Abstract

We propose a scheme to probe the non-Abelian statistics of the collective anyonic excitation in Kitaev’s honeycomb model with cold atoms in an optical lattice. The generation of the anyonic excitation can be realized by a simple rotating operation acting on an effective spin-1/2 system, which is encoded in the atomic hyperfine energy levels. The non-Abelian nature of the anyonic excitation is manifested by the braiding of four vortices, which leads to different operations on the subspace of degenerate ground states and thus results in different final states. Here, by introducing an ancilla atom, the effective control over the lattice atoms can be realized and the final different states can also be imprinted on the ancilla and further distinguished by measurement.

© 2013 Optical Society of America

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  1. P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University, 1930).
  2. A. Khare, Fractional Statistics and Quantum Theory (World Scientific, 2005).
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  5. G. Moore and N. Read, “Nonabelians in the fractional quantum Hall effect,” Nucl. Phys. B 360, 362–396 (1991).
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  6. A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303, 2–30 (2003).
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  7. A. Stern, “Non-Abelian states of matter,” Nature 464, 187–193 (2010).
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  8. I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885 (2008).
    [CrossRef]
  9. S. L. Zhu, L.-B. Shao, Z. D. Wang, and L.-M. Duan, “Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid,” Phys. Rev. Lett. 106, 100404 (2011).
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  10. Z.-Y. Xue, “Detecting non-Abelian statistics of Majorana fermions in quantum nanowire networks,” J. Exp. Theor. Phys. Lett. 94, 213 (2011).
    [CrossRef]
  11. S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and Majorana zero modes of a px+ipy superfluid of fermionic cold atoms,” Phys. Rev. Lett. 98, 010506 (2007).
    [CrossRef]
  12. Y.-J. Han, R. Raussendorf, and L.-M. Duan, “Scheme for demonstration of fractional statistics of anyons in an exactly solvable model,” Phys. Rev. Lett. 98, 150404 (2007).
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  13. Z.-Y. Xue, “Simulation of anyonic fractional statistics of Kitaev’s toric model in circuit QED,” Europhys. Lett. 93, 20007 (2011).
    [CrossRef]
  14. M. Aguado, G. K. Brennen, F. Verstraete, and J. I. Cirac, “Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices,” Phys. Rev. Lett. 101, 260501 (2008).
    [CrossRef]
  15. L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
    [CrossRef]
  16. C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma, “Anyonic braiding in optical lattices,” Proc. Natl. Acad. Sci. USA 104, 18415–18420 (2007).
    [CrossRef]
  17. J. Q. You, X.-F. Shi, X. Hu, and F. Nori, “Quantum emulation of a spin system with topologically protected ground states using superconducting quantum circuits,” Phys. Rev. B 81, 014505 (2010).
    [CrossRef]
  18. S. Dusuel, K. P. Schmidt, and J. Vidal, “Creation and manipulation of Anyons in the Kitaev model,” Phys. Rev. Lett. 100, 177204 (2008).
    [CrossRef]
  19. J. Vidal, K. P. Schmidt, and S. Dusuel, “Perturbative approach to an exactly solved problem: Kitaev honeycomb model,” Phys. Rev. B 78, 245121 (2008).
    [CrossRef]
  20. J. Zhang, C. Xie, K. Peng, and P. van Loock, “Anyon statistics with continuous variables,” Phys. Rev. A 78, 052121 (2008).
    [CrossRef]
  21. C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
    [CrossRef]
  22. J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
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  23. A. Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys. (N.Y.) 321, 2–111 (2006).
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  24. L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling spin exchange interactions of ultracold atoms in optical lattice,” Phys. Rev. Lett. 91, 090402 (2003).
    [CrossRef]
  25. L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012).
    [CrossRef]
  26. S.-L. Zhu, B. G. Wang, and L.-M. Duan, “Simulation and detection of Dirac fermions with cold atoms in an optical lattice,” Phys. Rev. Lett. 98, 260402 (2007).
    [CrossRef]
  27. K. L. Lee, B. Grmaud, R. Han, B.-G. Englert, and C. Miniatura, “Ultracold fermions in a graphene-type optical lattice,” Phys. Rev. A 80, 043411 (2009).
    [CrossRef]
  28. 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]
  29. M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
    [CrossRef]
  30. 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]
  31. S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
    [CrossRef]
  32. D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
    [CrossRef]
  33. D. A. Ivanov, “Non-Ablelian statistics of half-quantum vortices in p-wave superconductors,” Phys. Rev. Lett. 86, 268–271 (2001).
    [CrossRef]

