A toolbox for lattice-spin models with polar molecules

Abstract

There is growing interest in states of matter with topological order. These are characterized by highly stable ground states robust to perturbations that preserve the topology, and which support excitations with so-called anyonic statistics. Topologically ordered states can arise in two-dimensional lattice-spin models, which were proposed as the basis for a new class of quantum computation. Here, we show that the relevant hamiltonians for such spin lattice models can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single-valence electron of a heteronuclear molecule. The combination of microwave excitation with dipole–dipole interactions and spin–rotation couplings enables building a complete toolbox for effective two-spin interactions with designable range, spatial anisotropy and coupling strengths significantly larger than relevant decoherence rates. Finally, we illustrate two models: one with an energy gap providing for error-resilient qubit encoding, and another leading to topologically protected quantum memory.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Example anisotropic spin models that can be simulated with polar molecules trapped in optical lattices.
Figure 2: Movre–Pichler potentials for a pair of molecules as a function of their separation r.
Figure 3: Design and verification of noise-protected ground states arising from a simulation of Hspin(I).
Figure 4: Implementation of spin model Hspin(II).

References

  1. 1

    Levin, M. A. & Wen, X. G. String-net condensation: A physical mechanism for topological phases. Phys. Rev. B 71, 045110 (2005).

    ADS  Article  Google Scholar 

  2. 2

    Hermele, M., Fisher, M. P. A. & Balents, L. Pyrochlore photons: The U(1) spin liquid in aS=1/2 three-dimensional frustrated magnet. Phys. Rev. B 69, 064404 (2004).

    ADS  Article  Google Scholar 

  3. 3

    Einarsson, T. Fractional statistics on a torus. Phys. Rev. Lett. 64, 1995–1998 (1990).

    ADS  MathSciNet  Article  Google Scholar 

  4. 4

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

    ADS  Article  Google Scholar 

  5. 5

    Büchler, H. P., Hermele, M., Huber, S. D., Fisher, M. P. A. & Zoller, P. Atomic quantum simulator for lattice gauge theories and ring exchange models. Phys. Rev. Lett. 95, 040402 (2005).

    ADS  Article  Google Scholar 

  6. 6

    Santos, L. et al. Atomic quantum gases in kagomé lattices. Phys. Rev. Lett. 93, 030601 (2004).

    ADS  Article  Google Scholar 

  7. 7

    Special Issue on Ultracold Polar Molecules: Formation and Collisions. Eur. Phys. J. D 31, 149–444 (2004).

  8. 8

    Duoçot, B., Feigel’man, M. V., Ioffe, L. B. & Ioselevich, A. S. Protected qubits and Chern-Simons theories in Josephson junction arrays. Phys. Rev. B 71, 024505 (2005).

    ADS  Article  Google Scholar 

  9. 9

    Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

    ADS  MathSciNet  Article  Google Scholar 

  10. 10

    Dennis, E., Kitaev, A., Landahl, A. & Preskill, J. Topological quantum memory. J. Math. Phys. 43, 4452–4505 (2002).

    ADS  MathSciNet  Article  Google Scholar 

  11. 11

    Duan, L. M., Demler, E. & Lukin, M. D. Controlling spin exchange interactions of ultracold atoms in optical lattices. Phys. Rev. Lett. 91, 090402 (2003).

    ADS  Article  Google Scholar 

  12. 12

    Sage, J. M., Sainis, S., Bergeman, T. & DeMille, D. Optical production of ultracold polar molecules. Phys. Rev. Lett. 94, 203001 (2005).

    ADS  Article  Google Scholar 

  13. 13

    Jaksch, D., Venturi, V., Cirac, J. I., Williams, C. J. & Zoller, P. Creation of a molecular condensate by dynamically melting a Mott insulator. Phys. Rev. Lett. 89, 040402 (2002).

    ADS  Article  Google Scholar 

  14. 14

    Brennen, G. K., Deutsch, I. H. & Williams, C. J. Quantum logic for trapped atoms via molecular hyperfine interactions. Phys. Rev. A 65, 022313 (2002).

    ADS  Article  Google Scholar 

  15. 15

    Friedrich, B. & Herschbach, D. Alignment and trapping of molecules in intense laser fields. Phys. Rev. Lett. 74, 4623–4626 (1995).

    ADS  Article  Google Scholar 

  16. 16

    DeMille, D. Quantum computation with trapped polar molecules. Phys. Rev. Lett. 88, 067901 (2002).

    ADS  Article  Google Scholar 

  17. 17

    Kotochigova, S., Tiesinga, E. & Julienne, P. S. Photoassociative formation of ultracold polar KRb molecules. Eur. Phys. J. D 31, 189–194 (2004).

    ADS  Article  Google Scholar 

  18. 18

    Movre, M. & Pichler, G. Resonant interaction and self-broadening of alkali resonance lines I. Adiabatic potential curves. J. Phys. B 10, 2631–2638 (1977).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

A.M. thanks W. Ernst, and P.Z. thanks T. Calarco, L. Faoro, M. Lukin, and D. Petrov for helpful discussions. This work was supported by the Austrian Science Foundation, the European Union, OLAQUI, SCALA and the Institute for Quantum Information.

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. Micheli.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Micheli, A., Brennen, G. & Zoller, P. A toolbox for lattice-spin models with polar molecules. Nature Phys 2, 341–347 (2006). https://doi.org/10.1038/nphys287

Download citation

Further reading

Search

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing