Probing the Superfluid–to–Mott Insulator Transition at the Single-Atom Level

From Superfluid to Mott Insulator One of the most attractive characteristics of cold atomic gases in optical lattices is their ability to simulate condensed-matter systems. The results of these quantum simulations are usually averaged over the atomic ensemble, or course-grained over several lattice sites. Now, Bakr et al. (p. 547, published online 17 June; see the Perspective by DeMarco) provide a single lattice site view onto the transition of a Bose gas of Rb-87 from the superfluid to the Mott-insulating state. Characteristic concentric shells of uniform number density were observed deep in the Mott insulator regime, and probing the local quantum dynamics revealed unexpectedly short time scales. The low-defect Mott structures identified may provide a starting point for quantum magnetism experiments. Imaging of atoms that were optically trapped in lattice sites reveals local dynamics of a quantum phase transition. 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.

[1]  Thomas Basché,et al.  Single-molecule optical detection, imaging and spectroscopy , 1997 .

[2]  J. Ashby.  References and Notes , 1999 .

[3]  H. Eisaki,et al.  Imaging the granular structure of high-Tc superconductivity in underdoped Bi2Sr2CaCu2O8+δ , 2001, Nature.

[4]  D. Weiss,et al.  Unity Occupation of Sites in a 3D Optical Lattice , 1999 .

[5]  M. Lukin,et al.  Controlling spin exchange interactions of ultracold atoms in optical lattices. , 2002, Physical review letters.

[6]  W. Linden,et al.  Spectral properties of strongly correlated bosons in two-dimensional optical lattices , 2009, 0909.3228.

[7]  Imaging the Mott Insulator Shells by Using Atomic Clock Shifts , 2006, Science.

[8]  Lode Pollet,et al.  Engineering local optimality in quantum Monte Carlo algorithms , 2007, J. Comput. Phys..

[9]  M. Troyer,et al.  Temperature changes when adiabatically ramping up an optical lattice , 2008, 0801.1887.

[10]  Fisher,et al.  Boson localization and the superfluid-insulator transition. , 1989, Physical review. B, Condensed matter.

[11]  Ground-state cooling of atoms in optical lattices (11 pages) , 2006, cond-mat/0603859.

[12]  X. Zhuang,et al.  A single-molecule study of RNA catalysis and folding. , 2000, Science.

[13]  On-site number statistics of ultracold lattice bosons , 2006, cond-mat/0609600.

[14]  I Bloch,et al.  Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices , 2007, Science.

[15]  Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition. , 2005, Physical review letters.

[16]  F. Gerbier.  Boson Mott insulators at finite temperatures. , 2007, Physical review letters.

[17]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[18]  Andrew G. Glen,et al.  APPL , 2001 .

[19]  Boris Svistunov,et al.  “Worm” algorithm in quantum Monte Carlo simulations☆ , 1998 .

[20]  Superfluid to Mott insulator transition in one, two, and three dimensions , 2004, cond-mat/0404338.

[21]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[22]  W. Phillips,et al.  Mott-insulator transition in a two-dimensional atomic Bose gas. , 2007, Physical review letters.

[23]  N. Prokof'ev,et al.  Monte Carlo study of the two-dimensional Bose-Hubbard model , 2007, 0710.2703.

[24]  Mikhail D. Lukin,et al.  Phase diagram of two-component bosons on an optical lattice , 2003 .

[25]  Cheng Chin,et al.  In situ observation of incompressible Mott-insulating domains in ultracold atomic gases , 2009, Nature.

[26]  Markus Greiner,et al.  A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice , 2009, Nature.

[27]  Robert Jördens,et al.  A Mott insulator of fermionic atoms in an optical lattice , 2008, Nature.

[28]  D. Pritchard,et al.  Spin gradient thermometry for ultracold atoms in optical lattices. , 2009, Physical review letters.

[29]  C. Gardiner,et al.  Cold Bosonic Atoms in Optical Lattices , 1998, cond-mat/9805329.

[30]  Sebastian Will,et al.  Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice , 2008, Science.

[31]  Immanuel Bloch,et al.  Collapse and revival of the matter wave field of a Bose–Einstein condensate , 2002, Nature.

[32]  C. Chin,et al.  Slow mass transport and statistical evolution of an atomic gas across the superfluid-Mott-insulator transition. , 2009, Physical review letters.

[33]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.