2012

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012).
[CrossRef]

2011

S. L. Zhu, L.-B. Shao, Z. D. Wang, and L.-M. Duan, “Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid,” Phys. Rev. Lett. 106, 100404 (2011).
[CrossRef]

Z.-Y. Xue, “Detecting non-Abelian statistics of Majorana fermions in quantum nanowire networks,” J. Exp. Theor. Phys. Lett. 94, 213 (2011).
[CrossRef]

Z.-Y. Xue, “Simulation of anyonic fractional statistics of Kitaev’s toric model in circuit QED,” Europhys. Lett. 93, 20007 (2011).
[CrossRef]

2010

J. Q. You, X.-F. Shi, X. Hu, and F. Nori, “Quantum emulation of a spin system with topologically protected ground states using superconducting quantum circuits,” Phys. Rev. B 81, 014505 (2010).
[CrossRef]

A. Stern, “Non-Abelian states of matter,” Nature 464, 187–193 (2010).
[CrossRef]

2009

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
[CrossRef]

J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
[CrossRef]

K. L. Lee, B. Grmaud, R. Han, B.-G. Englert, and C. Miniatura, “Ultracold fermions in a graphene-type optical lattice,” Phys. Rev. A 80, 043411 (2009).
[CrossRef]

2008

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

S. Dusuel, K. P. Schmidt, and J. Vidal, “Creation and manipulation of Anyons in the Kitaev model,” Phys. Rev. Lett. 100, 177204 (2008).
[CrossRef]

J. Vidal, K. P. Schmidt, and S. Dusuel, “Perturbative approach to an exactly solved problem: Kitaev honeycomb model,” Phys. Rev. B 78, 245121 (2008).
[CrossRef]

J. Zhang, C. Xie, K. Peng, and P. van Loock, “Anyon statistics with continuous variables,” Phys. Rev. A 78, 052121 (2008).
[CrossRef]

M. Aguado, G. K. Brennen, F. Verstraete, and J. I. Cirac, “Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices,” Phys. Rev. Lett. 101, 260501 (2008).
[CrossRef]

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

2007

C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma, “Anyonic braiding in optical lattices,” Proc. Natl. Acad. Sci. USA 104, 18415–18420 (2007).
[CrossRef]

S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and Majorana zero modes of a px+ipy superfluid of fermionic cold atoms,” Phys. Rev. Lett. 98, 010506 (2007).
[CrossRef]

Y.-J. Han, R. Raussendorf, and L.-M. Duan, “Scheme for demonstration of fractional statistics of anyons in an exactly solvable model,” Phys. Rev. Lett. 98, 150404 (2007).
[CrossRef]

S.-L. Zhu, B. G. Wang, and L.-M. Duan, “Simulation and detection of Dirac fermions with cold atoms in an optical lattice,” Phys. Rev. Lett. 98, 260402 (2007).
[CrossRef]

2006

A. Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys. (N.Y.) 321, 2–111 (2006).
[CrossRef]

2004

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef]

2003

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling spin exchange interactions of ultracold atoms in optical lattice,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef]

A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303, 2–30 (2003).
[CrossRef]

2001

D. A. Ivanov, “Non-Ablelian statistics of half-quantum vortices in p-wave superconductors,” Phys. Rev. Lett. 86, 268–271 (2001).
[CrossRef]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[CrossRef]

1999

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]

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]

1991

G. Moore and N. Read, “Nonabelians in the fractional quantum Hall effect,” Nucl. Phys. B 360, 362–396 (1991).
[CrossRef]

1984

B. I. Halperin, “Statistics of quasi-particles and the hierarchy of fractional quantized Hall states,” Phys. Rev. Lett. 52, 1583–1586 (1984).
[CrossRef]

1983

R. B. Laughlin, “Anomalous quantum Hall effect: an incompressible quantum fluid with fractional charged excitation,” Phys. Rev. Lett. 50, 1395–1398 (1983).
[CrossRef]

Aguado, M.

