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

Optical Properties of Collective Excitations for Finite Chains of Trapped Atoms

Resonant dipole-dipole interaction modifies the energy and decay rate of electronic excitations for finite one dimensional chains of ultracold atoms in an optical lattice. We show that collective excited states of the atomic chain can be divided into dark and bright modes, where a superradiant mode with an enhanced collective effective dipole dominates the optical scattering. Studying the generic case of two chain segments of different length and position exhibits an interaction blockade and spatially structured light emission. Ultimately, an extended system of several interfering segments models a long chain with randomly distributed defects of vacant sites. The corresponding emission pattern provides a sensitive tool to study structural and dynamical properties of the system.Comment: 8 pages, 12 figure

Hybrid Quantum System of a Nanofiber Mode Coupled to Two Chains of Optically Trapped Atoms

A tapered optical nanofiber simultaneously used to trap and optically interface of cold atoms through evanescent fields constitutes a new and well controllable hybrid quantum system. The atoms are trapped in two parallel 1D optical lattices generated by suitable far blue and red detuned evanescent field modes very close to opposite sides of the nanofiber surface. Collective electronic excitations (excitons) of each of the optical lattices are resonantly coupled to the second lattice forming symmetric and antisymmetric common excitons. In contrast to the inverse cube dependence of the individual atomic dipole-dipole interaction, we analytically find an exponentially decaying coupling strength with distance between the lattices. The resulting symmetric (bright) excitons strongly interact with the resonant nanofiber photons to form fiber polaritons, which can be observed through linear optical spectra. For large enough wave vectors the polariton decay rate to free space is strongly reduced, which should render this system ideal for the realization of long range quantum communication between atomic ensembles.Comment: 9 pages, 9 figure

Dark bogolon-excitons in a linear atomic super-lattice

Dark and bright excitons are shown to appear naturally in a linear atomic super-lattice with two atoms per unit cell. In bringing the super-lattice into a strong coupling regime with a one-dimensional nanophotonic waveguide, bright excitons and photons are coherently mixed to form polaritons. Treating excitons as bosons implies a mechanism that forbids two excitations from being at the same atomic state, which is included here through a bosonization procedure with kinematic interactions. Interestingly these interactions couple dark and bright excitons, and which we exploit as a new tool for exciting dark states in a controllable way. We suggest a pump-probe experiment where two polaritons scatter into two dark excitons that found to be correlated and are represented as dark bogolon-excitons. The results can be adapted for any super-lattice of active materials, e.g., of organic molecules.Comment: 11 pages, 7 figure

Bright and dark excitons in an atom--pair filled optical lattice within a cavity

We study electronic excitations of a degenerate gas of atoms trapped in pairs in an optical lattice. Local dipole-dipole interactions produce a long lived antisymmetric and a short lived symmetric superposition of individual atomic excitations as the lowest internal on-site excitations. Due to the much larger dipole moment the symmetric states couple efficiently to neighbouring lattice sites and can be well represented by Frenkel excitons, while the antisymmetric dark states stay localized. Within a cavity only symmetric states couple to cavity photons inducing long range interactions to form polaritons. We calculate their dispersion curves as well as cavity transmission and reflection spectra to observe them. For a lattice with aspherical sites bright and dark states get mixed and their relative excitation energies depend on photon polarizations. The system should allow to study new types of solid state phenomena in atom filled optical lattices

Exciton-Polariton scattering for defect detection in cold atom Optical Lattices

We study the effect of defects in the Mott insulator phase of ultracold atoms in an optical lattice on the dynamics of resonant excitations. Defects, which can either be empty sites in a Mott insulator state with one atom per site or a singly occupied site for a filling factor two, change the dynamics of Frenkel excitons and cavity polaritons. While the vacancies in first case behave like hard sphere scatters for excitons, singly occupied sites in the latter case can lead to attractive or repulsive scattering potentials. We suggest cavity polaritons as observation tool of such defects, and show how the scattering can be controlled in changing the exciton-photon detuning. In the case of asymmetric optical lattice sites we present how the scattering effective potential can be detuned by the cavity photon polarization direction, with the possibility of a crossover from a repulsive into an attractive potential.Comment: 9 pages, 10 figure

Collective Electronic Excitation Coupling between Planar Optical Lattices using Ewald's Method

Using Ewald's summation method we investigate collective electronic excitations (excitons) of ultracold atoms in parallel planar optical lattices including long range interactions. The exciton dispersion relation can then be suitably rewritten and efficiently calculated for long range resonance dipole-dipole interactions. Such in-plane excitons resonantly couple for two identical optical lattices, with an energy transfer strength decreasing exponentially with the distance between the lattices. This allows a restriction of the transfer to neighboring planes and gives rise to excitons delocalized between the lattices. In general equivalent results will hold for any planar system containing lattice layers of optically active and dipolar materials.Comment: 6 pages, and 7 figure

Superradiant and Dark Exciton States in an Optical Lattice within a Cavity

We study ultracold atoms in a finite size one-dimensional optical lattice prepared in the Mott insulator phase and commonly coupled to a single cavity mode. Due to resonance dipole-dipole interactions among the atoms, electronic excitations delocalize and form {\it excitons}. These exciton modes are divided into two groups: antisymmetric modes which decouple from the cavity mode forming {\it dark states}, and symmetric modes significantly coupled to the cavity mode called {\it bright states}. In typical setups the lowest and most symmetric exciton is coupled to the cavity photons much stronger than the other bright states and dominates the optical properties response of the atoms ({\it superradiant state}). In the strong coupling regime this superradiant state is coherently mixed with the cavity photon to form a doublet of polariton states with the Rabi splitting.Comment: 4 pages, 11 figure

Visualizing the Quantum Interaction Picture in Phase Space

We illustrate the correspondence between the quantum Interaction Picture-evolution of the state of a quantum system in Hilbert space and a combination of local and global transformations of its Wigner function in phase space. To this aim, we consider the time-evolution of a quantized harmonic oscillator driven by both a linear and a quadratic (in terms of bosonic creation and annihilation operators) potentials and employ the Magnus series to derive the exact form of the time-evolution operator. In this case, the Interaction Picture corresponds to a local transformation of phase space-reference frame into the one that is co-moving with the Wigner function.Comment: Submitted to New Journal of Physic

Structural Insights from Recent CB1 X-Ray Crystal Structures

Over the past 2 years, X-ray crystal structures of the antagonist- and agonist-bound CB1 receptor have been reported. Such structures are expected to accelerate progress in the understanding of CB1 and should provide an exceptional starting point for structure-based drug discovery. This chapter examines the consistency of these X-ray structures with the CB1 experimental literature, including mutation, NMR and covalent labeling studies. These comparisons reveal discrepancies between this literature and the TMH1-2-3 region of each CB1 crystal structure. The chapter also examines crystal packing issues with each X-ray structure and shows that the discrepancies with the experimental literature can be attributed to crystal packing problems that force the N-terminus deep in the binding pocket of the two inactive state structures and force TMH2 to bend at G2.53/S2.54 and invade the binding pocket in the activated state structure. Revision is advisable before these structures are used for structure-based drug discovery