Abstract

In this paper, we propose an integrated optic waveguide device employing a modified Mach–Zehnder interferometer, capable of generating nondegenerate, hyperentangled photon pairs. The geometry enables multiple (eight) type-II phase-matched spontaneous parametric downconversion processes simultaneously, resulting in a biphoton state, which is simultaneously entangled in polarization and spatial modes. Using an electro-optic phase modulator, we show the possibility of altering modal entanglement without affecting polarization entanglement. Such switchable, maximally entangled photon pairs, entangled in multiple degrees of freedom, should be very useful in various on-chip quantum optics experiments and in the implementation of quantum information protocols employing higher dimensional entanglement.

© 2013 Optical Society of America

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2012 (2)

S. Tanzilli, A. Martin, F. Kaiser, M. P. De. Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143(2012).
[CrossRef]

J. Lugani, S. Ghosh, and K. Thyagarajan, “Electro-optically switchable spatial-mode entangled photon pairs using a modified Mach–Zehnder interferometer,” Opt. Lett. 37, 3729–3731 (2012).
[CrossRef]

2011 (3)

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal- and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83, 062333 (2011).
[CrossRef]

H. Yan, S. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106, 033601 (2011).
[CrossRef]

2010 (3)

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photonics J. 2, 736–752 (2010).
[CrossRef]

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

G. Vallone, G. Donati, R. Ceccarilli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: characterization and application to quantum computation,” Phys. Rev. A 81, 052301 (2010).
[CrossRef]

2009 (4)

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

R. Ceccarelli, G. Vallone, F. De. Martini, P. Mataloni, and A. Cabello, “Experimental entanglement and nonlocality of a two-photon six-qubit cluster state,” Phys. Rev. Lett. 103, 160401 (2009).
[CrossRef]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De. Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

2008 (2)

A. Eckstein and C. Silberhorn, “Broadband frequency mode entanglement in waveguided parametric downconversion,” Opt. Lett. 33, 1825–1827 (2008).
[CrossRef]

J. Chen, J. Fan, M. D. Eisaman, and A. Migdall, “Generation of high-flux hyperentangled photon pairs using a microstructure-fiber Sagnac interferometer,” Phys. Rev. A 77, 053812 (2008).
[CrossRef]

2007 (1)

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

2005 (2)

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[CrossRef]

2002 (4)

D. Bruss and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A 66, 062304 (2002).
[CrossRef]

2001 (1)

1999 (1)

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

1998 (1)

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[CrossRef]

1997 (1)

P. G. Kwiat, “Hyper-entangled states,” J. Mod. Opt. 44, 2173–2178 (1997).
[CrossRef]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

1993 (1)

A. Sharma and P. Bindal, “Analysis of diffused planar and channel waveguides,” IEEE J. Quantum Electron. 29, 150–153 (1993).
[CrossRef]

1989 (1)

1987 (1)

S. Fouchet, A. Carenco, C. Daguet, R. Guglielmi, and L. Riviere, “Wavelength dispersion of Ti-induced refractive index change in LiNbO3 as a function of diffusion parameters,” J. Lightwave Technol. 5, 700–708 (1987).
[CrossRef]

Alibart, O.

S. Tanzilli, A. Martin, F. Kaiser, M. P. De. Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143(2012).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Appelbaum, I.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

Baldi, P.

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

Banaszek, K.

Barreiro, J. T.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Bindal, P.

A. Sharma and P. Bindal, “Analysis of diffused planar and channel waveguides,” IEEE J. Quantum Electron. 29, 150–153 (1993).
[CrossRef]

Bourennane, M.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

Bruss, D.

D. Bruss and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[CrossRef]

Cabello, A.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

R. Ceccarelli, G. Vallone, F. De. Martini, P. Mataloni, and A. Cabello, “Experimental entanglement and nonlocality of a two-photon six-qubit cluster state,” Phys. Rev. Lett. 103, 160401 (2009).
[CrossRef]

Carenco, A.

S. Fouchet, A. Carenco, C. Daguet, R. Guglielmi, and L. Riviere, “Wavelength dispersion of Ti-induced refractive index change in LiNbO3 as a function of diffusion parameters,” J. Lightwave Technol. 5, 700–708 (1987).
[CrossRef]

Ceccarelli, R.

