Abstract

Unphysical solutions are ruled out in physical equations, as they lead to behavior that violates fundamental physical laws. One of the celebrated equations that allows unphysical solutions is the relativistic Majorana equation, thought to describe neutrinos and other exotic particles predicted in theories beyond the standard model. The neutrally charged Majorana fermion is the equation’s physical solution, whereas the charged version is, due to charge nonconservation, unphysical and cannot exist. Here, we present an experimental scheme simulating the dynamics of a charged Majorana particle by light propagation in a tailored waveguide chip. Specifically, we simulate the free-particle evolution as well as the unphysical operation of charge conjugation. We do this by exploiting the fact that the wave function is not a directly observable physical quantity and by decomposing the unphysical solution to observable entities. Our results illustrate the potential of investigating theories beyond the standard model in a compact laboratory setting.

© 2015 Optical Society of America

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References

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  7. C. Nayak, S. H. Simon, A. Stern, M. Freedman, S. Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
    [Crossref]
  8. J. Casanova, C. Sabin, J. León, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcya-Ripoll, E. Solano, “Quantum simulation of the Majorana equation and unphysical operations,” Phys. Rev. X 1, 021018 (2011).
    [Crossref]
  9. C. Noh, B. M. Rodríguez-Lara, D. G. Angelakis, “Proposal for realization of the Majorana equation in a tabletop experiment,” Phys. Rev. A 87, 040102(R) (2013).
    [Crossref]
  10. S. N. Gninenko, “Limit on the electric charge-nonconserving μ+ → invisible decay,” Phys. Rev. D 76, 055004 (2007).
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    [Crossref]
  12. R. Di Candia, B. Mejia, H. Castillo, J. S. Pedernales, J. Casanova, E. Solano, “Embedding quantum simulators for quantum computation of entanglement,” Phys. Rev. Lett. 111, 240502 (2013).
    [Crossref]
  13. L. Lamata, J. León, T. Schätz, E. Solano, “Dirac equation and quantum relativistic effects in a single trapped ion,” Phys. Rev. Lett. 98, 253005 (2007).
    [Crossref]
  14. R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
    [Crossref]
  15. F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
    [Crossref]
  16. L. Lamata, J. Casanova, I. L. Egusquiza, E. Solano, “The nonrelativistic limit of the Majorana equation and its simulation in trapped ions,” Phys. Scr. T147, 014017 (2012).
    [Crossref]
  17. T. Schwartz, G. Bartal, S. Fishman, M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
    [Crossref]
  18. J. W. Fleischer, M. Segev, N. K. Efremidis, D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
    [Crossref]
  19. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
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  20. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
    [Crossref]
  21. S. Longhi, “Photonic analog of Zitterbewegung in binary waveguide arrays,” Opt. Lett. 35, 235–237 (2010).
    [Crossref]
  22. R. Keil, J. M. Zeuner, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, A. Szameit, “The random mass Dirac model and long-range correlations on an integrated optical platform,” Nat. Commun. 4, 1368 (2013).
  23. E. Schrödinger, “Über die kräftefreie Bewegung in der relativistischen Quantenmechanik,” Sitz. Preuss. Akad. Wiss. Phys.-Math. Kl. 24, 418–428 (1930).
  24. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
    [Crossref]
  25. A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
    [Crossref]
  26. F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
    [Crossref]
  27. L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett. 108, 010502 (2012).
    [Crossref]
  28. J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wörhoff, M. G. Thompson, J. L. O’Brien, “Observing fermionic statistics with photons in arbitrary processes,” Sci. Rep. 3, 1539 (2013).
  29. G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, “Fractional Bloch oscillations in photonic lattices,” Nat. Commun. 4, 1555 (2013).
    [Crossref]
  30. X. Qin, Y. Ke, X. Guan, Z. Li, N. Andrei, C. Lee, “Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions,” Phys. Rev. A 90, 062301 (2014).
    [Crossref]
  31. X. Zhang, Y. Shen, J. Zhang, J. Casanova, L. Lamata, E. Solano, M.-H. Yung, J.-N. Zhang, K. Kim, “Time reversal and charge conjugation in an embedding quantum simulator,” arXiv:1409.3681 (2014).

2014 (1)

X. Qin, Y. Ke, X. Guan, Z. Li, N. Andrei, C. Lee, “Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions,” Phys. Rev. A 90, 062301 (2014).
[Crossref]

2013 (6)

J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wörhoff, M. G. Thompson, J. L. O’Brien, “Observing fermionic statistics with photons in arbitrary processes,” Sci. Rep. 3, 1539 (2013).

