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 ωpu and a weak probe at ωpr interacting with a solid state target to generate a conjugated beam ω c = 2 ω p u − ω p r 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.