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We study the strong coupling between photons and atoms that can be achievedin an optical nanofiber geometry when the interaction is dispersive. While thePurcell enhancement factor for spontaneous emission into the guided mode doesnot reach the strong-coupling regime for individual atoms, one can obtain highcooperativity for ensembles of a few thousand atoms due to the tightconfinement of the guided modes and constructive interference over the entirechain of trapped atoms. We calculate the dyadic Green's function, whichdetermines the scattering of light by atoms in the presence of the fiber, andthus the phase shift and polarization rotation induced on the guided light bythe trapped atoms. The Green's function is related to a fullHeisenberg-Langevin treatment of the dispersive response of the quantized fieldto tensor polarizable atoms. We apply our formalism to quantum nondemolition(QND) measurement of the atoms via polarimetry. We study shot-noise-limiteddetection of atom number for atoms in a completely mixed spin state and thesqueezing of projection noise for atoms in clock states. Compared withsqueezing of atomic ensembles in free space, we capitalize on unique featuresthat arise in the nanofiber geometry including anisotropy of both the intensityand polarization of the guided modes. We use a first principles stochasticmaster equation to model the squeezing as function of time in the presence ofdecoherence due to optical pumping. We find a peak metrological squeezing of ~5dB is achievable with current technology for ~2500 atoms trapped 180 nm fromthe surface of a nanofiber with radius a=225 nm.

physical review. a/physical review, a

Dispersive response of atoms trapped near the surface of an optical  nanofiber with applications to quantum nondemolition measurement and spin  squeezing