G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, “Fractional Bloch oscillations in photonic lattices,” Nat. Commun. 4, 1555 (2013).
[Crossref]

C. Noh, B. M. Rodríguez-Lara, D. G. Angelakis, “Proposal for realization of the Majorana equation in a tabletop experiment,” Phys. Rev. A 87, 040102(R) (2013).
[Crossref]

R. Di Candia, B. Mejia, H. Castillo, J. S. Pedernales, J. Casanova, E. Solano, “Embedding quantum simulators for quantum computation of entanglement,” Phys. Rev. Lett. 111, 240502 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

R. Keil, J. M. Zeuner, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, A. Szameit, “The random mass Dirac model and long-range correlations on an integrated optical platform,” Nat. Commun. 4, 1368 (2013).

2012 (2)

L. Lamata, J. Casanova, I. L. Egusquiza, E. Solano, “The nonrelativistic limit of the Majorana equation and its simulation in trapped ions,” Phys. Scr. T147, 014017 (2012).
[Crossref]

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett. 108, 010502 (2012).
[Crossref]

2011 (1)

J. Casanova, C. Sabin, J. León, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcya-Ripoll, E. Solano, “Quantum simulation of the Majorana equation and unphysical operations,” Phys. Rev. X 1, 021018 (2011).
[Crossref]

2010 (5)

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[Crossref]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[Crossref]

A. S. Goldhaber, M. M. Nieto, “Photon and graviton mass limits,” Rev. Mod. Phys. 82, 939–979 (2010).
[Crossref]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

S. Longhi, “Photonic analog of Zitterbewegung in binary waveguide arrays,” Opt. Lett. 35, 235–237 (2010).
[Crossref]

2008 (3)

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

C. Nayak, S. H. Simon, A. Stern, M. Freedman, S. Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
[Crossref]

2007 (3)

L. Lamata, J. León, T. Schätz, E. Solano, “Dirac equation and quantum relativistic effects in a single trapped ion,” Phys. Rev. Lett. 98, 253005 (2007).
[Crossref]

S. N. Gninenko, “Limit on the electric charge-nonconserving μ+ → invisible decay,” Phys. Rev. D 76, 055004 (2007).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

2006 (1)

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

2003 (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[Crossref]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[Crossref]

1937 (1)

E. Majorana, “Teoria simmetrica dell’elettrone e del positrone,” Nuovo Cimento 14, 171–184 (1937).
[Crossref]

1930 (1)

E. Schrödinger, “Über die kräftefreie Bewegung in der relativistischen Quantenmechanik,” Sitz. Preuss. Akad. Wiss. Phys.-Math. Kl. 24, 418–428 (1930).

Andrei, N.

X. Qin, Y. Ke, X. Guan, Z. Li, N. Andrei, C. Lee, “Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions,” Phys. Rev. A 90, 062301 (2014).
[Crossref]

Angelakis, D. G.

C. Noh, B. M. Rodríguez-Lara, D. G. Angelakis, “Proposal for realization of the Majorana equation in a tabletop experiment,” Phys. Rev. A 87, 040102(R) (2013).
[Crossref]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Barthélémy, A.

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Beenakker, C. W. J.

C. W. J. Beenakker, “Random-matrix theory of Majorana fermions and topological superconductors,” arXiv:1407.2131 (2015).

Blatt, R.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[Crossref]

Bromberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Casanova, J.

R. Di Candia, B. Mejia, H. Castillo, J. S. Pedernales, J. Casanova, E. Solano, “Embedding quantum simulators for quantum computation of entanglement,” Phys. Rev. Lett. 111, 240502 (2013).
[Crossref]

L. Lamata, J. Casanova, I. L. Egusquiza, E. Solano, “The nonrelativistic limit of the Majorana equation and its simulation in trapped ions,” Phys. Scr. T147, 014017 (2012).
[Crossref]

J. Casanova, C. Sabin, J. León, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcya-Ripoll, E. Solano, “Quantum simulation of the Majorana equation and unphysical operations,” Phys. Rev. X 1, 021018 (2011).
[Crossref]

X. Zhang, Y. Shen, J. Zhang, J. Casanova, L. Lamata, E. Solano, M.-H. Yung, J.-N. Zhang, K. Kim, “Time reversal and charge conjugation in an embedding quantum simulator,” arXiv:1409.3681 (2014).

Castillo, H.

