Quantum entanglement in coupled lossy waveguides

doi:10.1364/OE.18.006241

Quantum entanglement in coupled lossy waveguides

Amit Rai, Sumanta Das, and Girish Agarwal »View Author Affiliations

Optics Express, Vol. 18, Issue 6, pp. 6241-6254 (2010)
http://dx.doi.org/10.1364/OE.18.006241

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Abstract

We investigate the viability of coupled waveguides as basic units of quantum circuits. We study entanglement when the waveguides are fed in by light produced by a down-converter working either in low gain limit or under large gain. We present explicit analytical results for the measure of entanglement in terms of the logarithmic negativity for a variety of input states. We also address the effect of loss on entanglement dynamics of waveguide modes. Our results indicate that the waveguide structures are reasonably robust against the effect of loss and thus quite appropriate for quantum architectures as well as for the study of coherent phenomena like random walks. Our analysis is based on realistic structures used currently.

OCIS Codes
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

History
Original Manuscript: December 21, 2009
Manuscript Accepted: February 18, 2010
Published: March 12, 2010

Citation
Amit Rai, Sumanta Das, and Girish Agarwal, "Quantum entanglement in coupled lossy waveguides," Opt. Express 18, 6241-6254 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-6241

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References

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999). [CrossRef]
D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003). [CrossRef]
S. Longhi, "Optical analog of population trapping in the continuum: Classical and quantum interference effects," Phys. Rev. A 79, 023811 (2009). [CrossRef]
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]
Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, "Quantum and Classical Correlations in Waveguide Lattices," Phys. Rev. Lett. 102, 253904 (2009). [CrossRef] [PubMed]
U. Peschel, T. Pertsch, and F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998). [CrossRef]
T. Pertsch, P. Dannberg,W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays," Phys. Rev. Lett. 83, 4752-4755 (1999). [CrossRef]
R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot Effect in Waveguide Arrays," Phys. Rev. Lett. 95, 053902 (2005). [CrossRef] [PubMed]
S. Longhi, "Optical Bloch Oscillations and Zener Tunneling with Nonclassical Light," Phys. Rev. Lett. 101, 193902 (2008). [CrossRef] [PubMed]
A. Rai, G. S. Agarwal, and J. H. H. Perk, "Transport and quantum walk of nonclassical light in coupled waveguides," Phys. Rev. A 78, 042304 (2008). [CrossRef]
A. Rai and G. S. Agarwal, "Possibility of coherent phenomena such as Bloch oscillations with single photons via W states," Phys. Rev. A 79, 053849 (2009). [CrossRef]
A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, "Silica-on-Silicon Waveguide Quantum Circuits," Science 320, 646-649 (2008). [CrossRef] [PubMed]
J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, "Manipulation of multiphoton entanglement in waveguide quantum circuits," Nature Photonics 3, 346-350 (2009). [CrossRef]
A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit," Phys. Rev. Lett. 85, 2733-2736 (2000). [CrossRef] [PubMed]
C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000). [CrossRef] [PubMed]
W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical, " Rev. Mod. Phys. 75, 715-775 (2003). [CrossRef]
B. Do, M. L. Stohler, S. Balasubramanian, D. S. Elliott, C. Eash, E. Fischbach, M. A. Fischbach, A. Mills, and B. Zwickl, "Experimental realization of a quantum quincunx by use of linear optical elements," J. Opt. Soc. Am. B 22, 499-504 (2005). [CrossRef]
P. K. Pathak and G. S. Agarwal, "Quantum random walk of two photons in separable and entangled states," Phys. Rev. A 75, 032351 (2007). [CrossRef]
A. Politi, J. C. F. Matthews, and J. L. O’Brien, "Shors Quantum Factoring Algorithm on a Photonic Chip," Science 325, 1221 (2009). [CrossRef] [PubMed]
B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Edition, (Wiley, New York 2007), p. 319.
W. K. Lai, V. Buˇzek, and P. L. Knight, "Nonclassical fields in a linear directional coupler, " Phys. Rev. A 43, 6323-6336 (1991). [CrossRef] [PubMed]
R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of Discrete Quadratic Solitons, " Phys. Rev. Lett. 93, 113902 (2004). [CrossRef] [PubMed]
U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, "Optical Discrete Solitons in Waveguide Arrays. 2. Dynamic Properties," J. Opt. Soc. Am. B 19, 2637- 2644 (2002). [CrossRef]
K. B. Mogensen, F. Eriksson, O. Gustafsson, R. P. H. Nikolajsen, and J. P. Kutter, "Pure-silica optical waveguides, fiber couplers, and high-aspect ratio submicrometer channels for electrokinetic separation devices," Electrophoresis 25, 3788-3795 (2004). [CrossRef]
G. Vidal and R. F. Werner, "Computable measure of entanglement," Phys. Rev. A 65, 032314 (2002). [CrossRef]
C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987). [CrossRef] [PubMed]
G. S. Agarwal, "Entropy, the Wigner Distribution Function, and the Approach to Equilibrium of a System of Coupled Harmonic Oscillators, " Phys. Rev. A 3, 828-831 (1971). [CrossRef]
P. J. Dodd and J. J. Halliwell, "Disentanglement and decoherence by open system dynamics, " Phys. Rev. A 69, 052105 (2004). [CrossRef]
L. -M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability Criterion for Continuous Variable Systems," Phys. Rev. Lett. 84, 2722-2725 (2000). [CrossRef] [PubMed]
R. Simon, "Peres-Horodecki Separability Criterion for Continuous Variable Systems," Phys. Rev. Lett. 84, 2726- 2729 (2000). [CrossRef] [PubMed]
G. Adesso, A. Serafini, and F. Illuminati, "Extremal entanglement and mixedness in continuous variable systems," Phys. Rev. A 70, 022318 (2004). [CrossRef]
S. M. Barnett and P. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 2002), p. 168.
Sumanta Das and G. S. Agarwal, "Bright and dark periods in the entanglement dynamics of interacting qubits in contact with the environment," J. Phys. B 42, 141003 (2009). [CrossRef]
Sumanta Das and G. S. Agarwal, "Decoherence effects in interacting qubits under the influence of various environments," J. Phys. B 42, 205502 (2009). [CrossRef]
S. Longhi, "Transfer of light waves in optical waveguides via a continuum," Phys. Rev. A 78, 013815 (2008). [CrossRef]

