains. In the single-excitation sector, we show how to sum the diagrammatic perturbation series to all orders and thus obtain explicit expressions for physical quantities such as the spectral density and the scattering matrix. In the two-excitation sector, we show that strictly linear dispersion relations exhibit the special property that the corresponding diagrammatic perturbation series terminates after two terms, again allowing for closed-form expressions for physical quantities. In the case of general dispersion relations, notably those exhibiting a band edge or waveguide cutoff frequencies, the perturbation series cannot be summed explicitly. Instead, we derive a self-consistent
T-matrix equation that reduces the computational effort to that of a single-excitation computation. This analysis allows us to identify a Fano resonance between the occupied quantum impurity and a free photon in the waveguide as a unique signature of the few-photon nonlinearity inherent in such systems. In addition, our diagrammatic approach allows for the classification of different physical processes such as the creation of photon-photon correlations and interaction-induced radiation trapping, the latter being absent for strictly linear dispersion relations. Our framework can serve as the basis for further studies that involve more complex scenarios such as several and many-level quantum impurities, networks of coupled waveguides, disordered systems, and nonequilibrium effects.