R. Di Candia, B. Mejia, H. Castillo, J. S. Pedernales, J. Casanova, E. Solano, “Embedding quantum simulators for quantum computation of entanglement,” Phys. Rev. Lett. 111, 240502 (2013).
[Crossref]

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[Crossref]

Corrielli, G.

G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, “Fractional Bloch oscillations in photonic lattices,” Nat. Commun. 4, 1555 (2013).
[Crossref]

Crespi, A.

G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, “Fractional Bloch oscillations in photonic lattices,” Nat. Commun. 4, 1555 (2013).
[Crossref]

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett. 108, 010502 (2012).
[Crossref]

Das Sarma, S.

C. Nayak, S. H. Simon, A. Stern, M. Freedman, S. Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
[Crossref]

Della Valle, G.

G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, “Fractional Bloch oscillations in photonic lattices,” Nat. Commun. 4, 1555 (2013).
[Crossref]

Di Candia, R.

R. Di Candia, B. Mejia, H. Castillo, J. S. Pedernales, J. Casanova, E. Solano, “Embedding quantum simulators for quantum computation of entanglement,” Phys. Rev. Lett. 111, 240502 (2013).
[Crossref]

Döring, S.

Dreisow, F.

R. Keil, J. M. Zeuner, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, A. Szameit, “The random mass Dirac model and long-range correlations on an integrated optical platform,” Nat. Commun. 4, 1368 (2013).

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[Crossref]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[Crossref]

Egusquiza, I. L.

L. Lamata, J. Casanova, I. L. Egusquiza, E. Solano, “The nonrelativistic limit of the Majorana equation and its simulation in trapped ions,” Phys. Scr. T147, 014017 (2012).
[Crossref]

J. Casanova, C. Sabin, J. León, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcya-Ripoll, E. Solano, “Quantum simulation of the Majorana equation and unphysical operations,” Phys. Rev. X 1, 021018 (2011).
[Crossref]

Fahr, S.

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[Crossref]

Freedman, M.

C. Nayak, S. H. Simon, A. Stern, M. Freedman, S. Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
[Crossref]

Garcya-Ripoll, J. J.

J. Casanova, C. Sabin, J. León, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcya-Ripoll, E. Solano, “Quantum simulation of the Majorana equation and unphysical operations,” Phys. Rev. X 1, 021018 (2011).
[Crossref]

Gerritsma, R.

J. Casanova, C. Sabin, J. León, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcya-Ripoll, E. Solano, “Quantum simulation of the Majorana equation and unphysical operations,” Phys. Rev. X 1, 021018 (2011).
[Crossref]

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[Crossref]

Giunti, C.

C. Giunti, C. W. Kim, Fundamentals of Neutrino Physics and Astrophysics (Oxford University, 2007).

Gninenko, S. N.

S. N. Gninenko, “Limit on the electric charge-nonconserving μ+ → invisible decay,” Phys. Rev. D 76, 055004 (2007).
[Crossref]

Goldhaber, A. S.

A. S. Goldhaber, M. M. Nieto, “Photon and graviton mass limits,” Rev. Mod. Phys. 82, 939–979 (2010).
[Crossref]

Guan, X.

X. Qin, Y. Ke, X. Guan, Z. Li, N. Andrei, C. Lee, “Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions,” Phys. Rev. A 90, 062301 (2014).
[Crossref]

Heinrich, M.

R. Keil, J. M. Zeuner, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, A. Szameit, “The random mass Dirac model and long-range correlations on an integrated optical platform,” Nat. Commun. 4, 1368 (2013).

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[Crossref]

F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, F. Lederer, “Spectral resolved dynamic localization in curved fs laser written waveguide arrays,” Opt. Express 16, 3474–3483 (2008).
[Crossref]

A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, S. Longhi, “Image reconstruction in segmented femtosecond laser-written waveguide arrays,” Appl. Phys. Lett. 93, 181109 (2008).
[Crossref]

Ismail, N.

J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wörhoff, M. G. Thompson, J. L. O’Brien, “Observing fermionic statistics with photons in arbitrary processes,” Sci. Rep. 3, 1539 (2013).

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Ke, Y.

X. Qin, Y. Ke, X. Guan, Z. Li, N. Andrei, C. Lee, “Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions,” Phys. Rev. A 90, 062301 (2014).
[Crossref]

Keil, R.

R. Keil, J. M. Zeuner, F. Dreisow, M. Heinrich, A. Tünnermann, S. Nolte, A. Szameit, “The random mass Dirac model and long-range correlations on an integrated optical platform,” Nat. Commun. 4, 1368 (2013).