Electrophoresis

K. B. Mogensen, F. Eriksson, O. Gustafsson, R. P. H. Nikolajsen, and J. P. Kutter, "Pure-silica optical waveguides, fiber couplers, and high-aspect ratio submicrometer channels for electrokinetic separation devices," Electrophoresis 25, 3788-3795 (2004). [CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

Sumanta Das and G. S. Agarwal, "Bright and dark periods in the entanglement dynamics of interacting qubits in contact with the environment," J. Phys. B 42, 141003 (2009). [CrossRef]
Sumanta Das and G. S. Agarwal, "Decoherence effects in interacting qubits under the influence of various environments," J. Phys. B 42, 205502 (2009). [CrossRef]

Nature

C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000). [CrossRef] [PubMed]

Nature (London)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003). [CrossRef]

Nature Photonics

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

Opt. Lett.

U. Peschel, T. Pertsch, and F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998). [CrossRef]

Phys. Rev. A

S. Longhi, "Optical analog of population trapping in the continuum: Classical and quantum interference effects," Phys. Rev. A 79, 023811 (2009). [CrossRef]
A. Rai, G. S. Agarwal, and J. H. H. Perk, "Transport and quantum walk of nonclassical light in coupled waveguides," Phys. Rev. A 78, 042304 (2008). [CrossRef]
A. Rai and G. S. Agarwal, "Possibility of coherent phenomena such as Bloch oscillations with single photons via W states," Phys. Rev. A 79, 053849 (2009). [CrossRef]
P. K. Pathak and G. S. Agarwal, "Quantum random walk of two photons in separable and entangled states," Phys. Rev. A 75, 032351 (2007). [CrossRef]
W. K. Lai, V. Buˇzek, and P. L. Knight, "Nonclassical fields in a linear directional coupler, " Phys. Rev. A 43, 6323-6336 (1991). [CrossRef] [PubMed]
G. Vidal and R. F. Werner, "Computable measure of entanglement," Phys. Rev. A 65, 032314 (2002). [CrossRef]
S. Longhi, "Transfer of light waves in optical waveguides via a continuum," Phys. Rev. A 78, 013815 (2008). [CrossRef]
G. Adesso, A. Serafini, and F. Illuminati, "Extremal entanglement and mixedness in continuous variable systems," Phys. Rev. A 70, 022318 (2004). [CrossRef]
G. S. Agarwal, "Entropy, the Wigner Distribution Function, and the Approach to Equilibrium of a System of Coupled Harmonic Oscillators, " Phys. Rev. A 3, 828-831 (1971). [CrossRef]
P. J. Dodd and J. J. Halliwell, "Disentanglement and decoherence by open system dynamics, " Phys. Rev. A 69, 052105 (2004). [CrossRef]

