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arXiv:0803.3797 · Physical Review Letters

Condensate Fraction in a 2D Bose Gas Measured across the Mott-Insulator Transition

Ian B. Spielman, William D. Phillips, J. V. Porto

Published Mar 26, 2008• 131 citations
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Abstract

We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty.

DOI
10.1103/physrevlett.100.120402

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Ultracold atoms in optical lattices realize simple condensed matter models. We create an ensemble of ≈60 harmonically trapped 2D Bose-Hubbard systems from a 87Rb Bose-Einstein condensate in an optical lattice and use a magnetic resonance imaging approach to select a few 2D systems for study, thereby eliminating ensemble averaging. Our identification of the transition from superfluid to Mott insulator, as a function of both atom density and lattice depth, is in excellent agreement with a universal state diagram [M. Rigol, Phys. Rev. A 79 053605 (2009)] suitable for our trapped system. In agreement with theory, our data suggest a failure of the local density approximation in the transition region.
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Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We used single atom-single lattice site imaging to investigate the Bose-Hubbard model on a microscopic level. Our technique enables space- and time-resolved characterization of the number statistics across the superfluid-Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low-entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition time scales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low-entropy phases in a lattice.
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