Placing an ensemble of 10 6 ultracold atoms in the near field of a superconducting coplanar waveguide resonator (CPWR) with Q ∼ 10 6 one can achieve strong coupling between a single microwave photon in the CPWR and a collective hyperfine qubit state in the ensemble with g eff /2π ∼ 40 kHz larger than the cavity line width of κ/2π ∼ 7 kHz. Integrated on an atomchip such a system constitutes a hybrid quantum device, which also can be used to interconnect solid-state and atomic qubits, to study and control atomic motion via the microwave field, observe microwave super-radiance, build an integrated micro maser or even cool the resonator field via the atoms.PACS numbers: 42.50.Pq, 37.30.+i In the past decade important breakthroughs in implementing quantum information processing were reached in different physical implementations [1], each showing advantages and shortcomings. For quantum information to emerge as a valuable technology, it is mandatory to pool their strengths. Solid-state systems allow fast processing and dense integration; atom or ion based systems are slower but exhibit long qubit coherence times. Ensembles of atoms constitute a quantum memory, it can be read out onto photons [2] which can then be transmitted over long distances [3]. Here we analyze a device to quantum interconnect superconducting solid-state qubits to an atomic quantum memory.The challenge in transferring the state of a solidstate qubit to atoms is bridging the tremendous gap in time scales that govern solid-state and atomic physics devices. This difference can be overcome using a coplanar waveguide resonator (CPWR) [4,5,6], which can be electrically coupled to single superconducting qubits [7,8,9,10,11]. Various ways were proposed to couple to atomic and molecular systems [12,13,14,15,16,17,18]. The small effective mode volume together with the long photon lifetime allow a strong coupling.The superconducting qubit to CPWR coupling has been implemented and studied by several groups [7,8,9,10,11]. In this letter we concentrate on the magnetic coupling of a microwave photon in a CPWR to a collective hyperfine qubit in an ensemble of ultracold atoms. We show below that even though the magnetic coupling strength is much weaker than the optical dipole coupling, one can achieve strong coupling with currently available technology of circuit cavity quantum electro dynamics and ultracold atomic ensembles on an atomchip.As particular qubit example we consider a hyperfine transition in 87 Rb between |F = 2, m F and |F = 1, m F states which frequency of 6.83 GHz being ideally suited for a CPWR. In principle both systems can be integrated in a hybrid device on an single su- perconducting atomchip [19,20]. Besides the transfer of a single photon to the atomic ensemble as a quantum memory and back, such a hybrid quantum system opens up many different other possibilities. For example nondestructive microwave detection of the atomic density will allow to continuously monitor BEC formation or changing operating parameters one can achieve a superrad...

We study the resonant electronic excitation dynamics for ultracold atoms trapped in a deep optical lattice prepared in a Mott insulator state. Excitons in these artificial crystals are similar to Frenkel excitons in Noble atom or molecular crystals. They appear when the atomic excited state line width is smaller than the exciton band width generated by dipole-dipole coupling. When the atoms are placed within a cavity the electronic excitations and the quantized cavity mode get coupled. In the collective strong coupling regime excitations form two branches of cavity polaritons with Rabi splitting larger than the atomic and the cavity line width. To demonstrate their properties we calculate the transmission, reflection, and absorption spectra for an incident weak probe field, which show resonances at the polariton frequencies.Comment: 9 pages, 9 figure

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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.

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.PACS numbers: 71.36.+c, 71.35.Lk A dilute gas of bosonic atoms near T = 0 in an opticallattice has proved an ideal test-system to study important quantum phenomena of solid state physics with well controllable parameters [1,2]. A striking example is a reversible quantum phase transition from the superfluid into the Mott-insulator phase [3] simply by changing the optical potential depth. In the Mott insulator case each optical-lattice site is filled with a fixed number of atoms down to one or two atoms per site. For a deep enough lattice the atoms cannot move and form an artificial crystal. Naturally it is now interesting to study further complex solid state phenomena in this system, e.g. by exploiting the internal atomic level structure, which bears a strong analogy to excitonic dynamics of molecular crystals (Frenkel excitons) as predicted in Ref. [4]. By the help of an optical cavity these excitons get strongly coupled over large distances via photons and form polaritons. In the present paper we investigate a special interesting case of such excitons [5] and cavity polaritons [6] which can appear only for lattice filled with two atoms per site, which is a straight forward to prepare in optical lattices by the help of a Mott insulator state with filling factor 2.Let us start from a degenerate gas of effective two-level atoms trapped in a 2D optical lattice, located within a cavity with a single cavity mode close to resonance with an internal atomic transition. The lattice laser is tuned far off resonance to the atomic excitations and results in light shifts of the ground and excited states with periodicity of half the laser wave length. Here we assume the two optical-lattices for ground and excited states located at the same positions, which can be realized for Alkali or Alkaline atoms. At certain magic laser frequencies the excited state even experiences an equal shift as the ground state [2,7]. We believe that more general lattice configurations might imply new physics, but this goes beyond our aim here. At temperatures close to T = 0, the atomic center of mass mo...