Abstract

In this Letter we report the investigation of transport and static properties of a Bose-Einstein condensate in a large-spaced optical lattice. The lattice spacing can be easily tuned starting from few micrometers by adjusting the relative angle of two partially reflective mirrors. We have performed in-situ imaging of the atoms trapped in the potential wells of a 20 µm spaced lattice. For a lattice spacing of 10 µm we have studied the transport properties of the system and the interference pattern after expansion, evidencing quite different results with respect to the physics of BECs in ordinary near-infrared standing wave lattices, owing to the different length and energy scales.

© 2005 Optical Society of America

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References

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  1. B. P. Anderson and M. A. Kasevich, �??Macroscopic Quantum Interference from Atomic Tunnel Arrays,�?? Science 282, 1686�??1689 (1998).
    [CrossRef] [PubMed]
  2. F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, �??Josephson Junction Arrays with Bose-Einstein Condensates,�?? Science 293, 843�??846 (2001).
    [CrossRef] [PubMed]
  3. M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, and I. Bloch, �??Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,�?? Nature 415, 39�??44 (2002).
    [CrossRef] [PubMed]
  4. G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, �??Quantum Logic Gates in Optical Lattices,�?? Phys. Rev. Lett. 82, 1060�??1063 (1999).
    [CrossRef]
  5. D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, �??Entanglement of Atoms via Cold Controlled Collisions,�?? Phys. Rev. Lett. 82, 1975�??1978 (1999).
    [CrossRef]
  6. O. Mandel, M. Greiner, A.Widera, T. Rom, T.W. Hänsch, and I. Bloch, �??Controlled collisions for multi-particle entanglement of optically trapped atoms,�?? Nature 425, 937�??940 (2003).
    [CrossRef] [PubMed]
  7. D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, �??Neutral Atom Quantum Register,�?? Phys. Rev. Lett. 93, 150501 (2004).
    [CrossRef] [PubMed]
  8. R. Scheunemann, F. S. Cataliotti, T. W. Hänsch, and M. Weitz, �??Resolving and addressing atoms in individual sites of a CO2-laser optical lattice,�?? Phys. Rev. A 62, 051801(R) (2000).
    [CrossRef]
  9. R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, �??Micro-optical Realization of Arrays of Selectively Addressable Dipole Traps: A Scalable Configuration for Quantum Computation with Atomic Qubits,�?? Phys. Rev. Lett. 89, 097903 (2002).
    [CrossRef] [PubMed]
  10. O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, �??Bloch Oscillations and Mean-Field Effects of Bose-Einstein Condensates in 1D Optical Lattices�??, Phys. Rev. Lett. 87, 140402 (2001).
    [CrossRef] [PubMed]
  11. S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, �??Patterned loading of a Bose-Einstein condensate into an optical lattice,�?? Phys. Rev. A 67, 051603(R) (2003).
    [CrossRef]
  12. Z. Hadzibabic, S. Stock, B. Battelier, V. Bretin, and J. Dalibard, �??Interference of an Array of Independent Bose-Einstein Condensates,�?? Phys. Rev. Lett. 93, 180403 (2004).
    [CrossRef] [PubMed]
  13. M. Greiner, I. Bloch, O. Mandel, T.W. Hänsch, and T. Esslinger, �??Exploring Phase Coherence in a 2D Lattice of Bose-Einstein Condensates,�?? Phys. Rev. Lett. 87, 160405 (2001).
    [CrossRef] [PubMed]
  14. P. Pedri, L. Pitaevskii, S. Stringari, C. Fort, S. Burger, F. S. Cataliotti, P. Maddaloni, F. Minardi, and M. Inguscio, �??Expansion of a Coherent Array of Bose-Einstein Condensates,�?? Phys. Rev. Lett. 87, 220401 (2001).
    [CrossRef] [PubMed]
  15. W. Zwerger, �??MottHubbard transition of cold atoms in optical lattices,�?? J. Opt. B 5 S9�??S16 (2003).
    [CrossRef]
  16. M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, �??Observation of Interference Between Two Bose Condensates,�?? Science 275, 637�??641 (1997).
    [CrossRef] [PubMed]
  17. J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, �??A Bose-Einstein condensate in a random potential,�?? preprint arXiv:cond-mat/0412167 (2004).

J. Opt. B

W. Zwerger, �??MottHubbard transition of cold atoms in optical lattices,�?? J. Opt. B 5 S9�??S16 (2003).
[CrossRef]

Nature

M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, and I. Bloch, �??Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,�?? Nature 415, 39�??44 (2002).
[CrossRef] [PubMed]

O. Mandel, M. Greiner, A.Widera, T. Rom, T.W. Hänsch, and I. Bloch, �??Controlled collisions for multi-particle entanglement of optically trapped atoms,�?? Nature 425, 937�??940 (2003).
[CrossRef] [PubMed]

Phys. Rev. A

R. Scheunemann, F. S. Cataliotti, T. W. Hänsch, and M. Weitz, �??Resolving and addressing atoms in individual sites of a CO2-laser optical lattice,�?? Phys. Rev. A 62, 051801(R) (2000).
[CrossRef]

S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, �??Patterned loading of a Bose-Einstein condensate into an optical lattice,�?? Phys. Rev. A 67, 051603(R) (2003).
[CrossRef]

Phys. Rev. Lett.