M. Aguado, G. K. Brennen, F. Verstraete, and J. I. Cirac, “Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices,” Phys. Rev. Lett. 101, 260501 (2008).
[CrossRef]

Alt, W.

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Bloch, I.

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

Brennen, G. K.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

M. Aguado, G. K. Brennen, F. Verstraete, and J. I. Cirac, “Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices,” Phys. Rev. Lett. 101, 260501 (2008).
[CrossRef]

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]

Briegel, H.-J.

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]

Caves, C. M.

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]

Chen, Z.-B.

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
[CrossRef]

Cirac, J. I.

M. Aguado, G. K. Brennen, F. Verstraete, and J. I. Cirac, “Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices,” Phys. Rev. Lett. 101, 260501 (2008).
[CrossRef]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[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]

Cote, R.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[CrossRef]

Dalibard, J.

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

Das Sarma, S.

S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and Majorana zero modes of a px+ipy superfluid of fermionic cold atoms,” Phys. Rev. Lett. 98, 010506 (2007).
[CrossRef]

C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma, “Anyonic braiding in optical lattices,” Proc. Natl. Acad. Sci. USA 104, 18415–18420 (2007).
[CrossRef]

Demler, E.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling spin exchange interactions of ultracold atoms in optical lattice,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef]

Deutsch, I. H.

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]

Dirac, P. A. M.

P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University, 1930).

Dotsenko, I.

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef]

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Duan, L. M.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[CrossRef]

Duan, L.-M.

S. L. Zhu, L.-B. Shao, Z. D. Wang, and L.-M. Duan, “Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid,” Phys. Rev. Lett. 106, 100404 (2011).
[CrossRef]

Y.-J. Han, R. Raussendorf, and L.-M. Duan, “Scheme for demonstration of fractional statistics of anyons in an exactly solvable model,” Phys. Rev. Lett. 98, 150404 (2007).
[CrossRef]

S.-L. Zhu, B. G. Wang, and L.-M. Duan, “Simulation and detection of Dirac fermions with cold atoms in an optical lattice,” Phys. Rev. Lett. 98, 260402 (2007).
[CrossRef]

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling spin exchange interactions of ultracold atoms in optical lattice,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef]

Dusuel, S.

S. Dusuel, K. P. Schmidt, and J. Vidal, “Creation and manipulation of Anyons in the Kitaev model,” Phys. Rev. Lett. 100, 177204 (2008).
[CrossRef]

J. Vidal, K. P. Schmidt, and S. Dusuel, “Perturbative approach to an exactly solved problem: Kitaev honeycomb model,” Phys. Rev. B 78, 245121 (2008).
[CrossRef]

Englert, B.-G.

K. L. Lee, B. Grmaud, R. Han, B.-G. Englert, and C. Miniatura, “Ultracold fermions in a graphene-type optical lattice,” Phys. Rev. A 80, 043411 (2009).
[CrossRef]

Esslinger, T.

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012).
[CrossRef]

Fleischhauer, M.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[CrossRef]

Gao, W.-B.

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
[CrossRef]

Gardiner, C. W.

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]

Gomer, V.

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Gorshkov, A. V.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

Greif, D.

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012).
[CrossRef]

Grmaud, B.

K. L. Lee, B. Grmaud, R. Han, B.-G. Englert, and C. Miniatura, “Ultracold fermions in a graphene-type optical lattice,” Phys. Rev. A 80, 043411 (2009).
[CrossRef]

Gühne, O.

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
[CrossRef]

Hafezi, M.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

Halperin, B. I.

B. I. Halperin, “Statistics of quasi-particles and the hierarchy of fractional quantized Hall states,” Phys. Rev. Lett. 52, 1583–1586 (1984).
[CrossRef]

Hammerer, K.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

Han, R.

K. L. Lee, B. Grmaud, R. Han, B.-G. Englert, and C. Miniatura, “Ultracold fermions in a graphene-type optical lattice,” Phys. Rev. A 80, 043411 (2009).
[CrossRef]

Han, Y.-J.

