# Heidelberg 2015 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 15: Poster: Quantum Optics and Photonics I

### Q 15.24: Poster

### Montag, 23. März 2015, 17:00–19:00, C/Foyer

**Theoretical study of the Bose-Hubbard model in the presence of cavity-mediated long-range interactions** — •Nishant Dogra^{1}, Ferdinand Brennecke^{2}, Rafael Mottl^{1}, Lorenz Hruby^{1}, Renate Landig^{1}, Sebastian Huber^{3}, Tobias Donner^{1}, and Tilman Esslinger^{1} — ^{1}HPF D4, Quantum Optics Group, Institute for Quantum Electronics, ETH Zurich,Otto-Stern-Weg-1,Zurich-8093 — ^{2}Physikalisches Institut, Universität Bonn, Wegelerstrasse 8, Bonn-53115 — ^{3}HIT K 23.4, Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, Zurich-8093

The Bose-Hubbard model has been a paramount example of quantum simulation of many-body systems. It is realized by loading a quantum gas in a 3D optical lattice. This system undergoes a phase transition from superfluid to the Mott-insulator phase due to the competition between the kinetic energy and the short-range interactions. We study the effect of long-range interactions on this system generated by strongly coupling the quantum gas to a high finesse cavity and pumping it with a transverse laser field. This system can be mapped to an extended Bose-Hubbard model. In the limit where the classical lattice is commensurate with the cavity generated dynamical lattice, we calculate the phase diagram of this system using different mean-field approaches. We find that the cavity-mediated long-range interactions give rise to additional phases: charge density wave insulator and supersolid phase. We also calculate the excitation spectrum of these phases and relate it to the nature of the transition between them. We further briefly discuss the status of the experimental implementation of this scheme.