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Time-resolved observation of coherent multi-body interactions in quantum phase revivals

Abstract

Interactions lie at the heart of correlated many-body quantum phases1,2,3. Typically, the interactions between microscopic particles are described as two-body interactions. However, it has been shown that higher-order multi-body interactions could give rise to novel quantum phases with intriguing properties. So far, multi-body interactions have been observed as inelastic loss resonances in three- and four-body recombinations of atom–atom and atom–molecule collisions4,5,6. Here we demonstrate the presence of effective multi-body interactions7 in a system of ultracold bosonic atoms in a three-dimensional optical lattice, emerging through virtual transitions of particles from the lowest energy band to higher energy bands. We observe such interactions up to the six-body case in time-resolved traces of quantum phase revivals8,9,10,11, using an atom interferometric technique that allows us to precisely measure the absolute energies of atom number states at a lattice site. In addition, we show that the spectral content of these time traces can reveal the atom number statistics at a lattice site, similar to foundational experiments in cavity quantum electrodynamics that yield the statistics of a cavity photon field12. Our precision measurement of multi-body interaction energies provides crucial input for the comparison of optical-lattice quantum simulators with many-body quantum theory.

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Figure 1: Signature of multi-body interactions in quantum phase revivals.
Figure 2: Multi-orbital quantum phase revivals of atom number superposition states.
Figure 3: Multi-orbital energies and effective multi-body interactions.
Figure 4: Global number statistics on approaching the Mott insulator transition.

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References

  1. Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, 1994)

    Book  Google Scholar 

  2. Jaksch, D. & Zoller, P. The cold atom Hubbard toolbox. Ann. Phys. 315, 52–79 (2005)

    Article  ADS  CAS  Google Scholar 

  3. Lewenstein, M. et al. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007)

    Article  ADS  Google Scholar 

  4. Kraemer, T. et al. Evidence for Efimov quantum states in an ultracold gas of caesium atoms. Nature 440, 315–318 (2006)

    Article  ADS  CAS  Google Scholar 

  5. Knoop, S. et al. Observation of an Efimov-like trimer resonance in ultracold atom–dimer scattering. Nature Phys. 5, 227–230 (2009)

    Article  ADS  CAS  Google Scholar 

  6. Zaccanti, M. et al. Observation of an Efimov spectrum in an atomic system. Nature Phys. 5, 586–591 (2009)

    Article  ADS  CAS  Google Scholar 

  7. Johnson, P. R., Tiesinga, E., Porto, J. V. & Williams, C. J. Effective three-body interactions of neutral bosons in optical lattices. N. J. Phys. 11, 093022 (2009)

    Article  Google Scholar 

  8. Yurke, B. & Stoler, D. Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion. Phys. Rev. Lett. 57, 13–16 (1986)

    Article  ADS  CAS  Google Scholar 

  9. Wright, E. M., Walls, D. F. & Garrison, J. C. Collapses and revivals of Bose-Einstein condensates formed in small atomic samples. Phys. Rev. Lett. 77, 2158–2161 (1996)

    Article  ADS  CAS  Google Scholar 

  10. Imamoglu, A., Lewenstein, M. & You, L. Inhibition of coherence in trapped Bose-Einstein condensates. Phys. Rev. Lett. 78, 2511–2514 (1997)

    Article  ADS  CAS  Google Scholar 

  11. Castin, Y. & Dalibard, J. Relative phase of two Bose-Einstein condensates. Phys. Rev. A 55, 4330–4337 (1997)

    Article  ADS  CAS  Google Scholar 

  12. Brune, M. et al. Quantum Rabi oscillation: a direct test of field quantization in a cavity. Phys. Rev. Lett. 76, 1800–1803 (1996)

    Article  ADS  CAS  Google Scholar 

  13. Glauber, R. J. Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766–2788 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  14. Meekhof, D. M., Monroe, C., King, B. E., Itano, W. M. & Wineland, D. J. Generation of nonclassical motional states of a trapped atom. Phys. Rev. Lett. 76, 1796–1799 (1996)

    Article  ADS  CAS  Google Scholar 

  15. Greiner, M., Mandel, M. O., Hänsch, T. & Bloch, I. Collapse and revival of the matter wave field of a Bose-Einstein condensate. Nature 419, 51–54 (2002)

    Article  ADS  CAS  Google Scholar 

  16. Sebby-Strabley, J. et al. Preparing and probing atomic number states with an atom interferometer. Phys. Rev. Lett. 98, 200405 (2007)

