Far-off resonant optical lattices are the starting point for achieving Bose-Einstein condensation (BEC) using only optical trapping. Our all-optical approach obtains a 2.5x10^{5} BEC every 3 s. When we transfer our BEC back into a FORL, it constitutes an ordered quantum system with a perfection that is hard to achieve in condensed matter physics.

Atoms in 1D and 2D FORLs are 2D and 1D quantum systems. Using a 2D FORL, we have observed a 1D Tonks-Girardeau gas of freely moving bosons (see Science article). We have performed a series of experimental tests of the exact 1D Bose gas theory from the weak to the strong coupling regimes. We have also embarked on a series of experiments with gases out of equilibrium. The first such experiment, the quantum Newton's cradle, is the first to demonstrate the central feature of integrable many-body systems, that they do not approach thermal equilibrium.

S. Li, A. M. Rey, R. Hipolito, A. Reinhard, J. Riou, L. Zundel, S. Manmana and D. S. Weiss, "Self-trapping dynamics in a 2D optical lattice," Phys. Rev. A **88**, 023419 (2013)

A. Reinhard, J. Riou, L. Zundel and D. S. Weiss, "Self trapping in an array of coupled 1D Bose gases," Phys. Rev. Lett. **110**, 033001 (2013)

J. Riou, A. Reinhard, L. Zundel and D. S. Weiss, "Spontaneous-emission-induced transition rates between atomic states in optical lattices," Phys. Rev. A **86**, 033412 (2012)

T. Kinoshita, T. R. Wenger and D. S. Weiss, "A quantum Newton's cradle," Nature **440**, 900 – 903 (2006)

T. Kinoshita, T. R. Wenger and D. S. Weiss, "All-optical Bose-Einstein condensation using a compressible crossed dipole trap," Phys. Rev. A **71**, 011602(R) (2005)

T. Kinoshita, T. R. Wenger and D. S. Weiss, "Local Pair Correlations in 1D Bose gases," Phys. Rev. Lett. **95**, 190406 (2005)

D. S. Weiss, J. Vala, A. V. Thapliyal, S. Myrgren, U. Vazirani and K. B. Whaley, "Another way to approach zero entropy for a finite system of atoms," Phys. Rev. A **70**, 040302(R) (2004)

T. Kinoshita, T. R. Wenger and D. S. Weiss, "Observation of a one-dimensional Tonks-Girardeau gas," Science **305**, 1125 – 1128 (2004)

M. Olshanii and D. S. Weiss, "Producing Bose condensates using optical lattices," Phys. Rev. Lett. **89**, 090404-1 (2002)

*Interacting atoms in optical lattices*, National Science Foundation*Optical Lattice Emulation*, Defense Advanced Research Projects Agency

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.