Z. Hadzibabic, S. Stock, B. Battelier, V. Bretin, and J. Dalibard, �??Interference of an Array of Independent Bose-Einstein Condensates,�?? Phys. Rev. Lett. 93, 180403 (2004).
[CrossRef] [PubMed]

M. Greiner, I. Bloch, O. Mandel, T.W. Hänsch, and T. Esslinger, �??Exploring Phase Coherence in a 2D Lattice of Bose-Einstein Condensates,�?? Phys. Rev. Lett. 87, 160405 (2001).
[CrossRef] [PubMed]

P. Pedri, L. Pitaevskii, S. Stringari, C. Fort, S. Burger, F. S. Cataliotti, P. Maddaloni, F. Minardi, and M. Inguscio, �??Expansion of a Coherent Array of Bose-Einstein Condensates,�?? Phys. Rev. Lett. 87, 220401 (2001).
[CrossRef] [PubMed]

R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, G. Birkl, and W. Ertmer, �??Micro-optical Realization of Arrays of Selectively Addressable Dipole Traps: A Scalable Configuration for Quantum Computation with Atomic Qubits,�?? Phys. Rev. Lett. 89, 097903 (2002).
[CrossRef] [PubMed]

O. Morsch, J. H. Müller, M. Cristiani, D. Ciampini, and E. Arimondo, �??Bloch Oscillations and Mean-Field Effects of Bose-Einstein Condensates in 1D Optical Lattices�??, Phys. Rev. Lett. 87, 140402 (2001).
[CrossRef] [PubMed]

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, �??Neutral Atom Quantum Register,�?? Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef] [PubMed]

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, �??Quantum Logic Gates in Optical Lattices,�?? Phys. Rev. Lett. 82, 1060�??1063 (1999).
[CrossRef]

D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, �??Entanglement of Atoms via Cold Controlled Collisions,�?? Phys. Rev. Lett. 82, 1975�??1978 (1999).
[CrossRef]

Science

B. P. Anderson and M. A. Kasevich, �??Macroscopic Quantum Interference from Atomic Tunnel Arrays,�?? Science 282, 1686�??1689 (1998).
[CrossRef] [PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, �??Josephson Junction Arrays with Bose-Einstein Condensates,�?? Science 293, 843�??846 (2001).
[CrossRef] [PubMed]

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, �??Observation of Interference Between Two Bose Condensates,�?? Science 275, 637�??641 (1997).
[CrossRef] [PubMed]

Other

J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, �??A Bose-Einstein condensate in a random potential,�?? preprint arXiv:cond-mat/0412167 (2004).

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Figures (7)

Fig. 1.
Fig. 1.

Optical setup for the production and detection of a large spacing optical lattice. The two beams creating the interference pattern are obtained from the multiple reflections of a laser beam by a pair of partially reflective mirrors placed with a relative angle one in front of the other. The lattice spacing d can be tuned by changing the angle δ between the two partially reflecting mirrors. The vertical axis is orthogonal to the page.

Fig. 2.
Fig. 2.

An optical lattice with d=20 µm spacing. In the top row we show the intensity distribution of the light recorded by the CCD (a) and the corresponding Fourier transform (c). In the bottom row we show the density distribution (b) of the atoms trapped in the lattice sites imaged in situ a few µs after switching off the lattice, together with its Fourier transform (d), showing well resolved peaks in the same position as the ones in (c).

Fig. 3.
Fig. 3.

In situ images of the atoms trapped in the lattice sites (left) and Fourier transform of the density distribution (right) for different lattice spacings from 20 to 80 µm. The different spacings have been obtained by changing the angle δ between the mirrors shown in Fig. 1.

Fig. 4.
Fig. 4.

Expansion from an optical lattice with 10 µm spacing. a) The intensity of the lattice is increased adiabatically from zero to the final value in 100 ms, then after 50 ms the lattice is abruptly switched off together with the harmonic trapping potential. b) Absorption images after 28 ms of expansion (left) and corresponding Fourier transform (right) for different lattice heights V 0. c) Expanded density profile for V 0=4.6 kHz: we observe the clear presence of interference fringes.

Fig. 5.
Fig. 5.

Far-field intensity obtained from the interference of a linear chain of 20 point-like emitters. On the left of each row the diagrams show the particular set of positions and phases of the sources used to calculate, with Eq. (6), the interferograms shown on the right. The three sets refer to: a) uniform phase and uniform spacing; b) random phase and uniform spacing; c) uniform phase and random spacing.

Fig. 6.
Fig. 6.

Dipole oscillations of a harmonically trapped BEC in the presence of an optical lattice with 10 µm spacing. The dotted line is the initial position of the atoms at t=0. The dashed line is the center of the magnetic trap after the excitation of the dipole mode. The black points refer to the oscillation without lattice, the gray points show a damped oscillation in a lattice with height V 0=170 Hz, while the empty circles show the localization in a lattice with height V 0=5 kHz.

Fig. 7.
Fig. 7.

a) Band structure for a quantum particle in a periodic potential with spacing d=10 µm for a lattice height V 0=28ER (solid line) and V 0=0 (dotted line). The width of the graph (50π/d) corresponds to the extension of the first Brillouin zone for a regular lattice with 0.4 µm spacing. b) Zoom of the gray box. The width of this graph is the actual range of momenta spanned by the atoms during the oscillation in the harmonic potential for the trap displacement Δz=32 µm used in the experiment. The thin line represents the extension of the atomic wavepacket in momentum space.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

d = λ 2 sin ( α 2 ) .
I L = I max I min = 4 t 2 ( 1 t ) I 0 ,
d = h t exp m d ,
A ( z ) n e i ( ϕ n + k d n ) ,
d n = D 2 + ( z n z ) 2 D [ 1 + 1 2 ( z n z D ) 2 ] .
A ( z ) 2 n e i ( ϕ n + k 2 D ( z n z ) 2 ) 2 .

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