Abstract
Ultracold atomic gases in optical lattices have proven to be a controllable, tunable and clean implementation of strongly interacting quantum many-body systems. An essential prospect for such quantum simulators is their ability to map out the phase diagram of fundamental many-body model Hamiltonians. However, the results need to be validated first for representative benchmark problems through state-of-the-art numerical methods of quantum many-body theory. Here we present the first ab initio comparison between experiments and quantum Monte Carlo simulations for strongly interacting Bose gases on a lattice for large systems (up to particles). The comparison enables thermometry for the interacting quantum gas and to experimentally determine the finite-temperature phase diagram for bosonic superfluids in an optical lattice, revealing a suppression of the critical temperature as the transition to the Mott insulator is approached.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Jaksch, D. & Zoller, P. The cold atom Hubbard toolbox. Ann. Phys. 315, 52–79 (2005).
Lewenstein, M. et al. Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007).
Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).
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).
Paredes, B. et al. Tonks–Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004).
Kinoshita, T., R. W., T. & Weiss, D. S. Observation of a one-dimensional Tonks–Girardeau gas. Science 305, 1125–1128 (2004).
Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006).
Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid–insulator transition. Phys. Rev. B 40, 546–570 (1989).
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).
Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, 1999).
Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition form a strongly interacting 1d superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004).
Gerbier, F. et al. Phase coherence of an atomic Mott insulator. Phys. Rev. Lett. 95, 050404 (2005).
Gerbier, F., Fölling, S., Widera, A., Mandel, O. & Bloch, I. Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition. Phys. Rev. Lett. 96, 090401 (2006).
Fölling, S., Widera, A., Müller, T., Gerbier, F. & Bloch, I. Formation of spatial shell structure in the superfluid to Mott insulator transition. Phys. Rev. Lett. 97, 060403 (2006).
Campbell, G. K. et al. Imaging the Mott insulator shells by using atomic clock shifts. Science 313, 649–652 (2006).
Spielman, I. B., Phillips, W. D. & Porto, J. V. Mott-insulator transition in a two-dimensional atomic Bose gas. Phys. Rev. Lett. 98, 080404 (2007).
Mun, J., Campbell, G. K., Marcassa, L. G., Pritchard, D. E. & Ketterle, W. Phase diagram for a Bose–Einstein condensate moving in an optical lattice. Phys. Rev. Lett. 99, 150604 (2007).
Spielman, I. B., Phillips, W. D. & Porto, J. V. Condensate fraction in a 2d Bose gas measured across the Mott-insulator transition. Phys. Rev. Lett. 100, 120402 (2008).
Guarrera, V. et al. Noise correlation spectroscopy of the broken order of a Mott insulating phase. Phys. Rev. Lett. 100, 250403 (2008).
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).
Elstner, N. & Monien, H. Dynamics and thermodynamics of the Bose–Hubbard model. Phys. Rev. B 59, 12184–12187 (1999).
Dickerscheid, D. B. M., van Oosten, D., Denteneer, P. J. H. & Stoof, H. T. C. Ultracold atoms in optical lattices. Phys. Rev. A 68, 043623 (2003).
DeMarco, B., Lannert, C., Vishveshwara, S. & Wei, T-C. Structure and stability of Mott-insulator shells of bosons trapped in an optical lattice. Phys. Rev. A 71, 063601 (2005).
Pupillo, G., Williams, C. J. & Prokof’ev, N. V. Effects of finite temperature on the Mott-insulator state. Phys. Rev. A 73, 013408 (2006).
Blakie, P. B., Rey, A-M. & Bezett, A. Thermodynamics of quantum degenerate gases in optical lattices. Laser Phys. 17, 198–204 (2007).
Capogrosso-Sansone, B., Prokof’ev, N. & Svistunov, B. Phase diagram and thermodynamics of the three-dimensional Bose–Hubbard model. Phys. Rev. B 75, 134302 (2007).
Diener, R. B., Zhou, Q., Zhai, H. & Ho, T-L. Criterion for bosonic superfluidity in an optical lattice. Phys. Rev. Lett. 98, 180404 (2007).
Kato, Y., Zhou, Q., Kawashima, N. & Trivedi, N. Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state. Nature Phys. 4, 617–621 (2008).