Y.-J. Han, R. Raussendorf, and L.-M. Duan, “Scheme for demonstration of fractional statistics of anyons in an exactly solvable model,” Phys. Rev. Lett. 98, 150404 (2007).
[CrossRef]

Hu, X.

J. Q. You, X.-F. Shi, X. Hu, and F. Nori, “Quantum emulation of a spin system with topologically protected ground states using superconducting quantum circuits,” Phys. Rev. B 81, 014505 (2010).
[CrossRef]

Ivanov, D. A.

D. A. Ivanov, “Non-Ablelian statistics of half-quantum vortices in p-wave superconductors,” Phys. Rev. Lett. 86, 268–271 (2001).
[CrossRef]

Jaksch, D.

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[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]

Jessen, P. S.

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]

Jiang, L.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

Jotzu, G.

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012).
[CrossRef]

Khare, A.

A. Khare, Fractional Statistics and Quantum Theory (World Scientific, 2005).

Khudaverdyan, M.

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef]

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Kiesel, N.

J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
[CrossRef]

Kitaev, A.

A. Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys. (N.Y.) 321, 2–111 (2006).
[CrossRef]

Kitaev, A. Yu.

A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303, 2–30 (2003).
[CrossRef]

Kuhr, S.

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Laughlin, R. B.

R. B. Laughlin, “Anomalous quantum Hall effect: an incompressible quantum fluid with fractional charged excitation,” Phys. Rev. Lett. 50, 1395–1398 (1983).
[CrossRef]

Lee, K. L.

K. L. Lee, B. Grmaud, R. Han, B.-G. Englert, and C. Miniatura, “Ultracold fermions in a graphene-type optical lattice,” Phys. Rev. A 80, 043411 (2009).
[CrossRef]

Lu, C.-Y.

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
[CrossRef]

Lukin, M. D.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling spin exchange interactions of ultracold atoms in optical lattice,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[CrossRef]

Meschede, D.

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef]

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Miniatura, C.

K. L. Lee, B. Grmaud, R. Han, B.-G. Englert, and C. Miniatura, “Ultracold fermions in a graphene-type optical lattice,” Phys. Rev. A 80, 043411 (2009).
[CrossRef]

Miroshnychenko, Y.

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef]

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Moore, G.

G. Moore and N. Read, “Nonabelians in the fractional quantum Hall effect,” Nucl. Phys. B 360, 362–396 (1991).
[CrossRef]

Nayak, C.

S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and Majorana zero modes of a px+ipy superfluid of fermionic cold atoms,” Phys. Rev. Lett. 98, 010506 (2007).
[CrossRef]

Nori, F.

J. Q. You, X.-F. Shi, X. Hu, and F. Nori, “Quantum emulation of a spin system with topologically protected ground states using superconducting quantum circuits,” Phys. Rev. B 81, 014505 (2010).
[CrossRef]

Pachos, J. K.

J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
[CrossRef]

Pan, J.-W.

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
[CrossRef]

Peng, K.

J. Zhang, C. Xie, K. Peng, and P. van Loock, “Anyon statistics with continuous variables,” Phys. Rev. A 78, 052121 (2008).
[CrossRef]

Pohlner, R.

J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
[CrossRef]

Rauschenbeutel, A.

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef]

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Raussendorf, R.

Y.-J. Han, R. Raussendorf, and L.-M. Duan, “Scheme for demonstration of fractional statistics of anyons in an exactly solvable model,” Phys. Rev. Lett. 98, 150404 (2007).
[CrossRef]

Read, N.

G. Moore and N. Read, “Nonabelians in the fractional quantum Hall effect,” Nucl. Phys. B 360, 362–396 (1991).
[CrossRef]

Rosenfeld, W.

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Scarola, V. W.

C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma, “Anyonic braiding in optical lattices,” Proc. Natl. Acad. Sci. USA 104, 18415–18420 (2007).
[CrossRef]

Schmid, C.

J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
[CrossRef]

Schmidt, K. P.

J. Vidal, K. P. Schmidt, and S. Dusuel, “Perturbative approach to an exactly solved problem: Kitaev honeycomb model,” Phys. Rev. B 78, 245121 (2008).
[CrossRef]

S. Dusuel, K. P. Schmidt, and J. Vidal, “Creation and manipulation of Anyons in the Kitaev model,” Phys. Rev. Lett. 100, 177204 (2008).
[CrossRef]

Schrader, D.

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef]

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

Shao, L.-B.

S. L. Zhu, L.-B. Shao, Z. D. Wang, and L.-M. Duan, “Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid,” Phys. Rev. Lett. 106, 100404 (2011).
[CrossRef]

Shi, X.-F.

J. Q. You, X.-F. Shi, X. Hu, and F. Nori, “Quantum emulation of a spin system with topologically protected ground states using superconducting quantum circuits,” Phys. Rev. B 81, 014505 (2010).
[CrossRef]

Stern, A.

A. Stern, “Non-Abelian states of matter,” Nature 464, 187–193 (2010).
[CrossRef]

Tarruell, L.

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012).
[CrossRef]

Tewari, S.

S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and Majorana zero modes of a px+ipy superfluid of fermionic cold atoms,” Phys. Rev. Lett. 98, 010506 (2007).
[CrossRef]

C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma, “Anyonic braiding in optical lattices,” Proc. Natl. Acad. Sci. USA 104, 18415–18420 (2007).
[CrossRef]

Uehlinger, T.

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012).
[CrossRef]

van Loock, P.

J. Zhang, C. Xie, K. Peng, and P. van Loock, “Anyon statistics with continuous variables,” Phys. Rev. A 78, 052121 (2008).
[CrossRef]

Verstraete, F.

M. Aguado, G. K. Brennen, F. Verstraete, and J. I. Cirac, “Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices,” Phys. Rev. Lett. 101, 260501 (2008).
[CrossRef]

Vidal, J.

S. Dusuel, K. P. Schmidt, and J. Vidal, “Creation and manipulation of Anyons in the Kitaev model,” Phys. Rev. Lett. 100, 177204 (2008).
[CrossRef]

J. Vidal, K. P. Schmidt, and S. Dusuel, “Perturbative approach to an exactly solved problem: Kitaev honeycomb model,” Phys. Rev. B 78, 245121 (2008).
[CrossRef]

Wang, B. G.

S.-L. Zhu, B. G. Wang, and L.-M. Duan, “Simulation and detection of Dirac fermions with cold atoms in an optical lattice,” Phys. Rev. Lett. 98, 260402 (2007).
[CrossRef]

Wang, Z. D.

S. L. Zhu, L.-B. Shao, Z. D. Wang, and L.-M. Duan, “Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid,” Phys. Rev. Lett. 106, 100404 (2011).
[CrossRef]

Weinfurter, H.

J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
[CrossRef]

Wieczorek, W.

J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
[CrossRef]

Xie, C.

J. Zhang, C. Xie, K. Peng, and P. van Loock, “Anyon statistics with continuous variables,” Phys. Rev. A 78, 052121 (2008).
[CrossRef]

Xue, Z.-Y.

Z.-Y. Xue, “Simulation of anyonic fractional statistics of Kitaev’s toric model in circuit QED,” Europhys. Lett. 93, 20007 (2011).
[CrossRef]

Z.-Y. Xue, “Detecting non-Abelian statistics of Majorana fermions in quantum nanowire networks,” J. Exp. Theor. Phys. Lett. 94, 213 (2011).
[CrossRef]

You, J. Q.

J. Q. You, X.-F. Shi, X. Hu, and F. Nori, “Quantum emulation of a spin system with topologically protected ground states using superconducting quantum circuits,” Phys. Rev. B 81, 014505 (2010).
[CrossRef]

Zhang, C.

S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and Majorana zero modes of a px+ipy superfluid of fermionic cold atoms,” Phys. Rev. Lett. 98, 010506 (2007).
[CrossRef]

C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma, “Anyonic braiding in optical lattices,” Proc. Natl. Acad. Sci. USA 104, 18415–18420 (2007).
[CrossRef]

Zhang, J.

J. Zhang, C. Xie, K. Peng, and P. van Loock, “Anyon statistics with continuous variables,” Phys. Rev. A 78, 052121 (2008).
[CrossRef]

Zhou, X.-Q.