R. Ceccarelli, G. Vallone, F. De. Martini, P. Mataloni, and A. Cabello, “Experimental entanglement and nonlocality of a two-photon six-qubit cluster state,” Phys. Rev. Lett. 103, 160401 (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De. Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

Ceccarilli, R.

G. Vallone, G. Donati, R. Ceccarilli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: characterization and application to quantum computation,” Phys. Rev. A 81, 052301 (2010).
[CrossRef]

Cerf, N. J.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

Chen, J.

J. Chen, J. Fan, M. D. Eisaman, and A. Migdall, “Generation of high-flux hyperentangled photon pairs using a microstructure-fiber Sagnac interferometer,” Phys. Rev. A 77, 053812 (2008).
[CrossRef]

Chen, J. F.

H. Yan, S. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106, 033601 (2011).
[CrossRef]

Chen, K.

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

Chen, S.

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

Chen, Y. A.

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

Chen, Z. B.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

Chuang, I. L.

M. A. Nielson and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2006).

Daguet, C.

S. Fouchet, A. Carenco, C. Daguet, R. Guglielmi, and L. Riviere, “Wavelength dispersion of Ti-induced refractive index change in LiNbO3 as a function of diffusion parameters,” J. Lightwave Technol. 5, 700–708 (1987).
[CrossRef]

de Micheli, M. P.

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

de Riedmatten, H.

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

De. Martini, F.

G. Vallone, R. Ceccarelli, F. De. Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

R. Ceccarelli, G. Vallone, F. De. Martini, P. Mataloni, and A. Cabello, “Experimental entanglement and nonlocality of a two-photon six-qubit cluster state,” Phys. Rev. Lett. 103, 160401 (2009).
[CrossRef]

De. Micheli, M. P.

S. Tanzilli, A. Martin, F. Kaiser, M. P. De. Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143(2012).
[CrossRef]

Deng, F. G.

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[CrossRef]

Di Giuseppe, G.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photonics J. 2, 736–752 (2010).
[CrossRef]

Donati, G.

G. Vallone, G. Donati, R. Ceccarilli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: characterization and application to quantum computation,” Phys. Rev. A 81, 052301 (2010).
[CrossRef]

Du, S.

H. Yan, S. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106, 033601 (2011).
[CrossRef]

Eberhard, P. H.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

Eckstein, A.

Eisaman, M. D.

J. Chen, J. Fan, M. D. Eisaman, and A. Migdall, “Generation of high-flux hyperentangled photon pairs using a microstructure-fiber Sagnac interferometer,” Phys. Rev. A 77, 053812 (2008).
[CrossRef]

Fan, J.

J. Chen, J. Fan, M. D. Eisaman, and A. Migdall, “Generation of high-flux hyperentangled photon pairs using a microstructure-fiber Sagnac interferometer,” Phys. Rev. A 77, 053812 (2008).
[CrossRef]

Fouchet, S.

S. Fouchet, A. Carenco, C. Daguet, R. Guglielmi, and L. Riviere, “Wavelength dispersion of Ti-induced refractive index change in LiNbO3 as a function of diffusion parameters,” J. Lightwave Technol. 5, 700–708 (1987).
[CrossRef]

Gao, W. B.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

Ghatak, A.

A. Ghatak and K. Thyagarajan, Optical Electronics (Cambridge University, 1989).

Ghosh, S.

J. Lugani, S. Ghosh, and K. Thyagarajan, “Electro-optically switchable spatial-mode entangled photon pairs using a modified Mach–Zehnder interferometer,” Opt. Lett. 37, 3729–3731 (2012).
[CrossRef]

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal- and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83, 062333 (2011).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Gisin, N.

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A 66, 062304 (2002).
[CrossRef]

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

Goebel, A.

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

Guglielmi, R.

S. Fouchet, A. Carenco, C. Daguet, R. Guglielmi, and L. Riviere, “Wavelength dispersion of Ti-induced refractive index change in LiNbO3 as a function of diffusion parameters,” J. Lightwave Technol. 5, 700–708 (1987).
[CrossRef]

Guhne, O.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

Hardy, A.

Kaiser, F.

S. Tanzilli, A. Martin, F. Kaiser, M. P. De. Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143(2012).
[CrossRef]

Karlsson, A.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

Kwiat, P. G.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[CrossRef]

P. G. Kwiat, “Hyper-entangled states,” J. Mod. Opt. 44, 2173–2178 (1997).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Laing, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

Langford, N. K.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Li, C. M.

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

Li, Y. S.

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[CrossRef]

Liu, X. S.

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[CrossRef]

Lobino, M.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

Long, G. L.

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[CrossRef]

Loy, M. M. T.

H. Yan, S. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106, 033601 (2011).
[CrossRef]

Lu, C. Y.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

Lugani, J.

J. Lugani, S. Ghosh, and K. Thyagarajan, “Electro-optically switchable spatial-mode entangled photon pairs using a modified Mach–Zehnder interferometer,” Opt. Lett. 37, 3729–3731 (2012).
[CrossRef]

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal- and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83, 062333 (2011).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Macchiavello, C.

D. Bruss and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[CrossRef]

Mair, A.

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Marom, E.

Martin, A.

S. Tanzilli, A. Martin, F. Kaiser, M. P. De. Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143(2012).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Mataloni, P.

G. Vallone, G. Donati, R. Ceccarilli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: characterization and application to quantum computation,” Phys. Rev. A 81, 052301 (2010).
[CrossRef]

R. Ceccarelli, G. Vallone, F. De. Martini, P. Mataloni, and A. Cabello, “Experimental entanglement and nonlocality of a two-photon six-qubit cluster state,” Phys. Rev. Lett. 103, 160401 (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De. Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

Matthews, J. C. F.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Migdall, A.

J. Chen, J. Fan, M. D. Eisaman, and A. Migdall, “Generation of high-flux hyperentangled photon pairs using a microstructure-fiber Sagnac interferometer,” Phys. Rev. A 77, 053812 (2008).
[CrossRef]

Nielson, M. A.

M. A. Nielson and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2006).

O’Brien, J. L.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

Ostrowsky, D. B.

S. Tanzilli, A. Martin, F. Kaiser, M. P. De. Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143(2012).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

Pan, J. W.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

Peng, C. Z.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

Peruzzo, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

Peters, N. A.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Politi, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

Riviere, L.

S. Fouchet, A. Carenco, C. Daguet, R. Guglielmi, and L. Riviere, “Wavelength dispersion of Ti-induced refractive index change in LiNbO3 as a function of diffusion parameters,” J. Lightwave Technol. 5, 700–708 (1987).
[CrossRef]

Saleh, B. E. A.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photonics J. 2, 736–752 (2010).
[CrossRef]

Saleh, M. F.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photonics J. 2, 736–752 (2010).
[CrossRef]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Shadbolt, P. J.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

Sharma, A.

A. Sharma and P. Bindal, “Analysis of diffused planar and channel waveguides,” IEEE J. Quantum Electron. 29, 150–153 (1993).
[CrossRef]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Silberhorn, C.

Sinha, K.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Stefanov, A.

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

Tanzilli, S.

S. Tanzilli, A. Martin, F. Kaiser, M. P. De. Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143(2012).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A 66, 062304 (2002).
[CrossRef]

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

Teich, M. C.

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photonics J. 2, 736–752 (2010).
[CrossRef]

Thew, R. T.

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A 66, 062304 (2002).
[CrossRef]

Thompson, M. G.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

Thyagarajan, K.

J. Lugani, S. Ghosh, and K. Thyagarajan, “Electro-optically switchable spatial-mode entangled photon pairs using a modified Mach–Zehnder interferometer,” Opt. Lett. 37, 3729–3731 (2012).
[CrossRef]

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal- and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83, 062333 (2011).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

A. Ghatak and K. Thyagarajan, Optical Electronics (Cambridge University, 1989).

Tittel, W.

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A 66, 062304 (2002).
[CrossRef]

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

URen, A. B.

Vallone, G.

G. Vallone, G. Donati, R. Ceccarilli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: characterization and application to quantum computation,” Phys. Rev. A 81, 052301 (2010).
[CrossRef]

R. Ceccarelli, G. Vallone, F. De. Martini, P. Mataloni, and A. Cabello, “Experimental entanglement and nonlocality of a two-photon six-qubit cluster state,” Phys. Rev. Lett. 103, 160401 (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De. Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

Verde, M. R.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

Waks, E.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

Walmsley, I. A.

Wang, C.

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[CrossRef]

Weinfurter, H.

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Weissman, Z.

White, A. G.

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Wong, G. K. L.

H. Yan, S. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106, 033601 (2011).
[CrossRef]

Xu, P.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

Yan, H.

H. Yan, S. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106, 033601 (2011).
[CrossRef]

Yao, X. C.

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1989).

Zbinden, H.

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A 66, 062304 (2002).
[CrossRef]

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

Zeilinger, A.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[CrossRef]

Zhang, Q.

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
[CrossRef]

Zhang, S.

H. Yan, S. Zhang, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Generation of narrow-band hyperentangled nondegenerate paired photons,” Phys. Rev. Lett. 106, 033601 (2011).
[CrossRef]

Eur. Phys. J. D (1)

S. Tanzilli, W. Tittel, H. de Riedmatten, H. Zbinden, P. Baldi, M. P. de Micheli, D. B. Ostrowsky, and N. Gisin, “PPLN waveguide for quantum communication,” Eur. Phys. J. D 18, 155–160(2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Sharma and P. Bindal, “Analysis of diffused planar and channel waveguides,” IEEE J. Quantum Electron. 29, 150–153 (1993).
[CrossRef]

IEEE Photonics J. (1)

M. F. Saleh, G. Di Giuseppe, B. E. A. Saleh, and M. C. Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photonics J. 2, 736–752 (2010).
[CrossRef]

J. Lightwave Technol. (1)

S. Fouchet, A. Carenco, C. Daguet, R. Guglielmi, and L. Riviere, “Wavelength dispersion of Ti-induced refractive index change in LiNbO3 as a function of diffusion parameters,” J. Lightwave Technol. 5, 700–708 (1987).
[CrossRef]

J. Mod. Opt. (1)

P. G. Kwiat, “Hyper-entangled states,” J. Mod. Opt. 44, 2173–2178 (1997).
[CrossRef]

Laser Photon. Rev. (1)

S. Tanzilli, A. Martin, F. Kaiser, M. P. De. Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photon. Rev. 6, 115–143(2012).
[CrossRef]

Nat. Photonics (2)

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics 6, 45–49 (2011).
[CrossRef]

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3, 346–350 (2009).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (9)

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A 60, R773–R776 (1999).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

J. Lugani, S. Ghosh, and K. Thyagarajan, “Generation of modal- and path-entangled photons using a domain-engineered integrated optical waveguide device,” Phys. Rev. A 83, 062333 (2011).
[CrossRef]

G. Vallone, G. Donati, R. Ceccarilli, and P. Mataloni, “Six-qubit two-photon hyperentangled cluster states: characterization and application to quantum computation,” Phys. Rev. A 81, 052301 (2010).
[CrossRef]

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[CrossRef]

R. T. Thew, S. Tanzilli, W. Tittel, H. Zbinden, and N. Gisin, “Experimental investigation of the robustness of partially entangled qubits over 11 km,” Phys. Rev. A 66, 062304 (2002).
[CrossRef]

J. Chen, J. Fan, M. D. Eisaman, and A. Migdall, “Generation of high-flux hyperentangled photon pairs using a microstructure-fiber Sagnac interferometer,” Phys. Rev. A 77, 053812 (2008).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De. Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[CrossRef]

Phys. Rev. Lett (1)

W. B. Gao, P. Xu, X. C. Yao, O. Guhne, A. Cabello, C. Y. Lu, C. Z. Peng, Z. B. Chen, and J. W. Pan, “Experimental realization of a controlled-NOT gate with four-photon six-qubit cluster states,” Phys. Rev. Lett 104, 020501 (2010).
[CrossRef]

