Mainz 2017 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 25: Quantum Effects: Cavity QED II

Q 25.7: Vortrag

Dienstag, 7. März 2017, 16:00–16:15, P 4

Localization transition in presence of cavity backaction — Katharina Rojan^1,2,3, •Rebecca Kraus¹, Thomás Fogarty^1,4, Hessam Habibian¹, Anna Minguzzi^2,3, and Giovanna Morigi¹ — ¹Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany — ²Université Grenoble-Alpes, LPMMC, BP166, F-38042 Grenoble, France — ³CNRS, LPMMC, BP166, F-38042 Grenoble, France — ⁴Quantum Systems Unit, OIST, Okinawa 904-0495, Japan

We study the localization transition of an atom confined by an external optical lattice in a high-finesse cavity. The atom-cavity coupling yields an effective secondary lattice potential, whose wavelength is incommensurate with the periodicity of the optical lattice. The cavity lattice can induce localization of the atomic wave function analogously to the Aubry-André localization transition. Starting from the master equation for the cavity and the atom we perform a mapping of the system dynamics to a Hubbard Hamiltonian, which can be reduced to the Harper's Hamiltonian in appropriate limits. We evaluate the phase diagram for the atom's ground state and show that the transition between extended and localized wave function is controlled by the strength of the cavity nonlinearity, which determines the size of the localized region and the behavior of the Lyapunov exponent. The Lyapunov exponent, in particular, exhibits resonancelike behavior in correspondence with the optomechanical resonances. We then analyse localization when this setup confines a gas of identical bosonic atoms, which solely interact via the cavity-mediated long-range forces.