Phys. Rev. Lett.

L. -M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability Criterion for Continuous Variable Systems," Phys. Rev. Lett. 84, 2722-2725 (2000). [CrossRef] [PubMed]
R. Simon, "Peres-Horodecki Separability Criterion for Continuous Variable Systems," Phys. Rev. Lett. 84, 2726- 2729 (2000). [CrossRef] [PubMed]
C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987). [CrossRef] [PubMed]
R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999). [CrossRef]
R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of Discrete Quadratic Solitons, " Phys. Rev. Lett. 93, 113902 (2004). [CrossRef] [PubMed]
A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit," Phys. Rev. Lett. 85, 2733-2736 (2000). [CrossRef] [PubMed]
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]
Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, "Quantum and Classical Correlations in Waveguide Lattices," Phys. Rev. Lett. 102, 253904 (2009). [CrossRef] [PubMed]
T. Pertsch, P. Dannberg,W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays," Phys. Rev. Lett. 83, 4752-4755 (1999). [CrossRef]
R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot Effect in Waveguide Arrays," Phys. Rev. Lett. 95, 053902 (2005). [CrossRef] [PubMed]
S. Longhi, "Optical Bloch Oscillations and Zener Tunneling with Nonclassical Light," Phys. Rev. Lett. 101, 193902 (2008). [CrossRef] [PubMed]

Rev. Mod. Phys.

W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical, " Rev. Mod. Phys. 75, 715-775 (2003). [CrossRef]

Science

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, "Silica-on-Silicon Waveguide Quantum Circuits," Science 320, 646-649 (2008). [CrossRef] [PubMed]
A. Politi, J. C. F. Matthews, and J. L. O’Brien, "Shors Quantum Factoring Algorithm on a Photonic Chip," Science 325, 1221 (2009). [CrossRef] [PubMed]

Other

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Edition, (Wiley, New York 2007), p. 319.
S. M. Barnett and P. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 2002), p. 168.

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[1] R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999). [CrossRef]

[2] D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003). [CrossRef]

[3] S. Longhi, "Optical analog of population trapping in the continuum: Classical and quantum interference effects," Phys. Rev. A 79, 023811 (2009). [CrossRef]

[4] 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]

[5] Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, "Quantum and Classical Correlations in Waveguide Lattices," Phys. Rev. Lett. 102, 253904 (2009). [CrossRef] [PubMed]

[6] U. Peschel, T. Pertsch, and F. Lederer, "Optical Bloch oscillations in waveguide arrays," Opt. Lett. 23, 1701-1703 (1998). [CrossRef]

[7] T. Pertsch, P. Dannberg,W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays," Phys. Rev. Lett. 83, 4752-4755 (1999). [CrossRef]

[8] R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot Effect in Waveguide Arrays," Phys. Rev. Lett. 95, 053902 (2005). [CrossRef] [PubMed]

[9] S. Longhi, "Optical Bloch Oscillations and Zener Tunneling with Nonclassical Light," Phys. Rev. Lett. 101, 193902 (2008). [CrossRef] [PubMed]

[10] A. Rai, G. S. Agarwal, and J. H. H. Perk, "Transport and quantum walk of nonclassical light in coupled waveguides," Phys. Rev. A 78, 042304 (2008). [CrossRef]

[11] A. Rai and G. S. Agarwal, "Possibility of coherent phenomena such as Bloch oscillations with single photons via W states," Phys. Rev. A 79, 053849 (2009). [CrossRef]