Phys. Rev. Lett. (7)

D. Bruss and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[CrossRef]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef]

R. Ceccarelli, G. Vallone, F. De. Martini, P. Mataloni, and A. Cabello, “Experimental entanglement and nonlocality of a two-photon six-qubit cluster state,” Phys. Rev. Lett. 103, 160401 (2009).
[CrossRef]

K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel, S. Chen, A. Mair, and J. W. Pan, “Experimental realization of one-way quantum computing with two-photon four-qubit cluster states,” Phys. Rev. Lett. 99, 120503 (2007).
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[CrossRef]

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[CrossRef]

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M. A. Nielson and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2006).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Waveguide circuit for generating polarization and modal entangled photon pairs. (b) Schematic of the evolution and propagation of the field profiles in the waveguide device, for pump (solid blue), signal (dotted green), and idler (dashed red) involved in four different SPDC processes enabled for the case when the EOPM is off. (c) Four SPDC processes enabled for the case when the EOPM is on.

Fig. 2.
Fig. 2.

Modal electric field profiles for the fields involved in the SPDC processes. (a) Field profile of symmetric and antisymmetric modes at the pump wavelength. (b) Cross-sectional view of the field profiles of the pump, signal, and idler for the process in which an ordinary symmetric pump downcoverts into an ordinary symmetric signal and extraordinary symmetric idler via K1 spatial frequency (switch is off). (c) Cross-sectional view of the field profiles for the process in which an ordinary antisymmetric pump downcoverts into an ordinary symmetric signal and extraordinary antisymmetric idler via K1 spatial frequency (EOPM is on).

Fig. 3.
Fig. 3.

Modal fields of pump (black solid curve), signal (red dashed), and idler (blue dotted) at a waveguide depth of 4 μm, involved in the four SPDC processes for the case when (a) switch is off and (b) switch if on.

Fig. 4.
Fig. 4.

(a) Variation of the overlap integrals: I1/nsonie and I3/nsenio. (b) Variation of Von Neumann entropy as a function of the width of the waveguide, depth=7μm.

Fig. 5.
Fig. 5.

(a) Variation of the overlap integrals and (b) variation of Von Neumann entropy as a function of the depth of the waveguide, width=7μm.

Fig. 6.
Fig. 6.

Efficiency of the downconversion processes as a function of the signal wavelength.

Fig. 7.
Fig. 7.

(a) Propagation of |E| through the Y junction. (b) Density plot, illustrating the coupling of the symmetric mode. (c) Propagation of |E| through the Y junction. (d) Density plot, illustrating coupling of the antisymmetric mode across the Y combiner for extraordinary polarized idler.

Equations (33)

