We show that proper engineering of a nonlinear interaction induces quantum entanglement between the spatial and spectral degrees of freedom of incident photons via the all-optical analogue of the Stern-Gerlach effect.
Multi-color photons are prominent candidates for carrying quantum information, as their unlimited dimensionality allows for novel qudit-based schemes. The generation and manipulation of such photons takes place in nonlinear optical media, and the coupling between the different frequency bins can be engineered to obtain the desired quantum state. Here, we propose the design of a frequency-domain Stern–Gerlach effect for photons, where quantum entanglement between the spatial and spectral degrees of freedom is manifested. In this scheme, orthogonal frequency-superposition states can be spatially separated, resulting in a direct projection of an input state onto the frequency-superposition basis. We analyze this phenomenon for two-color qubits and three-color qutrits, and present a generalized wavelength-domain analog of the Hong–Ou–Mandel interference with distinguishable photons. Our results pave the way toward realization of single-element, all-optically controlled spectral-to-spatial beam splitters and tritters that can benefit quantum information processing in the frequency domain.
We study the birefringence of quantized polarized light in a magneto-optically manipulated atomic ensemble as a generalized Stern-Gerlach effect of light. To explain this engineered birefringence microscopically, we derive an effective Shr\"odinger equation for the spatial motion of two orthogonally polarized components, which behave as a spin with an effective magnetic moment leading to a Stern-Gerlach split in a nonuniform magnetic field. We show that the electromagnetically-induced-transparency mechanism can enhance the magneto-optical Stern-Gerlach effect of light in the presence of a control field with a transverse spatial profile and a nonuniform magnetic field.