Abstract

Bound states in the continuum (BICs) of periodic lattices have been the recent focus in a variety of photonic nanostructures. Motivated by the recent results about the photons evolving in BIC structures, we investigate the quantum decay of entangled biphotons through disordered photonic lattices. We report that the persistence of bound states in disordered photonic lattices leads to an interplay between the BIC and disorder-induced Anderson localized states. We reveal a novel effect resulting from such an interplay: a nearly complete quantum survival for the entangled biphoton respecting the antisymmetric exchange symmetry. This is in contrast to the complete vanishment in a periodic photonic lattice.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  21. M. P. Van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
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    [Crossref] [PubMed]
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    [Crossref]
  24. P. Lodahl, A. P. Mosk, and A. Lagendijk, “Spatial quantum correlations in multiple scattered light,” Phys. Rev. Lett. 95, 173901 (2005).
    [Crossref]
  25. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984)
    [Crossref]
  26. P. W. Anderson, “The question of classical localization: A theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
    [Crossref]
  27. Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum Correlations in Two-Particle Anderson Localization,” Phys. Rev. Lett. 105, 163905 (2010).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  32. H. Tang, X. Lin, Z. Feng, J. Chen, J. Gao, X. Xu, Y. Wang, L. Qiao, A. Yang, and X. M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, eaat3174 (2018).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  34. M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18, 103002 (2016).
    [Crossref]
  35. Peter L. Knight, E. Roldán, and J. E. Sipe, “Quantum walk on the line as an interference phenomenon,” Phys. Rev. A 68, 02030 (2003).
    [Crossref]
  36. L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle Bosonic-Fermionic quantum walk via integrated photonics,” Phys. Rev. Lett. 108, 010502 (2012).
    [Crossref] [PubMed]
  37. J. Matthews, K. Poulios, J. Meinecke, A. Politi, A. Peruzzo, Nur Ismail, K. Wörhoff, M. G. Thompson, and J. O’Brien, “Observing fermionic statistics with photons in arbitrary processes,” Sci. Rep. 3, 1539 (2013).
    [Crossref] [PubMed]
  38. I. Pitsios, L. Banchi, A. S. Rab, M. Bentivegna, D. Caprara, A. Crespi, N. Spagnolo, S. Bose, P. Mataloni, R. Osellame, and F. Sciarrino, “Photonic simulation of entanglement growth and engineering after a spin chain quench,” Nature Commun. 8, 1569 (2017).
    [Crossref]
  39. Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. 102, 253904 (2009).
    [Crossref] [PubMed]
  40. B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
    [Crossref]
  41. M. C. Rechtsman, Y. Lumer, Y. Plotnik, A. Perez-Leija, A. Szameit, and M. Segev, “Topological protection of photonic path entanglement,” Optica 3, 925–930 (2016).
    [Crossref]
  42. C. Gross and I. Bloch, “Quantum simulations with ultracold atoms in optical lattices,” Science 357, 995–1001 (2017).
    [Crossref] [PubMed]

2018 (1)

H. Tang, X. Lin, Z. Feng, J. Chen, J. Gao, X. Xu, Y. Wang, L. Qiao, A. Yang, and X. M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, eaat3174 (2018).
[Crossref] [PubMed]

2017 (3)

I. Pitsios, L. Banchi, A. S. Rab, M. Bentivegna, D. Caprara, A. Crespi, N. Spagnolo, S. Bose, P. Mataloni, R. Osellame, and F. Sciarrino, “Photonic simulation of entanglement growth and engineering after a spin chain quench,” Nature Commun. 8, 1569 (2017).
[Crossref]

A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541, 196–199 (2017).
[Crossref] [PubMed]

C. Gross and I. Bloch, “Quantum simulations with ultracold atoms in optical lattices,” Science 357, 995–1001 (2017).
[Crossref] [PubMed]

2016 (5)

J. Gao, L. F. Qiao, X. F. Lin, Z. Q. Jiao, Z. Feng, Z. Zhou, Z. M. Gao, X. Y. Xu, Y. Chen, H. Tang, and X. M. Jin, “Nonclassical photon correlation in a two-dimensional photonic lattice,” Opt. Express 24, 12607–12616 (2016).
[Crossref] [PubMed]

M. C. Rechtsman, Y. Lumer, Y. Plotnik, A. Perez-Leija, A. Szameit, and M. Segev, “Topological protection of photonic path entanglement,” Optica 3, 925–930 (2016).
[Crossref]

M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18, 103002 (2016).
[Crossref]

For review, see C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nature Rev. Mat. 1, 16048 (2016).
[Crossref]

M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18, 103002 (2016).
[Crossref]

2015 (4)