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Ep=A0up0(y,z)ei(βpxωpt),
K1=2πΛ1=ωpcnpoωscnsoωicnie,
K2=2πΛ2=ωpcnpoωscnseωicnio,
|Hs0s,Vi0i+|Hs1s,Vi1i=|Hs,Vi(|0s,0i+|1s,1i).
|Vs0s,Hi0i+|Vs1s,Hi1i=|Vs,Hi(|0s,0i+|1s,1i).
(|Hs,Vi+|Vs,Hi)(|0s,0i+|1s,1i).
|Hs0s,Vi1i+|Hs1s,Vi0i=|Hs,Vi(|0s,1i+|1s,0i).
|V0s,H1i+|V1s,H0i=|Vs,Hi(|0s,1i+|1s,0i).
(|Hs,Vi+|Vs,Hi)(|0s,1i+|1s,0i).
Ep=A0(1+i)2up0(y,z)ei(βpxωpt)+A0(1i)2up1(y,z)ei(βpxωpt),
(|Hs,Vi+|Vs,Hi)(|+s,+i+eiπ/2|s,i),
E⃗pH,0(1)=12epH,0(1)(r⃗)EpH,0(1)(ei(βpH,0(1)xωpt)+ei(βp(H),0(1)xωpt))y^,
E^sH(V),0(1)=idωsesH(V),0(1)(r⃗)ωs2ϵsH(V),0(1)L(a^sH(V),0(1)eiβsiH(V),0(1)xa^sH(V),0(1)eiβsH(V),0(1)x)n^,
E^iH(V),0(1)=idωieiH(V),0(1)(r⃗)ωi2ϵiH(V),0(1)L(a^iH(V),0(1)eiβiH(V),0(1)xa^iH(V),0(1)eiβiH(V),0(1)x)n^,
H^int=4ϵ0d31(EpH,0EsH,0EiV,0+EpH,0EsH,1EiV,1+EpH,0EsV,0EiH,0+EpH,0EsV,1EiH,1)dxdydz.
H^int=dωsdωi(EpH,0ωsωiL)0Ld31[(I1nsH,0niV,0)(a^sH,0a^iV,0ei((βpH,0βsH,0βiV,0)xωpt)+h.c)+(I2nsH,1niV,1)(a^sH,0a^iV,0ei((βpH,0βsH,1βiV,1)xωpt)+h.c)+(I3nsV,0niH,0)(a^sV,0a^iH,0ei((βpH,0βsV,0βiH,0)xωpt)+h.c)+(I4nsV,1niH,1)(a^sV,1a^iH,1ei((βpH,0βsV,1βiH,1)xωpt)+h.c)]dx,
I1=epH,0(r⃗)esH,0(r⃗)eiV,0(r⃗)dydz,
I2=epH,0(r⃗)esH,1(r⃗)eiV,1(r⃗)dydz,
I3=epH,0(r⃗)esV,0(r⃗)eiH,0(r⃗)dydz,
I4=epH,0(r⃗)esV,1(r⃗)eiH,1(r⃗)dydz.
H^int=dωsdωi(C1(a^sH,0a^iV,0+h.c)+C2(a^sH,1a^iV,1+h.c)+C3(a^sV,0a^iH,0+h.c)+C4(a^sV,1a^iH,1+h.c)),
C1=(4d31ωsωiI1EpH,0π2nsH,0niV,0)eiΔk1L2sinc(Δk1L2),C2=(4d31ωsωiI2EpH,0π2nsH,1niV,1)eiΔk2L2sinc(Δk2L2),C3=(4d31ωsωiI3EpH,0π2nsV,0niH,0)eiΔk3L2sinc(Δk3L2),C4=(4d31ωsωiI4EpH,0π2nsV,1niH,1)eiΔk4L2sinc(Δk4L2).
Δk1=K1βpH,0+βsH,0+βiV,0,Δk2=K1βpH,0+βsH,1+βiV,1,Δk3=K2βpH,0+βsV,0+βiH,0,Δk4=K2βpH,0+βsV,1+βiH,1.
H^int=dωsdωi(C1(a^sH,0a^iV,0+a^sH,1a^iV,1+h.c)+C3(a^sV,0a^iH,0+a^sV,1a^iH,1+h.c)).
|ψ(t)=eiH^intt/|0,0.
|ψ=dωsdωi(C1(|H0,V0s,i+|H1,V1s,i)+C3(|V0,H0s,i+|V1,H1s,i)),
|ψ=dωsdωi(C1(|Hs|0s|Vi|0i+|Hs|1s|Vi|1i)+C3(|Vs|0s|Hi|0i+|Vs|1s|Hi|1i))=dωsdωi(C1|Hs|Vi(|0s|0i+|1s|1i)+C3|Vs|Hi(|0s|0i+|1s|1i)).
|ψ=dωsdωi(C1|Hs|Vi+C3|Vs|Hi)(|0s|0i+|1s|1i).
S=C12C12+C32log2C12C12+C32C32C12+C32log2C32C12+C32.
|ψ=dωsdωi(C1|Hs|Vi+C3|Vs|Hi)12(|0s|1i+|1s|0i).
|ψout=dωsdωi(C1|Hs|Vi+C3|Vs|Hi)12(|+s|+i+|s|i).
n2(y,z)=nb2+2nbΔney2/w2ez2/h2;z<0=nc2;z>0,
ψt(y,z)=16αyαzπwhαz(zh)eαy2y2/w2eαz2z2/h2;z<0=0;z>0,

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