    Article  ADS  CAS  Google Scholar 

  17. Sorensen, A., Duan, L. M., Cirac, J. I. & Zoller, P. Many-particle entanglement with Bose–Einstein condensates. Nature 409, 63–66 (2001)

    Article  ADS  CAS  Google Scholar 

  18. Pezzé, L. & Smerzi, A. Entanglement, nonlinear dynamics, and the Heisenberg limit. Phys. Rev. Lett. 102, 100401 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  19. Estève, J., Gross, C., Weller, A., Giovanazzi, S. & Oberthaler, M. K. Squeezing and entanglement in a Bose–Einstein condensate. Nature 455, 1216–1219 (2008)

    Article  ADS  Google Scholar 

  20. Campbell, G. et al. Imaging the Mott insulator shells by using atomic clock shifts. Science 313, 649–652 (2006)

    Article  ADS  CAS  Google Scholar 

  21. Muryshev, A., Shlyapnikov, G. V., Ertmer, W., Sengstock, K. & Lewenstein, M. Dynamics of dark solitons in elongated Bose-Einstein condensates. Phys. Rev. Lett. 89, 110401 (2002)

    Article  ADS  CAS  Google Scholar 

  22. Mazets, I. E., Schumm, T. & Schmiedmayer, J. Breakdown of integrability in a quasi-1D ultracold bosonic gas. Phys. Rev. Lett. 100, 210403 (2008)

    Article  ADS  CAS  Google Scholar 

  23. Alon, O. E., Streltsov, A. I. & Cederbaum, L. S. Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices. Phys. Rev. Lett. 95, 030405 (2005)

    Article  ADS  Google Scholar 

  24. Lühmann, D.-S., Bongs, K., Sengstock, K. & Pfannkuche, D. Self-trapping of bosons and fermions in optical lattices. Phys. Rev. Lett. 101, 050402 (2008)

    Article  ADS  Google Scholar 

  25. Li, J., Yu, Y., Dudarev, A. M. & Niu, Q. Interaction broadening of Wannier functions and Mott transitions in atomic BEC. N. J. Phys. 8, 154 (2006)

    Article  Google Scholar 

  26. Hazzard, K. R. A. & Mueller, E. J. On-site correlations in optical lattices: band mixing to coupled quantum Hall puddles. Phys. Rev. A 81, 031602 (2010)

    Article  ADS  Google Scholar 

  27. Gerbier, F. et al. Phase coherence of an atomic Mott insulator. Phys. Rev. Lett. 95, 050404 (2005)

    Article  ADS  Google Scholar 

  28. 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)

    Article  ADS  Google Scholar 

  29. Cheinet, P. et al. Counting atoms using interaction blockade in an optical superlattice. Phys. Rev. Lett. 101, 090404 (2008)

    Article  ADS  CAS  Google Scholar 

  30. Fischer, U. R. & Schützhold, R. Tunneling-induced damping of phase coherence revivals in deep optical lattices. Phys. Rev. A 78, 061603 (2008)

    Article  ADS  Google Scholar 

  31. Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Preprint at 〈http://arxiv.org/abs/0812.1496〉 (2009)

  32. Paredes, B., Keilmann, T. & Cirac, J. I. Pfaffian-like ground state for three-body hard-core bosons in one-dimensional lattices. Phys. Rev. A 75, 053611 (2007)

    Article  ADS  Google Scholar 

  33. Capogrosso-Sansone, B., Wessel, S., Büchler, H. P., Zoller, P. & Pupillo, G. Phase diagram of one-dimensional hard-core bosons with three-body interactions. Phys. Rev. B 79, 020503 (2009)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft, the European Union (Integrated Project SCALA), EuroQUAM (L.H.), the US Army Research Office with funding from the Defense Advanced Research Projects Agency (Optical Lattice Emulator programme), the US Air Force Office of Scientific Research, MATCOR (S.W.) and the Gutenberg Akademie (S.W.).

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Contributions

S.W. and T.B. carried out the measurements, S.W. performed the data analysis and D.-S.L. performed the numerical calculations. S.W. and I.B. wrote the manuscript with substantial contributions by all authors.

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Correspondence to Sebastian Will.

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The authors declare no competing financial interests.

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This file contains Supplementary Information and Data 1-4, Supplementary Figures 1-4 with legends and References. (PDF 275 kb)

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Will, S., Best, T., Schneider, U. et al. Time-resolved observation of coherent multi-body interactions in quantum phase revivals. Nature 465, 197–201 (2010). https://doi.org/10.1038/nature09036

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