Generation of microwave fields in cavities with laser-excited nonlinear media: competition between the second- and third-order optical nonlinearities

We discuss a scheme for the parametric amplification of the quantum fluctuations of the electromagnetic vacuum in a three-dimensional microwave resonator, and report the preliminary measurements to test its feasibility. In the present experimental scheme, the fundamental mode of a microwave cavity is nonadiabatically perturbed by modulating the index of refraction of the nonlinear optical crystal enclosed therein. Intense, multi-GHz laser pulses, such as those delivered by a mode-locked laser source, impinge on the crystal to accomplish the n-index modulation. We theoretically analyze the process of parametric generation, which is related to the third-order nonlinear coefficient χ(3) of the nonlinear crystal, and assess the suitable experimental conditions for generating real photons from the vacuum. Second-order nonlinear processes are first analyzed as a possible source of spurious photons in quantum vacuum experiments when an ideal, mode-locked laser source is considered. The combination of a crystal non-null χ(2) coefficient and a real mode-locked laser system—i.e. one featuring offset-fromcarrier noise and unwanted secondary oscillations—is also experimentally investigated, paving the way for future experiments in three-dimensional cavities.