A Bose–Einstein condensate represents the most ‘classical’ form of a matter wave, just as an optical laser emits the most classical form of an electromagnetic wave. Nevertheless, the matter wave field has a quantized structure owing to the granularity of the discrete underlying atoms. Although such a field is usually assumed to be intrinsically stable (apart from incoherent loss processes), this is no longer true when the condensate is in a coherent superposition of different atom number states1,2,3,4,5,6. For example, in a Bose–Einstein condensate confined by a three-dimensional optical lattice, each potential well can be prepared in a coherent superposition of different atom number states, with constant relative phases between neighbouring lattice sites. It is then natural to ask how the individual matter wave fields and their relative phases evolve. Here we use such a set-up to investigate these questions experimentally, observing that the matter wave field of the Bose–Einstein condensate undergoes a periodic series of collapses and revivals; this behaviour is directly demonstrated in the dynamical evolution of the multiple matter wave interference pattern. We attribute the oscillations to the quantized structure of the matter wave field and the collisions between individual atoms.
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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)
Wright, E. M., Wong, T., Collett, M. J., Tan, S. M. & Walls, D. F. Collapses and revivals in the interference between two Bose-Einstein condensates formed in small atomic samples. Phys. Rev. A 56, 591–602 (1997)
Imamoglu, A., Lewenstein, M. & You, L. Inhibition of coherence in trapped Bose-Einstein condensates. Phys. Rev. Lett. 78, 2511–2514 (1997)
Castin, Y. & Dalibard, J. Relative phase of two Bose-Einstein condensates. Phys. Rev. A 55, 4330–4337 (1997)
Dunningham, J. A., Collett, M. J. & Walls, D. F. Quantum state of a trapped Bose-Einstein condensate. Phys. Lett. A 245, 49–54 (1998)
Zhang, W. & Walls, D. F. Bosonic-degeneracy-induced quantum correlation in a nonlinear atomic beam splitter. Phys. Rev. A 52, 4696–4703 (1995)
Walls, D. F. & Milburn, G. J. Quantum Optics (Springer, Berlin, 1994)
Milburn, G. J. & Holmes, C. A. Dissipative quantum and classical Liouville mechanics of the anharmonic oscillator. Phys. Rev. Lett. 56, 2237–2240 (1986)
Daniel, D. J. & Milburn, G. J. Destruction of quantum coherence in a nonlinear oscillator via attenuation and amplification. Phys. Rev. A 39, 4628–4640 (1989)
Orzel, C., Tuchman, A. K., Fenselau, M. L., Yasuda, M. & Kasevich, M. A. Squeezed states in a Bose-Einstein condensate. Science 291, 2386–2389 (2001)
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)
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)
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, 160405-1–160405-4 (2001)
Greiner, M., Bloch, I., Hänsch, T. W. & Esslinger, T. Magnetic transport of trapped cold atoms over a large distance. Phys. Rev. A 63, 031401-1–031401-4 (2001)
Cataliotti, F. S. et al. Josephson junction arrays with Bose-Einstein condensates. Science 293, 843–846 (2001)
Rokhsar, D. S. & Kotliar, B. G. Gutzwiller projection for bosons. Phys. Rev. B 44, 10328–10332 (1991)
Jaksch, D., Briegel, H. J., Cirac, J. I., Gardiner, C. W. & Zoller, P. Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975–1978 (1999)
Briegel, H. J., Calarco, T., Jaksch, D., Cirac, J. I. & Zoller, P. Quantum computing with neutral atoms. J. Mod. Opt. 47, 415–451 (2000)
Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001)
Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001)
We thank W. Zwerger, T. Esslinger, A. Görlitz, H. Briegel, E. Wright and I. Cirac for discussions, and A. Altmeyer for help in the final stages of the experiment. This work was supported by the DFG.
The authors declare that they have no competing financial interests.
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Greiner, M., Mandel, O., Hänsch, T. et al. Collapse and revival of the matter wave field of a Bose–Einstein condensate. Nature 419, 51–54 (2002) doi:10.1038/nature00968
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