Collective Interactions in an Array of Atoms Coupled to a Nanophotonic Waveguide

A lattice of trapped atoms strongly coupled to a one-dimensional nanophotonic waveguide is investigated in exploiting the concept of polariton as the system natural eigenstate. We apply a bosonization procedure, which was presented separately by P. W. Anderson and V. M. Agranovich, to transform excitation spin-half operators into interacting bosons, and which shown here to confirm the hard-core boson model. We derive polariton-polariton kinematic interactions and study them by solving the scattering problem. In using the excitation-photon detuning as a control parameter, we examine the regime in which polaritons behave as weakly interacting photons, and propose the system for realizing superfluidity of photons. We implement the kinematic interaction as a mechanism for nonlinear optical processes that provide an observation tool for the system properties, e.g. the interaction strength produces a blue shift in pump-probe experiments.Comment: 12 pages, 12 figure

Van der Waals Interactions among Alkali Rydberg Atoms with Excitonic States

We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the $|ns\rangle$ and $|np\rangle$ states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients, $C_6^{sp}$, can be defined. We calculate the $C_6$ coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several $\mu m$, we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms.Comment: 9 pages, 9 figure

Collective Enhancement and Suppression of Excitation Decay in Optical Lattices

We calculate radiative lifetimes of collective electronic excitations of atoms in an infinite one dimensional lattice. The translational symmetry along the lattice restricts the photon wave vector component parallel to the lattice to the exciton wave number and thus the possible emission directions. The resulting radiation damping rate and emission pattern of the exciton strongly deviates from independent atom. For some wave numbers and polarizations the excitons superradiantly decay very fast, while other excitons show zero radiation damping rate and form propagating meta-stable excitations. Such states could be directly coupled via tailored evanescent fields from a nearby fiber.Comment: 4 pages, 7 figure

Entangled Photons and Phonons via Inter-Modal Brillouin Scattering

We explore the possibility of the formation of photon-phonon entangled states in nanoscale wires by exploiting stimulated inter-modal Brillouin scattering of co-propagating photons that belong to distinct spatial optical modes. Inside nanowires, the photon-phonon coupling is significantly enhanced owing to radiation pressure. The Stokes and anti-Stokes processes are decoupled as they involve different phonon modes that lead to symmetry breaking, which results from different phase-matching requirements. For the Stokes process photon-phonon pairs are annihilated or created, in the presence of a classical pump field, and for the anti-Stokes process we obtain coherent oscillations between photons and phonons. The appearance of entangled states can extend the use of nanowires, for example, those made of silicon, into quantum information processing involving photons and phonons in a setup that can be easily integrated into an on-chip network.Comment: 9 pages, 11 figure

Van-der-Waals stabilized Rydberg aggregates

Assemblies of Rydberg atoms subject to resonant dipole-dipole interactions form Frenkel excitons. We show that van-der-Waals shifts can significantly modify the exciton wave function, whenever atoms approach each other closely. As a result, attractive excitons and repulsive van-der-Waals interactions can be combined to form stable one-dimensional atom chains, akin to bound aggregates. Here the van-der-Waals shifts ensure a stronger homogeneous delocalisation of a single excitation over the whole chain, enabling it to bind up to six atoms. When brought into unstable configurations, such Rydberg aggregates allow the direct monitoring of their dissociation dynamics.Comment: 6 pages, 6 figure

Collective Light Emission of a Finite Size Atomic Chain

Radiative properties of collective electronic states in a one dimensional atomic chain are investigated. Radiative corrections are included with emphasize put on the effect of the chain size through the dependence on both the number of atoms and the lattice constant. The damping rates of collective states are calculated in considering radiative effects for different values of the lattice constant relative to the atomic transition wave length. Especially the symmetric state damping rate as a function of the number of the atoms is derived. The emission pattern off a finite linear chain is also presented. The results can be adopted for any chain of active material, e.g., a chain of semiconductor quantum dots or organic molecules on a linear matrix.Comment: 10 pages, 20 figure