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
[CrossRef]

Zhu, S. L.

S. L. Zhu, L.-B. Shao, Z. D. Wang, and L.-M. Duan, “Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid,” Phys. Rev. Lett. 106, 100404 (2011).
[CrossRef]

Zhu, S.-L.

S.-L. Zhu, B. G. Wang, and L.-M. Duan, “Simulation and detection of Dirac fermions with cold atoms in an optical lattice,” Phys. Rev. Lett. 98, 260402 (2007).
[CrossRef]

Zoller, P.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and Majorana zero modes of a px+ipy superfluid of fermionic cold atoms,” Phys. Rev. Lett. 98, 010506 (2007).
[CrossRef]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[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]

Zwerger, W.

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

Ann. Phys.

A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303, 2–30 (2003).
[CrossRef]

Ann. Phys. (N.Y.)

A. Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys. (N.Y.) 321, 2–111 (2006).
[CrossRef]

Europhys. Lett.

Z.-Y. Xue, “Simulation of anyonic fractional statistics of Kitaev’s toric model in circuit QED,” Europhys. Lett. 93, 20007 (2011).
[CrossRef]

J. Exp. Theor. Phys. Lett.

Z.-Y. Xue, “Detecting non-Abelian statistics of Majorana fermions in quantum nanowire networks,” J. Exp. Theor. Phys. Lett. 94, 213 (2011).
[CrossRef]

Nat. Phys.

L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin, and P. Zoller, “Anyonic interferometry and protected memories in atomic spin lattices,” Nat. Phys. 4, 482–488 (2008).
[CrossRef]

Nature

A. Stern, “Non-Abelian states of matter,” Nature 464, 187–193 (2010).
[CrossRef]

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012).
[CrossRef]

New J. Phys.

J. K. Pachos, W. Wieczorek, C. Schmid, N. Kiesel, R. Pohlner, and H. Weinfurter, “Revealing anyonic features in a toric code quantum simulation,” New J. Phys. 11, 083010 (2009).
[CrossRef]

Nucl. Phys. B

G. Moore and N. Read, “Nonabelians in the fractional quantum Hall effect,” Nucl. Phys. B 360, 362–396 (1991).
[CrossRef]

Phys. Rev. A

J. Zhang, C. Xie, K. Peng, and P. van Loock, “Anyon statistics with continuous variables,” Phys. Rev. A 78, 052121 (2008).
[CrossRef]

K. L. Lee, B. Grmaud, R. Han, B.-G. Englert, and C. Miniatura, “Ultracold fermions in a graphene-type optical lattice,” Phys. Rev. A 80, 043411 (2009).
[CrossRef]

Phys. Rev. B

J. Vidal, K. P. Schmidt, and S. Dusuel, “Perturbative approach to an exactly solved problem: Kitaev honeycomb model,” Phys. Rev. B 78, 245121 (2008).
[CrossRef]

J. Q. You, X.-F. Shi, X. Hu, and F. Nori, “Quantum emulation of a spin system with topologically protected ground states using superconducting quantum circuits,” Phys. Rev. B 81, 014505 (2010).
[CrossRef]

Phys. Rev. Lett.

S. Dusuel, K. P. Schmidt, and J. Vidal, “Creation and manipulation of Anyons in the Kitaev model,” Phys. Rev. Lett. 100, 177204 (2008).
[CrossRef]

S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and Majorana zero modes of a px+ipy superfluid of fermionic cold atoms,” Phys. Rev. Lett. 98, 010506 (2007).
[CrossRef]

Y.-J. Han, R. Raussendorf, and L.-M. Duan, “Scheme for demonstration of fractional statistics of anyons in an exactly solvable model,” Phys. Rev. Lett. 98, 150404 (2007).
[CrossRef]

M. Aguado, G. K. Brennen, F. Verstraete, and J. I. Cirac, “Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices,” Phys. Rev. Lett. 101, 260501 (2008).
[CrossRef]

S. L. Zhu, L.-B. Shao, Z. D. Wang, and L.-M. Duan, “Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid,” Phys. Rev. Lett. 106, 100404 (2011).
[CrossRef]

