In a pioneering experiment1, Hanbury Brown and Twiss (HBT) demonstrated that noise correlations could be used to probe the properties of a (bosonic) particle source through quantum statistics; the effect relies on quantum interference between possible detection paths for two indistinguishable particles. HBT correlations—together with their fermionic counterparts2,3,4—find numerous applications, ranging from quantum optics5 to nuclear and elementary particle physics6. Spatial HBT interferometry has been suggested7 as a means to probe hidden order in strongly correlated phases of ultracold atoms. Here we report such a measurement on the Mott insulator8,9,10 phase of a rubidium Bose gas as it is released from an optical lattice trap. We show that strong periodic quantum correlations exist between density fluctuations in the expanding atom cloud. These spatial correlations reflect the underlying ordering in the lattice, and find a natural interpretation in terms of a multiple-wave HBT interference effect. The method should provide a useful tool for identifying complex quantum phases of ultracold bosonic and fermionic atoms11,12,13,14,15.
This is a preview of subscription content
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Hanbury Brown, R. & Twiss, R. Q. Correlation between photons in two coherent beams of light. Nature 177, 27–29 (1956)
Henny, M. et al. The fermionic Hanbury Brown and Twiss experiment. Science 284, 296–298 (1999)
Oliver, W. D., Kim, J., Liu, R. C. & Yamamoto, Y. Hanbury Brown and Twiss-type experiment with electrons. Science 284, 299–301 (1999)
Kiesel, H., Renz, A. & Hasselbach, F. Observation of Hanbury Brown-Twiss anticorrelations for free electrons. Nature 418, 392–394 (2002)
Bachor, H. A. & Ralph, T. C. A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 2004)
Baym, G. The physics of Hanbury Brown-Twiss intensity interferometry: From stars to nuclear collisions. Act. Phys. Pol. B 29, 1839–1884 (1998)
Altman, E., Demler, E. & Lukin, M. D. Probing many-body states of ultracold atoms via noise correlations. Phys. Rev. A 70, 013603 (2004)
Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998)
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002)
Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004)
Hofstetter, W., Cirac, J. I., Zoller, P., Demler, E. & Lukin, M. D. High temperature superfluidity of fermionic atoms in optical lattices. Phys. Rev. Lett. 89, 220407 (2002)
Kuklov, A. & Svistunov, B. Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice. Phys. Rev. Lett. 90, 100401 (2003)
Duan, L.-M., Demler, E. & Lukin, M. Controlling spin exchange interactions of ultracold atoms in an optical lattice. Phys. Rev. Lett. 91, 090402 (2003)
Lewenstein, M., Santos, L., Baranov, M. A. & Fehrmann, H. Atomic Bose-Fermi mixtures in an optical lattice. Phys. Rev. Lett. 92, 050401 (2004)
Roth, R. & Burnett, K. Quantum phases of atomic boson-fermion mixtures in optical lattices. Phys. Rev. A 69, 021601(R) (2004)
Jurczak, C. et al. Atomic transport in an optical lattice: An investigation through polarization-selective intensity correlations. Phys. Rev. Lett. 77, 1727–1730 (1996)
Yasuda, M. & Shimizu, F. Observation of two-atom correlation of an ultracold neon atomic beam. Phys. Rev. Lett. 77, 3090–3093 (1996)
Kagan, Y., Svistunov, B. V. & Shlyapnikov, G. V. Effect of Bose condensation on inelastic processes in gases. Sov. Phys. JETP Lett. 42, 209–212 (1985)
Burt, E. A. et al. Coherence, correlations, and collisions: What one learns about Bose-Einstein condensates from their decay. Phys. Rev. Lett. 79, 337–340 (1997)
Laburthe-Tolra, B. et al. Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas. Phys. Rev. Lett. 92, 190401 (2004)
Grondalski, J., Alsing, P. M. & Deutsch, I. H. Spatial correlation diagnostics for atoms in optical lattices. Opt. Exp. 5, 249–261 (1999)
Kolovsky, A. R. Interference of cold atoms released from an optical lattice. Europhys. Lett. 68, 330–336 (2004)
Bach, R. & Rzazewski, K. Correlation functions of cold bosons in an optical lattice. Phys. Rev. A 70, 063622 (2004)
Ketterle, W., Durfee, D. S. & Stamper-Kurn, D. M. in Proc. Int. School of Physics “Enrico Fermi” (eds Inguscio, M., Stringari, S. & Wieman, C. E.) 67–176 (IOS Press, Amsterdam, 1999)
Greiner, M., Bloch, I., Mandel, O., Hänsch, T. W. & Esslinger, T. Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Phys. Rev. Lett. 87, 160405 (2001)
Hadzibabic, Z., Stock, S., Battelier, B., Bretin, V. & Dalibard, J. Interference of an array of independent Bose-Einstein condensates. Phys. Rev. Lett. 93, 180403 (2004)
Batrouni, G. G. et al. Mott domains of bosons confined on optical lattices. Phys. Rev. Lett. 89, 117203 (2003)
Naraschewski, M. & Glauber, R. Spatial coherence and density correlations of trapped Bose gases. Phys. Rev. A 59, 4595–4607 (1999)
Greiner, M., Regal, C. A., Stewart, J. T. & Jin, D. S. Probing pair-correlated fermionic atoms through correlations in atom shot noise. Preprint at http://arxiv.org/cond-mat/0502411 (2005).
Sheshadri, K., Krishnamurthy, H. R., Pandit, R. & Ramakrishnan, T. V. Superfluid and insulating phases in an interacting-boson model: mean-field theory and the RPA. Europhys. Lett. 22, 257–263 (1993)
We acknowledge discussions with E. Altman and M. Greiner, as well as financial support by the DFG, AFOSR and the EU under a Marie-Curie Fellowship (F.G.) and a Marie-Curie Excellence grant.
The authors declare that they have no competing financial interests.
About this article
Cite this article
Fölling, S., Gerbier, F., Widera, A. et al. Spatial quantum noise interferometry in expanding ultracold atom clouds. Nature 434, 481–484 (2005). https://doi.org/10.1038/nature03500
Nature Physics (2021)
Nature Communications (2021)
Experimental characterization of two-particle entanglement through position and momentum correlations
Nature Physics (2019)