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett. 105, 143902 (2010).
[Crossref]

Kim, C. W.

C. Giunti, C. W. Kim, Fundamentals of Neutrino Physics and Astrophysics (Oxford University, 2007).

Kim, K.

X. Zhang, Y. Shen, J. Zhang, J. Casanova, L. Lamata, E. Solano, M.-H. Yung, J.-N. Zhang, K. Kim, “Time reversal and charge conjugation in an embedding quantum simulator,” arXiv:1409.3681 (2014).

Kirchmair, G.

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[Crossref]

Kitaev, A. Y.

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

Lahini, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
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Figures (5)

Fig. 1.
Fig. 1.

Observation of photonic Zitterbewegung in a binary waveguide array. (a) Experimental data for a lattice of 26 guides. (b)  Numerical simulation using Eq. (5) with parameters κ = 0.064 mm 1 and β = 0.65 κ and an initial wave packet matching the experimental conditions. The different refractive indices of the waveguides in sublattices A and B are visualized by different radii of the channels.

Fig. 2.
Fig. 2.

Illustration of the waveguide sample, where two Dirac equations with opposite masses are simulated in two parallel planar lattices. The inset shows the phase segmentation in the upper lattice, which is used to impose a phase gradient of π / 2 between adjacent guides. The reverse segmentation profile is used in the lower plane. The calculated light intensity distribution with the same parameters as in Fig. 1 has been superimposed onto the illustration.

Fig. 3.
Fig. 3.

Simulation of a Majoranon with mass β = 0.65 κ . (a),(b) Calculated intensity evolution of the first spinor component ψ 1 , n and the second spinor component ψ 2 , n . In both panels, the number of transverse grid points n and the width of the initial wave packet correspond to the conditions in the experiment. The dashed lines indicate the evolution distances Z where a measurement is taken. (c),(d)  Experimentally observed (E) and numerically simulated (S) output light intensity distributions for Z = 0.55 κ 1 and Z = 4.4 κ 1 . (e) Spinor intensities reconstructed from the experimental data (symbols) in comparison to the theory (solid lines) for the short evolution length Z = 0.55 κ 1 and (f) the long evolution length Z = 4.4 κ 1 . (g) Pseudo-energy σ z versus Z . Again, the symbols represent experimental data, whereas the solid line shows the theoretical expectation. The calculation for the corresponding Dirac spinor is shown by the dashed line. The error bars represent the precision of the simulator within one standard deviation. The oscillations in pseudo-energy for the Dirac particle arise from nonzero momentum contributions in the initial wave packet, whereas the oscillation of the Majoranon is mostly caused by the unphysical mass term and its associated charge conjugation.

Fig. 4.
Fig. 4.

Simulation of a Majoranon with a larger mass compared to Fig. 3, β = 1.2 κ at the two evolution distances Z = 0.9 κ 1 and Z = 3.5 κ 1 . The subfigures are arranged as in Fig. 3. Due to the enlarged mass, the momentum contribution in the initial wave packet is decreased, which reduces the amplitude of the oscillation in pseudo-energy for the Dirac particle. The oscillations of the Majoranon, however, persist as they are caused by charge conjugation—an entirely different process.

Fig. 5.
Fig. 5.

Simulation of charge conjugation for the particle with mass β = 1.2 κ . (a) Measured (E) and calculated (S) output intensity profiles for Z = 0.9 κ 1 . The upper row of each image shows the waveguides from Fig. 4 that are used for a reconstruction of the Majorana spinor, whereas the lower row shows the auxillary waveguides from which the charge-conjugated spinor ψ c is obtained. The intensities of the two components of this spinor are displayed on the right. (b) Same as (a), but for the longer sample Z = 3.5 κ 1 . (c) Evolution of the pseudo-energy of the charge-conjugated (magenta) and the unconjugated particle (blue) for the Majorana equation (solid) and the Dirac equation (dashed).

Equations (6)

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

i γ μ μ ψ m ψ c = 0
i t ψ σ x p x ψ + i m σ y ψ * = 0 .
i t ψ ± σ x p x ψ ± m σ z ψ ± = 0 ,
ψ = ψ + + i ψ .
i Z ψ k + β k ψ k + κ ( ψ k + 1 + ψ k 1 ) = 0 ,
i Z ψ ± 2 d 0 κ σ x p x ψ ± β σ z ψ ± = 0 .

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