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 onedimensional 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.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 onedimensional 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.

Feb 18, 20150 citations

Revealing the dark side of a bright exciton–polariton condensate

Jean‐Michel Ménard, C. Poellmann, M. Porer +6 more

Condensation of bosons causes spectacular phenomena such as superfluidity or superconductivity. Understanding the nature of the condensed particles is crucial for active control of such quantum phases. Fascinating possibilities emerge from condensates of light–matter-coupled excitations, such as exciton–polaritons, photons hybridized with hydrogen-like bound electron–hole pairs. So far, only the photon component has been resolved, while even the mere existence of excitons in the condensed regime has been challenged. Here we trace the matter component of polariton condensates by monitoring intra-excitonic terahertz transitions. We study how a reservoir of optically dark excitons forms and feeds the degenerate state. Unlike atomic gases, the atom-like transition in excitons is dramatically renormalized on macroscopic ground state population. Our results establish fundamental differences between polariton condensation and photon lasing and open possibilities for coherent control of condensates. Exciton–polaritons are bosonic quasi-particles resulting from strong coupling of excitons and photons but so far only their photon component had been resolved. Here, Menard et al. monitor the intra-excitonic transitions and study how a reservoir of optically dark excitons forms and feeds the degenerate state.Condensation of bosons causes spectacular phenomena such as superfluidity or superconductivity. Understanding the nature of the condensed particles is crucial for active control of such quantum phases. Fascinating possibilities emerge from condensates of light–matter-coupled excitations, such as exciton–polaritons, photons hybridized with hydrogen-like bound electron–hole pairs. So far, only the photon component has been resolved, while even the mere existence of excitons in the condensed regime has been challenged. Here we trace the matter component of polariton condensates by monitoring intra-excitonic terahertz transitions. We study how a reservoir of optically dark excitons forms and feeds the degenerate state. Unlike atomic gases, the atom-like transition in excitons is dramatically renormalized on macroscopic ground state population. Our results establish fundamental differences between polariton condensation and photon lasing and open possibilities for coherent control of condensates. Exciton–polaritons are bosonic quasi-particles resulting from strong coupling of excitons and photons but so far only their photon component had been resolved. Here, Menard et al. monitor the intra-excitonic transitions and study how a reservoir of optically dark excitons forms and feeds the degenerate state.

Nature CommunicationsAug 13, 201458 citations

Superradiant and dark exciton states in an optical lattice within a cavity

Hashem Zoubi, Helmut Ritsch

We study ultracold atoms trapped in a one-dimensional optical lattice prepared in a Mott insulator state of finite extend and collectively coupled to a single cavity mode. Due to resonant dipole-dipole interactions among the atoms, electronic excitations get delocalized and form excitons . These excitons can be explicitly calculated and divided into two groups: antisymmetric modes which decouple from the cavity mode called dark excitons , and symmetric modes coupled to the cavity mode called bright excitons . In a typical geometry the most uniform exciton is coupled to the cavity photons much stronger than other symmetric bright states and dominates the optical response of the atoms ( superradiant state ). In the strong coupling regime this superradiant state mixes with a cavity photon to form a doublet of polariton states, and the other excitons play only a minor role in the dynamics. We analytically calculate the corresponding collective Rabi splitting including the nearest-neighbor dipole-dipole induced excitonic shifts, which strongly depend on the polarization of the cavity mode with respect to the lattice orientation.We study ultracold atoms trapped in a one-dimensional optical lattice prepared in a Mott insulator state of finite extend and collectively coupled to a single cavity mode. Due to resonant dipole-dipole interactions among the atoms, electronic excitations get delocalized and form excitons . These excitons can be explicitly calculated and divided into two groups: antisymmetric modes which decouple from the cavity mode called dark excitons , and symmetric modes coupled to the cavity mode called bright excitons . In a typical geometry the most uniform exciton is coupled to the cavity photons much stronger than other symmetric bright states and dominates the optical response of the atoms ( superradiant state ). In the strong coupling regime this superradiant state mixes with a cavity photon to form a doublet of polariton states, and the other excitons play only a minor role in the dynamics. We analytically calculate the corresponding collective Rabi splitting including the nearest-neighbor dipole-dipole induced excitonic shifts, which strongly depend on the polarization of the cavity mode with respect to the lattice orientation.