H. E. Kondakci, A. F. Abouraddy, and B. Saleh, “A photonic thermalization gap in disordered lattices,” Nature Physics 11, 930–935 (2015).
[Crossref]

Y. Gilead, M. Verbin, and Y. Silberberg, “Ensemble-averaged quantum correlations between path-entangled photons undergoing Anderson localization,” Phys. Rev. Lett. 115133602 (2015).
[Crossref] [PubMed]

A. Crespi, L. Sansoni, G. D. Valle, A. Ciamei, R. Ramponi, F. Sciarrino, P. Mataloni, S. Longhi, and R. Osellame, “Particle statistics affects quantum decay and Fano interference,” Phys. Rev. Lett. 114, 090201 (2015).
[Crossref] [PubMed]

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

2014 (2)

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

K. Poulios, R. Keil, D. Fry, J. Meinecke, J. Matthews, A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum walks of correlated photon pairs in two-dimensional waveguide arrays,” Phys. Rev. Lett. 112, 143604 (2014).
[Crossref] [PubMed]

2013 (6)

G. Corrielli, G. Della Valle, A. Crespi, R. Osellame, and S. Longhi, “Observation of surface states with algebraic localization,” Phys. Rev. Lett. 111, 220403 (2013).
[Crossref] [PubMed]

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, S. Nolte, A. A. Sukhorukov, A. Szameit, and Y. S. Kivshar, “Compact surface Fano states embedded in the continuum of waveguide array,” Phys. Rev. Lett. 111, 240403 (2013).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref] [PubMed]

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, and P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nature Photonics 7, 322–328 (2013).
[Crossref]

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. Abouraddy, D. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref] [PubMed]

J. Matthews, K. Poulios, J. Meinecke, A. Politi, A. Peruzzo, Nur Ismail, K. Wörhoff, M. G. Thompson, and J. O’Brien, “Observing fermionic statistics with photons in arbitrary processes,” Sci. Rep. 3, 1539 (2013).
[Crossref] [PubMed]

2012 (3)

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

S. Longhi and G. Della Valle, “Many-particle quantum decay and trapping: The role of statistics and Fano resonances,” Phys. Rev. A 86, 012112 (2012).
[Crossref]

A. Schreiber, A. Gábris, P. P. Rohde, K. Laiho, M. Štefaňák, V. Potoček, C. Hamilton, I. Jex, and C. Silberhorn, “A 2D quantum walk simulation of two-particle dynamics,” Science 336, 55–58 (2012).
[Crossref] [PubMed]

2011 (1)

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 183901 (2011).
[Crossref]

2010 (2)

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum Correlations in Two-Particle Anderson Localization,” Phys. Rev. Lett. 105, 163905 (2010).
[Crossref]

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

2009 (1)

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. 102, 253904 (2009).
[Crossref] [PubMed]

2008 (1)

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100, 170506 (2008).
[Crossref] [PubMed]

2007 (1)

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

2005 (1)

P. Lodahl, A. P. Mosk, and A. Lagendijk, “Spatial quantum correlations in multiple scattered light,” Phys. Rev. Lett. 95, 173901 (2005).
[Crossref]

2003 (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

Peter L. Knight, E. Roldán, and J. E. Sipe, “Quantum walk on the line as an interference phenomenon,” Phys. Rev. A 68, 02030 (2003).
[Crossref]

1999 (1)

M. C. W. van Rossum and Th. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

1993 (1)

B. Kramer and A. MacKinnon, “Localization: theory and experiment,” Rep. Prog. Phys. 56, 1469–1564 (1993).
[Crossref]

1985 (3)

M. P. Van Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[Crossref] [PubMed]

P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[Crossref] [PubMed]

P. W. Anderson, “The question of classical localization: A theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
[Crossref]

1984 (2)

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984)
[Crossref]

Y. Kuga and A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,”J. Opt. Soc. Am. A 8, 831–835 (1984).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
[Crossref]

1929 (1)

J. von Neumann and E. Wigner, “Uber merkwürdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen,” Z. Phys. 30, 465 (1929).

Abouraddy, A.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. Abouraddy, D. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref] [PubMed]

Abouraddy, A. F.

H. E. Kondakci, A. F. Abouraddy, and B. Saleh, “A photonic thermalization gap in disordered lattices,” Nature Physics 11, 930–935 (2015).
[Crossref]

Anderson, P. W.

P. W. Anderson, “The question of classical localization: A theory of white paint?” Philos. Mag. B 52, 505–509 (1985).
[Crossref]

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
[Crossref]

Bahari, B.

A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541, 196–199 (2017).
[Crossref] [PubMed]

Banchi, L.

