Article | Published:

Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms

Nature volume 415, pages 3944 (03 January 2002) | Download Citation

Subjects

Abstract

For a system at a temperature of absolute zero, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. Here we observe such a quantum phase transition in a Bose–Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential depth of the lattice is increased, a transition is observed from a superfluid to a Mott insulator phase. In the superfluid phase, each atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice; this phase is characterized by a gap in the excitation spectrum. We can induce reversible changes between the two ground states of the system.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    , , & Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989).

  2. 2.

    , , , & Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998).

  3. 3.

    Bose-Einstein condensation and superfluidity in trapped atomic gases. C.R. Acad. Sci. 4, 381–397 (2001).

  4. 4.

    Quantum Phase Transitions (Cambridge Univ. Press, Cambridge, 2001).

  5. 5.

    , , & Superfluid and insulating phases in an interacting-boson model: Mean-field theory and the RPA. Europhys. Lett. 22, 257–263 (1993).

  6. 6.

    & Phase diagram of the Bose Hubbard model. Europhys. Lett. 26, 545–550 (1995).

  7. 7.

    , & Quantum phases in an optical lattice. Phys. Rev. A 63, 053601-1–053601-12 (2001).

  8. 8.

    & Dynamics and thermodynamics of the Bose-Hubbard model. Phys. Rev. B 59, 12184–12187 (1999).

  9. 9.

    , , & Global phase coherence in two-dimensional granular superconductors. Phys. Rev. Lett. 56, 378–381 (1986).

  10. 10.

    , & Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180–2183 (1989).

  11. 11.

    & Quantum fluctuations in chains of Josephson junctions. Phys. Rev. B 30, 1138–1147 (1984).

  12. 12.

    , , , & Charging effects and quantum coherence in regular Josephson junction arrays. Phys. Rev. Lett. 63, 326–329 (1989).

  13. 13.

    Global and local phase coherence in dissipative Josephson-junction arrays. Europhys. Lett. 9, 421–426 (1989).

  14. 14.

    , , , & Field-induced superconductor-to-insulator transitions in Josephson-junction arrays. Phys. Rev. Lett. 69, 2971–2974 (1992).

  15. 15.

    & One-dimensional Mott insulator formed by quantum vortices in Josephson junction arrays. Phys. Rev. Lett. 76, 4947–4950 (1996).

  16. 16.

    , & Length-scale dependence of the superconductor-to-insulator quantum phase transition in one dimension. Phys. Rev. Lett. 81, 204–207 (1998).

  17. 17.

    , , , & Squeezed states in a Bose-Einstein condensate. Science 291, 2386–2389 (2001).

  18. 18.

    , , & Magnetic transport of trapped cold atoms over a large distance. Phys. Rev. A 63, 031401-1–031401-4 (2001).

  19. 19.

    , , , & Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Phys. Rev. Lett. 87, 160405-1–160405-4 (2001).

  20. 20.

    , & Optical dipole traps for neutral atoms. Adv. At. Mol. Opt. Phys. 42, 95–170 (2000).

  21. 21.

    , , , & Adiabatic cooling of cesium to 700 nK in an optical lattice. Phys. Rev. Lett. 74, 1542–1545 (1995).

  22. 22.

    , , & Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463–512 (1999).

  23. 23.

    et al. Observation of Feshbach resonances in a Bose–Einstein condensate. Nature 392, 151–154 (1998).

  24. 24.

    et al. Dynamics of collapsing and exploding Bose–Einstein condensates. Nature 412, 295–299 (2001).

  25. 25.

    & Heisenberg-limited spectroscopy with degenerate Bose-Einstein gases. Phys. Rev. A 56, R1083–R1086 (1997).

  26. 26.

    , , , & Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975–1978 (1999).

Download references

Acknowledgements

We thank W. Zwerger, H. Monien, I. Cirac, K. Burnett and Yu. Kagan for discussions. This work was supported by the DFG, and by the EU under the QUEST programme.

Author information

Affiliations

  1. *Sektion Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4/III, D-80799 Munich, Germany, and Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany

    • Markus Greiner
    • , Olaf Mandel
    • , Theodor W. Hänsch
    •  & Immanuel Bloch
  2. †Quantenelektronik, ETH Zürich, 8093 Zurich, Switzerland

    • Tilman Esslinger

Authors

  1. Search for Markus Greiner in:

  2. Search for Olaf Mandel in:

  3. Search for Tilman Esslinger in:

  4. Search for Theodor W. Hänsch in:

  5. Search for Immanuel Bloch in:

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Immanuel Bloch.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/415039a

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.