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Bulletin of the American Physical Society

Generalized Gradient Approximation for trapped ultracold atoms in optical lattices

James K. Freericks, Karlis Mikelsons, Hulikal Krishnamurthy

Published Jun 14, 2011• 0 citations
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We demonstrate spin gradient thermometry, a new general method of measuring the temperature of ultracold atoms in optical lattices. We realize a mixture of spins separated by a magnetic field gradient. Measurement of the width of the transition layer between the two spin domains serves as a new method of thermometry which is observed to work over a broad range of lattice depths and temperatures, including in the Mott insulator regime. We demonstrate the thermometry using ultracold rubidium atoms, and suggest that interesting spin physics can be realized in this system. The lowest measured temperature is 1 nK, indicating that the system has reached the quantum regime, where insulating shells are separated by superfluid layers.
We describe a generalization of the local density approximation for ultra-cold atomic systems, which takes into account the gradients of the Green’s functions with respect to position when solving the local Dyson equation and, hence, is sensitive to the local variation of the system within the trap. We use this technique along with dynamical mean-field theory to simulate the Hubbard model data of the Swiss group, which measured the Mott transition in a three-dimensional optical lattice with ultra-cold 40 K atoms. We simulate the same size system as used in experiment, which includes about 8 million lattice sites and up to 300,000 atoms. We describe our computational algorithm in detail, along with modifications needed for the communications to make it work on the Cray XE6. We show strong scaling curves up to approximately 43,500 cores. The code performs remarkably well with perfect linear scaling up to the largest systems we ran on. The results that we present are a comparison of the dynamical mean-field theory results within the generalized gradient approximation to the strong-coupling perturbation theory, which is known to be accurate for high-temperature and large interaction strength. This work is part of the Defense Advanced Research Projects Agency (DARPA) optical lattice emulator program.