# Project B1:

Strongly correlated quantum gases in optical lattices (2005-2009)

## Summary

This project focuses on quantum phase transitions of quantum gases in optical lattices. Our aim is the realization and study of new states of matter, ranging from novel Mott-like phases (correlated insulators) up to supersolids, which were predicted long ago, but an unambiguous realization is missing so far. We will control quantum phase transitions for fermionic potassium atoms with Feshbach-tuned, long scattering lengths in an optical lattice. Our effort is based on a close collaboration of a) theoretical atomic physics to determine how to steer the microscopic particle interactions, b) theoretical condensed matter physics for the prediction of possible quantum phase transitions, and c) experimental quantum optics for the physical realization of the propositions. We will study experimentally a strongly correlated system of the fermionic potassium isotope (40K) in a far detuned optical lattice. For fermionic atoms, extremely long scattering lengths can be reached by Feshbach tuning, since detrimental three-body decay processes are suppressed by Pauli-blocking. Initially, we will investigate the Mott phase transition in the previously inaccessible regime of long scattering length in periodic potentials, where a detailed comparison with theoretical predictions is possible. When the scattering length approaches the lattice constant, novel Mott-like phases, like the checkerboard and stripe phase become possible. In a second step, we plan to investigate a possible phase transitions towards the supersolid phase, where diagonal and off-diagonal long range order coexist. We plan to realize such a supersolid using fermions with attractive interactions, where the interplay of a supersolid with fermionic superfluidity will be at the center of our studies. The experiments will be accompanied by a detailed theoretical study of the basic physical mechanisms in Feshbach scattering resonances in a deep periodic lattice, in the presence of a surrounding medium. The simple binary scattering picture in vaccuo will have to be modified as the asymptotic collision trajectories are no longer attainable due to the presence of external trapping potentials. Intermediate interactions with other particles will upgrade the bare two-body scattering amplitude in vaccuo to a genuine many-body R-matrix. Moreover, we will investigate if a molecular bound state, which can be formed dynamically from of atomic pairs, can be utilized in the effort to create the supersolid phase. The experimental realization of a Mott-transition will be closely accompanied with quantum Monte-Carlo simulations, where a detailed examination of observables like the momentum distribution function and compressibility will be contrasted to the experimental results. The question of stability of possible correlated insulators and of a supersolid will be investigated taking into account the trapping potential with extensive simulations analyzing the scaling behavior from few body to many body systems.

## Project leaders

Prof. Dr. Alejandro Muramatsu, Institut für Theoretische Physik III, Universität Stuttgart

Prof. Dr. Reinhold Walser, Institut für Angewandte Physik, TU Darmstadt

Prof. Dr. Martin Weitz, Institut für Angewandte Physik, Universität Bonn

## Refs & Publications

S. Kling, T. Salger, C. Geckeler, G. Ritt, J. Plumhof, and M. Weitz*"Atomic Bose-Einstein condensates in optical lattices with variable spatial symmetry"*

*In: C. Denz, S. Flach und Y. Kivshar (ed.): Nonlinearities in Periodic Structures and Metamaterials (2009)*

T. Salger, G. Ritt, C. Geckeler, S. Kling, and M. Weitz

*"Bloch oscillations of a Bose-Einstein condensate in a subwavelength optical lattice"*

*Phys. Rev. A*

**79**, 011605 (2009)G. Cennini, C. Geckeler, G. Ritt, and M. Weitz

*"Interference of an array of atom lasers"*

*Phys. Rev. A*

**77**, 013613 (2008)T. Salger, C. Geckeler, S. Kling, and M. Weitz

*"Atomic Landau-Zener tunneling in Fourier-synthesized optical lattices"*

*Phys. Rev. Lett.*

**99**, 190405 (2007)M. Grupp, R. Walser, W.P. Schleich, A. Muramatsu, and M. Weitz

*"Resonant Feschbach scattering of fermions in one-dimensional optical lattices"*

*J. Phys. B: At. Mol. Opt. Phys.*

**40**, 2703 (2007)F. Karim Pour, M. Rigol, S. Wessel, and A. Muramatsu

*"Supersolids in confined fermions on one-dimensional optical lattices"*

*Phys. Rev. B*

**75**, 161104(R) (2007)G. Ritt, C. Geckeler, T. Salger, G. Cennini, and M. Weitz

*"Fourier synthesis of optical potentials for atomic quantum gases"*

*Phys. Rev. A*

**74**, 063622 (2006)M. Grupp, G. Nandi, R. Walser, and W. Schleich

*"Collective Feshbach scattering of a superfluid droplet from a mesoscopic two-component Bose-Einstein condensate"*

*Phys. Rev. A*

**73**, 50701 (2006)M. Rigol, S.R. Manmana, A. Muramatsu, R.T. Scalettar, R.R.P. Singh, and S. Wessel

*"Comment on “Novel Superfluidity in a Trapped Gas of Fermi Atoms with Repulsive Interaction Loaded on an Optical Lattice"*

*Phys. Rev. Lett.*

**95**, 218901 (2005)M. Rigol and A. Muramatsu

*"Ground-state properties of hard-core bosons confined on one-dimensional optical lattices"*

*Phys. Rev. A*

**72**, 013604 (2005)