Direct experimental observation of sub-Poissonian photon statistics by means of multiphoton scattering on a two-level system

A cascade of two-level superconducting artificial atoms---a source and a probe---strongly coupled to a semi-infinite waveguide is a promising tool for observing nontrivial phenomena in quantum nonlinear optics. The probe atom can scatter an antibunched radiation emitted from the source, thereby generating a field with specific properties. We experimentally demonstrate wave mixing between nonclassical light from the coherently cw-pumped source and another coherent wave acting on the probe. We observe unique features in the wave mixing stationary spectrum which differs from the mixing spectrum of two classical waves on the probe. These features are well described by adapting the theory of Gardiner et al. [Phys. Rev. A 50, 1792 (1994)] for a strongly coupled cascaded system of two atoms. We further analyze the theory to predict nonclassical mixing spectra for various ratios of atoms' radiative constants. Both experimental and numerical results confirm the domination of the multiphoton scattering process with only a single photon from the source. We evaluate entanglement of atoms in the quasistationary state and illustrate the connection between the expected second-order correlation function of the source field and wave mixing side peaks corresponding to a certain number of scattered photons.