Strong coupling between atoms and light is critical for quantum information processing and precise sensing. A nanophotonic waveguide is a promising platform for realizing an atom-light interface that reaches the strong coupling regime. We study the dispersive response theory of the nanowaveguide system as the means to create an entangling atom-light interface, with applications to quantum non-demolition (QND) measurement and spin squeezing.

We calculate the dyadic Green’s function, which determines the scattering of light by atoms in the presence of a nanowaveguide, and thus the phase shift and polarization rotation induced on the guided light. The Green’s function is related to the full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. Using the Green’s tensors, we calculate the modified spontaneous emission rates for classical dipoles and quantum alkali atoms.

We model QND measurement and spin squeezing using first-principles stochastic master equations. Based on the birefringence effect, we propose a spin squeezing protocol for the spins encoded in the clock transition of cesium-133. We generalize the concept of cooperativity, which is determined by the ratio between the measurement strength and the decoherence rate in the context of the dispersive waveguide interface. By maximizing the cooperativity per atom, we find the optimal choice of quantization axis that defines the clock states. With this, we predict a peak squeezing of 4.7 dB with 2500 atoms trapped along a realistic nanofiber.

To enhance the squeezing and for applications in magnetometry, we propose a protocol based on the Faraday effect for a nanofiber and a square waveguide. Counterintuitively, by placing the atoms at an azimuthal position where the guided probe mode has the lowest intensity, we increase the cooperativity. This arises because the measurement strength depends on the interference between the probe and scattered light into an orthogonal mode, while the decoherence rate depends on the local intensity of the probe. We find 6.3 dB and 13 dB of peak squeezing for the nanofiber and the square waveguide, respectively, with 2500 atoms.