arXiv:0905.0601Europhysics Letters (EPL)Jul 1, 200916 citations

Collective interactions in an array of atoms coupled to a nanophotonic waveguide

Hashem Zoubi

A lattice of trapped atoms strongly coupled to a one-dimensional nanophotonic waveguide is investigated in exploiting polaritons as natural collective eigenstates. We derive polariton-polariton kinematic interactions by applying a bosonization procedure to transform excitation spin- $\frac{1}{2}$ operators into interacting bosons. In solving the scattering problem we extract the effective potential, which is shown to be modulated by using the excitation-photon detuning as a control parameter. We examine the regime in which polaritons behave as a dilute degenerate boson gas and in the limit where polaritons can be treated as weakly interacting photons we 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.A lattice of trapped atoms strongly coupled to a one-dimensional nanophotonic waveguide is investigated in exploiting polaritons as natural collective eigenstates. We derive polariton-polariton kinematic interactions by applying a bosonization procedure to transform excitation spin-$\frac{1}{2}$ operators into interacting bosons. In solving the scattering problem we extract the effective potential, which is shown to be modulated by using the excitation-photon detuning as a control parameter. We examine the regime in which polaritons behave as a dilute degenerate boson gas and in the limit where polaritons can be treated as weakly interacting photons we 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.

arXiv:1310.6241Physical Review AApr 18, 201417 citations

Excitons and Cavity Polaritons for Optical Lattice Ultracold Atoms

Zoubi, H., Ritsch, H.

Ultracold atoms uniformly filling an optical lattice can be treated like an artificial crystal. An implementation including the atomic occupation of a single excited atomic state can be represented by a two-component Bose-Hubbard model. Its phase diagram exhibits a quantum phase transition from a superfluid to a Mott insulator phase. The dynamics of electronic excitations governed by electrostatic dipole-dipole interactions in the ordered regime can be well described by wave-like collective excitations called excitons. Here we present an extensive study of such excitons for a wide range of geometries and dimensionality. Their lifetimes can vary over many orders of magnitude from metastable propagation to superradiant decay. Particularly strong effects occur in one dimensional atomic chains coupled to tapered optical fibers. For an optical lattice within a cavity the excitons are coupled to cavity photons and the resulting collective cavity QED model can be efficiently formulated in terms of polaritons. Their properties are explicitly calculated for different lattices and they constitute a non-destructive monitoring tool for important system properties. Even the formation of molecules in optical lattices manifests itself in modified polariton properties as e.g. an anisotropic optical spectrum. Partial dissipation of the exciton energy in the lattice leads to heating, which can be microscopically understood through a mechanism transferring atoms into higher Bloch bands via a resonant excitation transfer among neighboring lattice sites. The presence of lattice defects like vacancies in the Mott insulator induces a characteristic scattering of polaritons, which can be optically observed to monitor the lattice integrity. Our models can be applied to simulate and understand corresponding collective phenomena in solid crystals, where many effects are often masked by noise and disorder.Ultracold atoms uniformly filling an optical lattice can be treated like an artificial crystal. An implementation including the atomic occupation of a single excited atomic state can be represented by a two-component Bose-Hubbard model. Its phase diagram exhibits a quantum phase transition from a superfluid to a Mott insulator phase. The dynamics of electronic excitations governed by electrostatic dipole-dipole interactions in the ordered regime can be well described by wave-like collective excitations called excitons. Here we present an extensive study of such excitons for a wide range of geometries and dimensionality. Their lifetimes can vary over many orders of magnitude from metastable propagation to superradiant decay. Particularly strong effects occur in one dimensional atomic chains coupled to tapered optical fibers. For an optical lattice within a cavity the excitons are coupled to cavity photons and the resulting collective cavity QED model can be efficiently formulated in terms of polaritons. Their properties are explicitly calculated for different lattices and they constitute a non-destructive monitoring tool for important system properties. Even the formation of molecules in optical lattices manifests itself in modified polariton properties as e.g. an anisotropic optical spectrum. Partial dissipation of the exciton energy in the lattice leads to heating, which can be microscopically understood through a mechanism transferring atoms into higher Bloch bands via a resonant excitation transfer among neighboring lattice sites. The presence of lattice defects like vacancies in the Mott insulator induces a characteristic scattering of polaritons, which can be optically observed to monitor the lattice integrity. Our models can be applied to simulate and understand corresponding collective phenomena in solid crystals, where many effects are often masked by noise and disorder.

Jan 1, 20138 citations

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

Hashem Zoubi, Helmut Ritsch

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.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.

arXiv:0707.4432Europhysics Letters (EPL)Mar 7, 200824 citations

\frac{1}{2}

operators into interacting bosons. In solving the scattering problem we extract the effective potential, which is shown to be modulated by using the excitation-photon detuning as a control parameter. We examine the regime in which polaritons behave as a dilute degenerate boson gas and in the limit where polaritons can be treated as weakly interacting photons we 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.