Gerbier, F. et al. Expansion of a quantum gas released from an optical lattice. Phys. Rev. Lett. 101, 155303 (2008).
Kollath, C., Schollwöck, U., von Delft, J. & Zwerger, W. Spatial correlations of trapped one-dimensional bosons in an optical lattice. Phys. Rev. A 69, 031601 (2004).
Kashurnikov, V., Prokofiev, N. & Svistunov, B. Revealing the superfluid–Mott-insulator transition in an optical lattice. Phys. Rev. A 66, 031601 (2002).
Muradyan, G. & Anglin, J. R. Finite-temperature coherence of the ideal Bose gas in an optical lattice. Phys. Rev. A 78, 053628 (2008).
McKay, D., White, M. & DeMarco, B. Lattice thermodynamics for ultracold atoms. Phys. Rev. A 79, 063605 (2009).
Rey, A. M., Pupillo, G. & Porto, J. V. The role of interactions, tunneling and harmonic confinement on the adiabatic loading of bosons in an optical lattice. Phys. Rev. A 73, 023608 (2006).
Ho, T-L. & Zhou, Q. Intrinsic heating and cooling in adiabatic processes for bosons in optical lattices. Phys. Rev. Lett. 99, 120404 (2007).
Gerbier, F. Boson Mott insulators at finite temperatures. Phys. Rev. Lett. 99, 120405 (2007).
Pollet, L., Kollath, C., Houcke, K. V. & Troyer, M. Temperature changes when adiabatically ramping up an optical lattice. New J. Phys. 10, 065001 (2008).
Zhou, Q., Kato, Y., Kawashima, N. & Trivedi, N. Direct mapping of the finite temperature phase diagram of strongly correlated quantum models. Phys. Rev. Lett. 103, 085701 (2009).
Gericke, T. et al. Adiabatic loading of a Bose–Einstein condensate in a 3d optical lattice. J. Mod. Opt. 54, 735–743 (2007).
Prokof’ev, N. V., Svistunov, B. V. & Tupitsyn, I. Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems. Sov. Phys. JETP 87, 310–321 (1998).
Pollet, L., Houcke, K. V. & Rombouts, S. M. A. Engineering local optimality in quantum Monte Carlo algorithms. J. Comput. Phys. 225, 2249–2266 (2007).
Fölling, S. et al. Spatial quantum noise interferometry in expanding ultracold atom clouds. Nature 434, 481–484 (2005).
Leggett, A. J. Superfluidity. Rev. Mod. Phys. 71, S318–S323 (1999).
Gerbier, F. et al. Critical temperature of a trapped, weakly interacting Bose gas. Phys. Rev. Lett. 92, 030405 (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, 1999).
Acknowledgements
We would like to thank B. Capogrosso-Sansone, P. N. Ma, F. C. Zhang, S. Fölling, H. Moritz, T. Esslinger and J. Dalibard for stimulating discussions. This work was supported by the DFG, the SNF, the EU (IP SCALA), DARPA (OLE program) and AFOSR. The simulations were run on the Brutus cluster at the ETH in Zürich.
Author information
Authors and Affiliations
Contributions
S.T. and U.S. carried out the experiments and L.P., B.S., M.T. and N.V.P. performed the numerical simulations. S.T., L.P., F.G., N.V.P., B.S. and M.T. were involved in the analysis of the data. All authors conceived the research, discussed the results and wrote the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary Information (PDF 415 kb)
Rights and permissions
About this article
Cite this article
Trotzky, S., Pollet, L., Gerbier, F. et al. Suppression of the critical temperature for superfluidity near the Mott transition. Nature Phys 6, 998–1004 (2010). https://doi.org/10.1038/nphys1799
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphys1799
This article is cited by
-
Multipolar condensates and multipolar Josephson effects
Nature Communications (2024)
-
A cool quantum simulator
Nature Physics (2022)
-
Quantum gas magnifier for sub-lattice-resolved imaging of 3D quantum systems
Nature (2021)
-
Quantum certification and benchmarking
Nature Reviews Physics (2020)
-
Extended Bose-Hubbard Model with Cavity-Mediated Infinite-Range Interactions at Finite Temperatures
Scientific Reports (2020)