Single-site- and single-atom-resolved measurement of correlation functions
- 1.1k Downloads
Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments, whereas in cold gases systems, time-of-flight, and in situ absorption imaging are the standard observation techniques. However, none of these methods allow the in situ detection of spatially resolved correlation functions at the single-particle level. Here, we give a more detailed account of recent advances in the detection of correlation functions using in situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site- and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense.
KeywordsCorrelation Function String Operator Occupation Number Mott Insulator Superfluid Phase
We thank Jacob Sherson for his contribution to the experimental setup. We acknowledge helpful discussions with Ehud Altman, Emanuele Dalla Torre, Matteo Rizzi, Ignacio Cirac, Andrew Daley, Peter Zoller, Steffen Patrick Rath, Wolfgang Simeth and Wilhelm Zwerger. This work was supported by MPG, DFG, EU (NAMEQUAM, AQUTE, Marie Curie Fellowship to M.C.), and JSPS (Postdoctoral Fellowship for Research Abroad to T.F.). LM acknowledges the economical support from Regione Toscana, POR FSE 2007–2013. DMRG simulations were performed using code released within the PwP project (http://www.qti.sns.it).
- 7.M. Randeria, W. Zwerger, M. Zwierlein (eds.), The BCS-BEC Crossover and the Unitary Fermi Gas, vol 836. Lecture Notes in Physics (Springer, 2012)Google Scholar
- 18.S. Sachdev, Quantum Phase Transitions, 2nd edn. (Cambridge University Press, Cambridge, 2011). ISBN 0521514681Google Scholar
- 24.T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schauss, S. Hild, D. Bellem, U. Schollwöck, T. Giamarchi, C. Gross, I. Bloch, S. Kuhr, Quantum dynamics of a mobile spin impurity. Nat. Phys. 9, 235–241 (2013)Google Scholar
- 29.C. Weitenberg, Single-Atom Resolved Imaging and Manipulation in an Atomic Mott Insulator. PhD thesis, Ludwig-Maximilians-Universität München, 2011Google Scholar
- 51.M. Endres, Probing correlated quantum many-body systems at the single-particle level. PhD thesis, Ludwig-Maximilians-Universität München (2013)Google Scholar
- 52.S.P. Rath, W. Simeth, M. Endres, W. Zwerger, Non-local order in Mott insulators, Duality and Wilson Loops. Ann. Phys. 334, 256–271 (2013)Google Scholar
- 60.H. Pichler, L. Bonnes, A.J. Daley, A.M. Läuchli, P. Zoller, Thermal vs. entanglement entropy: a measurement protocol for fermionic atoms with a quantum gas microscope. New J. Phys. 15, 063003 (2013) Google Scholar