R. B. Laughlin, “Anomalous quantum Hall effect: an incompressible quantum fluid with fractional charged excitation,” Phys. Rev. Lett. 50, 1395–1398 (1983).
[CrossRef]

B. I. Halperin, “Statistics of quasi-particles and the hierarchy of fractional quantized Hall states,” Phys. Rev. Lett. 52, 1583–1586 (1984).
[CrossRef]

C.-Y. Lu, W.-B. Gao, O. Gühne, X.-Q. Zhou, Z.-B. Chen, and J.-W. Pan, “Demonstrating anyonic fractional statistics with a six-qubit quantum simulator,” Phys. Rev. Lett. 102, 030502 (2009).
[CrossRef]

S.-L. Zhu, B. G. Wang, and L.-M. Duan, “Simulation and detection of Dirac fermions with cold atoms in an optical lattice,” Phys. Rev. Lett. 98, 260402 (2007).
[CrossRef]

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling spin exchange interactions of ultracold atoms in optical lattice,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef]

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]

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, “Dipole blockade and quantum information processing in mesoscopic atomic ensembles,” Phys. Rev. Lett. 87, 037901 (2001).
[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]

S. Kuhr, W. Alt, D. Schrader, I. Dotsenko, Y. Miroshnychenko, W. Rosenfeld, M. Khudaverdyan, V. Gomer, A. Rauschenbeutel, and D. Meschede, “Coherence properties and quantum state transportation in an optical conveyor belt,” Phys. Rev. Lett. 91, 213002 (2003).
[CrossRef]

D. Schrader, I. Dotsenko, M. Khudaverdyan, Y. Miroshnychenko, A. Rauschenbeutel, and D. Meschede, “Neutral atom quantum register,” Phys. Rev. Lett. 93, 150501 (2004).
[CrossRef]

D. A. Ivanov, “Non-Ablelian statistics of half-quantum vortices in p-wave superconductors,” Phys. Rev. Lett. 86, 268–271 (2001).
[CrossRef]

Proc. Natl. Acad. Sci. USA

C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma, “Anyonic braiding in optical lattices,” Proc. Natl. Acad. Sci. USA 104, 18415–18420 (2007).
[CrossRef]

Rev. Mod. Phys.

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

Other

P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University, 1930).

A. Khare, Fractional Statistics and Quantum Theory (World Scientific, 2005).

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Figures (3)

Fig. 1.
Fig. 1.

Implementation of the Kitaev model. (a) The model is a honeycomb lattice model of a spin-1/2 system in a plane. The index of the six atoms within a plaquette is indicated. (b) There are three different interaction between the nearest neighbor of the lattice along the xx, yy, and zz directions. (c) The pseudo spin states are encoded by | and | of an atom; an excited state |e is also introduced. Two coupling laser beams L1 and L2 are used to realize the interaction in three independent directions as we needed.

Fig. 2.
Fig. 2.

Creation and manipulation of non-Abelian anyons. (a) Initial state of the ancilla atom (red dot) is |+a|0a+|1a, and the solid blue circle denotes a vortex excitation bound to a plaquette. When moving the ancilla close enough to the code atom, a two-qubit Uiz gate is achieved. (b) Manipulation of the anyons. Only when the ancilla is in state |1a will an effective operation act on the atom transforming the wp from one to the other sector, and thus the vortex configuration can be changed as we needed.

Fig. 3.
Fig. 3.

Braiding of two non-Abelian anyons. In a topological sense, a counterclockwise braiding (or exchange) of two anyons is equivalent to move an anyon counterclockwise by 2π around the other. We choose the braiding to take place between anyons 2 and 3 due to the superselection rule. The operator S23=σ5yσ4zσ3xσ2yσ1zσ6x corresponds to a looping trajectory, which is exactly the loop when anyon 3 moves around anyon 2.

Equations (5)

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

H=Jxx-linksσjxσkxJyy-linksσjyσkyJzz-linksσjzσkz,
H=i4j,kA^jkcjck,
Heff=i,j,νJνσiνσjνhνjνσjν.
H2v=σizHσiz=H+2Jxσixσjx+2Jyσiyσky,
R2=12(1ii1),

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