Collective Electronic Excitations For Optical Lattice Ultracold Atoms Within A Cavity

Collective Electronic Excitations for Optical Lattice Ultracold Atoms within a Cavity

Hasem Zoubi
University of Innsbruck

ABSTRACT:

We study solid-state effects, e.g. excitons and cavity-polaritons, in ultracold-atoms loaded on an optical-lattice within a cavity. In the Mott-insulator phase the system can be considered as an artificial crystal, and for the case of one atom per site, an electronic excitation can transfer among the lattice sites due to electrostatic interactions [1]. We investigate the formation of excitons in such a system, similar to Frenkel-excitons in molecular or Noble-atom crystals. Excitons can appear only if the atom excited state line-width is smaller than the exciton band-width. Within a cavity, the electronic excitations and the cavity-photons are coupled, and in the strong coupling regime they form cavity-polaritons. In the Mott-insulator phase with two atoms per site, an on-site single excitation forms entangled symmetric and antisymmetric states [2]. The antisymmetric states are localized, while the symmetric ones can transfer among the lattice sites, and are represented as excitons. Within a cavity the symmetric state excitations and the cavity-photons are coupled, and in the strong coupling regime they form cavity-polaritons. But, the antisymmetric states found to be dark states. For the two cases of one and two atoms per site, we calculate the transmission, reflection, and absorption spectra of an incident external filed. The linear optical spectra show resonances at the polariton frequencies. Cavity polaritons can be used as an observation tool of different kinds of defects in optical lattices [3]. The electronic excitations coupling to vibrational modes of atoms excited to higher Bloch bands in optical lattices is shown to be a significant mechanism for excitation and de-excitation of such vibrational modes [4].

[1] H. Zoubi, and H. Ritsch, {\it Phys. Rev. A}, {\bf 76}, 13817 (2007).

[2] H. Zoubi, and H. Ritsch, {\it Europhys. Lett.} {\bf 82}, 14001 (2008).

[3] H. Zoubi, and H. Ritsch, {\it New J. Phys.} {\bf 10}, 23001 (2008).

[4] H. Zoubi, and H. Ritsch, arXiv:0802.1618 [quant-ph]