I. Pitsios, L. Banchi, A. S. Rab, M. Bentivegna, D. Caprara, A. Crespi, N. Spagnolo, S. Bose, P. Mataloni, R. Osellame, and F. Sciarrino, “Photonic simulation of entanglement growth and engineering after a spin chain quench,” Nature Commun. 8, 1569 (2017).
[Crossref]

Bartal, G.

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

Bentivegna, M.

I. Pitsios, L. Banchi, A. S. Rab, M. Bentivegna, D. Caprara, A. Crespi, N. Spagnolo, S. Bose, P. Mataloni, R. Osellame, and F. Sciarrino, “Photonic simulation of entanglement growth and engineering after a spin chain quench,” Nature Commun. 8, 1569 (2017).
[Crossref]

Bloch, I.

C. Gross and I. Bloch, “Quantum simulations with ultracold atoms in optical lattices,” Science 357, 995–1001 (2017).
[Crossref] [PubMed]

Bose, S.

I. Pitsios, L. Banchi, A. S. Rab, M. Bentivegna, D. Caprara, A. Crespi, N. Spagnolo, S. Bose, P. Mataloni, R. Osellame, and F. Sciarrino, “Photonic simulation of entanglement growth and engineering after a spin chain quench,” Nature Commun. 8, 1569 (2017).
[Crossref]

Boyd, R. W.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

Bromberg, Y.

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

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum Correlations in Two-Particle Anderson Localization,” Phys. Rev. Lett. 105, 163905 (2010).
[Crossref]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett. 102, 253904 (2009).
[Crossref] [PubMed]

Caprara, D.

I. Pitsios, L. Banchi, A. S. Rab, M. Bentivegna, D. Caprara, A. Crespi, N. Spagnolo, S. Bose, P. Mataloni, R. Osellame, and F. Sciarrino, “Photonic simulation of entanglement growth and engineering after a spin chain quench,” Nature Commun. 8, 1569 (2017).
[Crossref]

Cardano, F.

F. Cardano, F. Massa, H. Qassim, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref] [PubMed]

Chen, J.

H. Tang, X. Lin, Z. Feng, J. Chen, J. Gao, X. Xu, Y. Wang, L. Qiao, A. Yang, and X. M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, eaat3174 (2018).
[Crossref] [PubMed]

Chen, Y.

Christodoulides, D.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. Abouraddy, D. Christodoulides, and B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref] [PubMed]

Christodoulides, D. N.

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H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett. 100, 170506 (2008).
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M. C. Rechtsman, Y. Lumer, Y. Plotnik, A. Perez-Leija, A. Szameit, and M. Segev, “Topological protection of photonic path entanglement,” Optica 3, 925–930 (2016).
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M. Gräfe, R. Heilmann, M. Lebugle, D. Guzman-Silva, A. Perez-Leija, and A. Szameit, “Integrated photonic quantum walks,” J. Opt. 18, 103002 (2016).
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Figures (4)

Fig. 1
Fig. 1 (a) A sketch of a photonic implementation of the Fano-Anderson model [Eq. (1) in the text]. The light can hop along the transverse directions x, y and propagate along the longitudinal direction z. The nonclassical excitations correspond to the polarization-entangled biphoton (arrows) launched into the two side-coupled waveguides n = 1, 2. (b) Energy spectrum and (c) the corresponding inverse participation ratio (IPR) of eigenmodes for the disordered lattices with disorder strength W = 2. The inset in (b) gives a close-up of the energy spectrum around zero energy. (d) Evolution of IPRs of the eigenstates in a disordered BIC photonic lattice, calculated as function of the disorder strength W. Red empty circles indicates the IPR values of the BIC states formed, exactly equal to 1/2.
Fig. 2
Fig. 2 Mode profiles of the BIC (a) and a typical localized state (b) in the disorder scenarios. In the inset, a phase difference at π is revealed for the BIC.
Fig. 3
Fig. 3 (a) Evolution of light intensity and (b) the survival probability for the classical excitation at the waveguide n = 1. The color bar indicates the normalized light intensity.
Fig. 4
Fig. 4 (a) Ensemble-averaged decay dynamics of the survival probability of the entangled biphoton in the disordered BIC photonic lattices. (b) Asymptotic survival probability S(z → ∞) as a function of the disorder level W in the disordered BIC lattices.

Equations (2)

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i d a 1 , 2 d z = β 1 , 2 a 1 , 2 + κ a 3 , i d a 3 d z = β 3 a 3 + κ a 1 + κ a 2 + κ a 4 , i d a n d z = β n a n + κ a n 1 + κ a n + 1 , n 4 .
IPR ( i ) = n | ψ n ( i ) | 4 ( n | ψ n ( i ) | 2 ) 2 ,