Transcript Non-Equilibrium Dynamics in Ultracold Interacting Atoms

Non-Equilibrium Dynamics in
Ultracold Interacting Atoms
Simulations of Ultracold Atoms in
Optical Lattices
Sergio Smith (Howard University)
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
Quantum effects
1. Quantized energy levels
• Lowest energy state
2. Wave-particle duality
3. Tunneling
E4
E3
E2
E1
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
α=0.6
• Good qualitative agreement
• Calculated value of J was wrong
• Possibly due to screening effect
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.