Non-Equilibrium Dynamics in Ultracold Interacting Atoms Sergio Smith (Howard University) Simulations of Ultracold Atoms in Optical Lattices

Introduction Ultracold atoms ( <1μK ) Cold enough to be trapped and studied Laser and evaporative cooling Bose-Einstein Condensates (BECs) Magnetic moment Two-level system: spin up and spin down Optical lattice Grid of standing light waves Potential wells at highest intensity locations

E4E4 E3E3 E2E2 E1E1 Quantum effects 1. Quantized energy levels Lowest energy state 2.Wave-particle duality 3.Tunneling

The Experiment Two-dimensional lattice Atoms loaded into wells Two sub-lattices Rubidum-87 atoms Cool evaporatively Become BECs Potential lowered to allow tunneling Measured quantity: Staggered Magnetization Distribution of atoms on sub-lattices

Simulation Wave function Single site ≈ Gaussian Random initial phase Some phase “memory” governed by α. Many-body system Sum of local functions Disregard spatial evolution Discretized Gross-Pitaevskii Equation

Results J →J+δJ U=0.03J O= Experimental Data Good qualitative agreement Calculated value of J was wrong Possibly due to screening effect α=0.6 α=0.8

Relevance and Future Research Optical lattice experiments provide a highly tunable environment to study magnetism in BECs, with relevance to high-temperature superconductors. Future research includes: Fine-tuning J and α to fit experimental results Studying what causes these discrepancies

Acknowledgements Dr. Michael Foss-Feig Staff of Joint Quantum Institute (JQI) and Institute for Research in Electronics and Applied Physics (IRAEP) at the University of Maryland, College park.