[12] A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, "Silica-on-Silicon Waveguide Quantum Circuits," Science 320, 646-649 (2008). [CrossRef] [PubMed]

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

[14] A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, "Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit," Phys. Rev. Lett. 85, 2733-2736 (2000). [CrossRef] [PubMed]

[15] C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000). [CrossRef] [PubMed]

[16] W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical, " Rev. Mod. Phys. 75, 715-775 (2003). [CrossRef]

[17] B. Do, M. L. Stohler, S. Balasubramanian, D. S. Elliott, C. Eash, E. Fischbach, M. A. Fischbach, A. Mills, and B. Zwickl, "Experimental realization of a quantum quincunx by use of linear optical elements," J. Opt. Soc. Am. B 22, 499-504 (2005). [CrossRef]

[18] P. K. Pathak and G. S. Agarwal, "Quantum random walk of two photons in separable and entangled states," Phys. Rev. A 75, 032351 (2007). [CrossRef]

[19] A. Politi, J. C. F. Matthews, and J. L. O’Brien, "Shors Quantum Factoring Algorithm on a Photonic Chip," Science 325, 1221 (2009). [CrossRef] [PubMed]

[20] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd Edition, (Wiley, New York 2007), p. 319.

[21] W. K. Lai, V. Buˇzek, and P. L. Knight, "Nonclassical fields in a linear directional coupler, " Phys. Rev. A 43, 6323-6336 (1991). [CrossRef] [PubMed]

[22] R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of Discrete Quadratic Solitons, " Phys. Rev. Lett. 93, 113902 (2004). [CrossRef] [PubMed]

[23] U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, "Optical Discrete Solitons in Waveguide Arrays. 2. Dynamic Properties," J. Opt. Soc. Am. B 19, 2637- 2644 (2002). [CrossRef]

[24] K. B. Mogensen, F. Eriksson, O. Gustafsson, R. P. H. Nikolajsen, and J. P. Kutter, "Pure-silica optical waveguides, fiber couplers, and high-aspect ratio submicrometer channels for electrokinetic separation devices," Electrophoresis 25, 3788-3795 (2004). [CrossRef]

[25] G. Vidal and R. F. Werner, "Computable measure of entanglement," Phys. Rev. A 65, 032314 (2002). [CrossRef]

[26] C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987). [CrossRef] [PubMed]

[27] G. S. Agarwal, "Entropy, the Wigner Distribution Function, and the Approach to Equilibrium of a System of Coupled Harmonic Oscillators, " Phys. Rev. A 3, 828-831 (1971). [CrossRef]

[28] P. J. Dodd and J. J. Halliwell, "Disentanglement and decoherence by open system dynamics, " Phys. Rev. A 69, 052105 (2004). [CrossRef]

[29] L. -M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability Criterion for Continuous Variable Systems," Phys. Rev. Lett. 84, 2722-2725 (2000). [CrossRef] [PubMed]

[30] R. Simon, "Peres-Horodecki Separability Criterion for Continuous Variable Systems," Phys. Rev. Lett. 84, 2726- 2729 (2000). [CrossRef] [PubMed]

[31] G. Adesso, A. Serafini, and F. Illuminati, "Extremal entanglement and mixedness in continuous variable systems," Phys. Rev. A 70, 022318 (2004). [CrossRef]

[32] S. M. Barnett and P. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 2002), p. 168.

[33] Sumanta Das and G. S. Agarwal, "Bright and dark periods in the entanglement dynamics of interacting qubits in contact with the environment," J. Phys. B 42, 141003 (2009). [CrossRef]

[34] Sumanta Das and G. S. Agarwal, "Decoherence effects in interacting qubits under the influence of various environments," J. Phys. B 42, 205502 (2009). [CrossRef]

[35] S. Longhi, "Transfer of light waves in optical waveguides via a continuum," Phys. Rev. A 78, 013815 (2008). [CrossRef]

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Quantum entanglement in coupled lossy waveguides

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Abstract

References

Electrophoresis

J. Opt. Soc. Am. B

J. Phys. B

Nature

Nature (London)

Nature Photonics

Opt. Lett.

Phys. Rev. A

Phys. Rev. Lett.

Rev. Mod. Phys.

Science

Other

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