Excitons and cavity polaritons for ultracold atoms in an optical lattice

Zoubi, Hashem; Ritsch, Helmut

doi:10.1103/physreva.76.013817

Cited by 32 publications

(95 citation statements)

References 18 publications

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“…Similarly we will include atomic spontaneous emission via an effective exciton damping. In figure (4) we plot the corresponding transmission and reflection spectra [4] for an incident field with zero in-plane wave vector, k = 0, where the electric field is parallel to the mirrors. We choose the following numbers for the line widths, the symmetric exciton line width is Γ s = 10 −7 eV , the mirror line widths is γ = 10 −5 eV .…”

Section: Withmentioning

confidence: 99%

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

Zoubi

Ritsch

2008

Europhys. Lett.

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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...

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Section: Withmentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

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

Zoubi

Ritsch

2008

Europhys. Lett.

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“…The similarity between optical lattice ultracold atoms in the Mott insulator phase and molecular crystals encourages us to introduce collective electronic excitations into such a system [14]. The physics is similar to Frenkel excitons in which an electronic excitation can be transferred among atoms at different sites and delocalized in the lattice due to electrostatic interactions, i.e.…”

Section: Introductionmentioning

confidence: 99%

Optical properties of collective excitations for an atomic chain with vacancies

Zoubi

Ritsch

2012

Eur. Phys. J. D

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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.

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“…The lattice is formed by two counterpropagating laser beams entering the cavity from the sides and forming a standing wave in the direction perpendicular to the direction of the cavity mode. The cold atoms loaded on the optical lattice are confined in an array of microscopic trapping potentials, forming a Mottinsulator-like medium with one atom per site [28,29].…”

Section: The Modelmentioning

confidence: 99%

“…As a check on the validity of the limitation to only the k = 1 exciton, we evaluate the formula (13) for f k using experimentally realistic parameters of an optical lattice composed of 85 Rb atoms [27,28]. By taking N = 10 3 sites, the cavity mode volume V = 10 −10 [m 3 ], the atomic transition dipole moment µ = 5 × 10 −29 [Cm] of the hyperfine transition 5 2 S 1/2 − 5 2 P 3/2 in an 85 Rb atom, and the cavity frequency ω c on resonance with the first k = 1 exciton mode that is comparable to the atomic transition frequency of ω a = 2.5 × 10 15 [Hz], we obtain for the coupling strength of the first k = 1 exciton, f 1 / = 1.6×10 8 [Hz], and for the third k = 3 exciton, f 3 / = 5.3 × 10 7 [Hz] that is one order smaller than the k = 1 coupling strength.…”

Section: Experimental Considerationsmentioning

confidence: 99%

First-order coherence versus entanglement in a nanomechanical cavity

Sun

Ficek

2012

Phys. Rev. A

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The coherence and correlation properties of effective bosonic modes of a nano-mechanical cavity composed of an oscillating mirror and containing an optical lattice of regularly trapped atoms are studied. The system is modelled as a three-mode system, two orthogonal polariton modes representing the coupled optical lattice and the cavity mode, and one mechanical mode representing the oscillating mirror. We examine separately the cases of two-mode and three-mode interactions which are distinguished by a suitable tuning of the mechanical mode to the polariton mode frequencies. In the two-mode case, we find that the occurrence of entanglement in the system is highly sensitive to the presence of the first-order coherence between the modes. In particular, the creation of the first-order coherence among the polariton and mechanical modes is achieved at the expense of entanglement between them. In the three-mode case, we show that no entanglement is created between the independent polariton modes if both modes are coupled to the mechanical mode by the parametric interaction. There is no entanglement between the polaritons even if the oscillating mirror is damped by a squeezed vacuum field. The interaction creates the first-order coherence between the polaritons and the degree of coherence can, in principle, be as large as unity. This demonstrates that the oscillating mirror can establish the first-order coherence between two independent thermal modes. A further analysis shows that two independent thermal modes can be made entangled in the system only when one of the modes is coupled to the intermediate mode by a parametric interaction and the other is coupled by a linear-mixing interaction.

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Excitons and cavity polaritons for ultracold atoms in an optical lattice

Cited by 32 publications

References 18 publications

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

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

Optical properties of collective excitations for an atomic chain with vacancies

First-order coherence versus entanglement in a nanomechanical cavity

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