Multidimensional four-wave-mixing spectroscopy with squeezed light

A set of nonlinear spectroscopic measurements with quantum light is presented. It involves a strong pump with frequency ω_pu and a weak probe at ω_pr interacting with a solid state target to generate a conjugated beam $ωc=2ωpu−ωpr$ via nondegenerate four-wave mixing. The $χ(3)$ susceptibility can be measured by the noise spectra of the intensity difference of the squeezed beams. We discuss three spectroscopic setups based on squeezed light: first, single four-wave mixing in a single crystal; second, cascading scheme involving two crystals; third, an SU(1, 1) interferometer based on two separate four-wave mixing processes. We further investigate the microscopic noise and optical losses in all three setups. Simulations are presented for silicon-vacancy color centers in diamond.