Orbital excitation blockade and algorithmic cooling in quantum gases

Article metrics



Interaction blockade occurs when strong interactions in a confined, few-body system prevent a particle from occupying an otherwise accessible quantum state. Blockade phenomena reveal the underlying granular nature of quantum systems and allow for the detection and manipulation of the constituent particles, be they electrons1, spins2, atoms3,4,5 or photons6. Applications include single-electron transistors based on electronic Coulomb blockade7 and quantum logic gates in Rydberg atoms8,9. Here we report a form of interaction blockade that occurs when transferring ultracold atoms between orbitals in an optical lattice. We call this orbital excitation blockade (OEB). In this system, atoms at the same lattice site undergo coherent collisions described by a contact interaction whose strength depends strongly on the orbital wavefunctions of the atoms. We induce coherent orbital excitations by modulating the lattice depth, and observe staircase-like excitation behaviour as we cross the interaction-split resonances by tuning the modulation frequency. As an application of OEB, we demonstrate algorithmic cooling10,11 of quantum gases: a sequence of reversible OEB-based quantum operations isolates the entropy in one part of the system and then an irreversible step removes the entropy from the gas. This technique may make it possible to cool quantum gases to have the ultralow entropies required for quantum simulation12,13 of strongly correlated electron systems. In addition, the close analogy between OEB and dipole blockade in Rydberg atoms provides a plan for the implementation of two-quantum-bit gates14 in a quantum computing architecture with natural scalability.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Orbital excitation blockade mechanism in an optical lattice.
Figure 2: Time-, frequency- and site-resolved coherent transfer of atoms between orbitals in a Mott insulator.
Figure 3: Algorithmic cooling in an optical lattice.
Figure 4: Experimental realization of algorithmic cooling.


  1. 1

    Grabert, H., Devoret, M. H., eds. Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures 21–137 (Springer, 1992)

  2. 2

    Ono, K., Austing, D. G., Tokura, Y. & Tarucha, S. Current rectification by Pauli exclusion in a weakly coupled double quantum dot system. Science 297, 1313–1317 (2002)

  3. 3

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

  4. 4

    Urban, E. et al. Observation of Rydberg blockade between two atoms. Nature Phys. 5, 110–114 (2009)

  5. 5

    Gaëtan, A. et al. Observation of collective excitation of two individual atoms in the Rydberg blockade regime. Nature Phys. 5, 115–118 (2009)

  6. 6

    Birnbaum, K. M. et al. Photon blockade in an optical cavity with one trapped atom. Nature 436, 87–90 (2005)

  7. 7

    Kastner, M. A. The single-electron transistor. Rev. Mod. Phys. 64, 849–858 (1992)

  8. 8

    Isenhower, L. et al. Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett. 104, 010503 (2010)

  9. 9

    Wilk, T. et al. Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett. 104, 010502 (2010)

  10. 10

    Boykin, P., Mor, T., Roychowdhury, V., Vatan, F. & Vrijen, R. Algorithmic cooling and scalable NMR quantum computers. Proc. Natl Acad. Sci. USA 99, 3388–3393 (2002)

  11. 11

    Baugh, J., Moussa, O., Ryan, C., Nayak, A. & Laflamme, R. Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance. Nature 438, 470–473 (2005)

  12. 12

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

  13. 13

    Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

  14. 14

    Schneider, P. & Saenz, A. Quantum computation with ultracold atoms in a driven optical lattice. Preprint at 〈http://arxiv.org/abs/1103.4950〉 (2011)

  15. 15

    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)

  16. 16

    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)

  17. 17

    Müller, T., Fölling, S., Widera, A. & Bloch, I. State preparation and dynamics of ultracold atoms in higher lattice orbitals. Phys. Rev. Lett. 99, 200405 (2007)

  18. 18

    Will, S. et al. Time-resolved observation of coherent multi-body interactions in quantum phase revivals. Nature 465, 197–201 (2010)

  19. 19

    Wirth, G., Ölschläger, M. & Hemmerich, A. Evidence for orbital superfluidity in the p-band of a bipartite optical square lattice. Nature Phys. 7, 147–153 (2011)

  20. 20

    Soltan-Panahi, P. et al. Multi-component quantum gases in spin-dependent hexagonal lattices. Nature Phys. 7, 434–440 (2011)

  21. 21

    Bakr, W. S. et al. Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329, 547–550 (2010)

  22. 22

    McKay, D. C. & DeMarco, B. Cooling in strongly correlated optical lattices: prospects and challenges. Rep. Prog. Phys. 74, 054401 (2011)

  23. 23

    Medley, P., Weld, D. M., Miyake, H., Pritchard, D. E. & Ketterle, W. Spin gradient demagnetization cooling of ultracold atoms. Phys. Rev. Lett. 106, 195301 (2011)

  24. 24

    Rabl, P., Daley, A. J., Fedichev, P. O., Cirac, J. I. & Zoller, P. Defect-suppressed atomic crystals in an optical lattice. Phys. Rev. Lett. 91, 110403 (2003)

  25. 25

    Popp, M., Garcia-Ripoll, J.-J., Vollbrecht, K. G. & Cirac, J. I. Ground-state cooling of atoms in optical lattices. Phys. Rev. A 74, 013622 (2006)

  26. 26

    Nikolopoulos, G. M. & Petrosyan, D. Atom-number filter in an optical lattice. J. Phys. B 43, 131001 (2010)

  27. 27

    Sherson, J. F. & Mølmer, K. Shaking the entropy out of a lattice: atomic filtering by vibrational excitations. Preprint at 〈http://arxiv.org/abs/1012.1457〉 (2010)

  28. 28

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

  29. 29

    Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319–324 (2011)

  30. 30

    Nelson, K. D., Li, X. & Weiss, D. Imaging single atoms in a three-dimensional array. Nature Phys. 3, 556–560 (2007)

  31. 31

    Weiss, D. S. et al. Another way to approach zero entropy for a finite system of atoms. Phys. Rev. A 70, 040302 (2004)

Download references


We would like to thank S. Fölling for discussions. This work was supported by grants from the US Army Research Office with funding from the DARPA OLE program, an AFOSR MURI programme and by grants from the US NSF.

Author information

All authors contributed to the construction of the experiment, the collection and analysis of the data, and the writing of the manuscript.

Correspondence to Markus Greiner.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Tables

This file contains Supplementary Table 1. (PDF 98 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bakr, W., Preiss, P., Tai, M. et al. Orbital excitation blockade and algorithmic cooling in quantum gases. Nature 480, 500–503 (2011) doi:10.1038/nature10668

Download citation

Further reading


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.