We experimentally investigate the effects of cascade third-order and fifth-order nonlinear optical processes in a four-level atomic system. The relative strengths of these high-order nonlinear optical processes can be manipulated by controlling the atomic coherence.
The atomic optical bistability (AOB) in multi-level systems has advantages over the two-level system as absorption, dispersion, and nonlinear optical properties of one optical field coupled to one atomic transition can be greatly modified by other optical fields coupled to other connected nearby atomic transitions in multi-level atomic systems due to induced atomic coherences. By making use of such changes in linear and nonlinear optical properties around resonance, which are related to the electromagnetically induced transparency (EIT), it is easy to manipulate and control nonlinear optical processes in the multi-level atomic systems. We review earlier two-level AOB theory, as well as experiments and some recent studies that made use of multi-level atomic EIT systems in achieving controls of nonlinear optical processes such as instabilities and stochastic resonance associated with the coupled atom–cavity systems.
Contributions to the fifth-order nonlinear optical susceptibility ${\ensuremath{\chi}}^{(5)}$ of a collection of homogeneously broadened two-level atoms that scale as ${N}^{2}{({\ensuremath{\gamma}}_{\mathrm{at}}^{(3)})}^{2}$ and ${N}^{2}{\ensuremath{\mid}{\ensuremath{\gamma}}_{\mathrm{at}}^{(3)}\ensuremath{\mid}}^{2}$, where ${\ensuremath{\gamma}}_{\mathrm{at}}^{(3)}$ is the lower-order atomic hyperpolarizability and N is the atomic number density, are predicted theoretically. These ``cascaded'' contributions are a consequence of local-field effects. We determine them from a fifth-order solution of the Lorentz-Maxwell-Bloch equations. They are missing from a straightforward generalization of Bloembergen's result for the local field correction to the second order nonlinearity, but are recovered by a careful application of his general approach. We find that at high atomic densities $(N>{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ the value of the cascaded third-order contribution can be as large as the ``direct'' fifth-order term in the expression for the fifth-order susceptibility.
We experimentally investigate the soliton formation and dynamics in the nonlinear propagation of the generated signal and probe beams in four-wave mixing (FWM) process with atomic coherence in a three-level atomic system, under the competition between focusing and defocusing nonlinearities, as well as between gain and dissipation, due to the third- and fifth-order nonlinear susceptibilities with opposite signs. With multi-parameter controllability and nonlinear competition in the system, fundamental, dipole, and azimuthally-modulated vortex FWM solitons can transform mutually from one to the other. Such investigations have potential applications in optical pattern formation and control, and all-optical communication.