Directly produced three-color entanglement by quasi-phase-matched third-harmonic generation

doi:10.1364/OE.19.013949

Directly produced three-color entanglement by quasi-phase-matched third-harmonic generation

Y. B. Yu, H. J. Wang, M. Xiao, and S. N. Zhu »View Author Affiliations

Optics Express, Vol. 19, Issue 15, pp. 13949-13956 (2011)
http://dx.doi.org/10.1364/OE.19.013949

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Abstract

A new scheme is presented to directly produce fundamental, second-, and third-harmonic three-color continuous-variable (CV) entangled beams by cascaded quasi-phase-matched third-harmonic generation (THG) in an optical cavity. THG can be achieved with high efficiency through a coupled sum-frequency process between the second-harmonic and the fundamental fields. It is demonstrated that the three beams (fundamental, second-, and third-harmonic fields) are entangled with each other according to the CV entanglement criterion. In this scheme, only one crystal and one pump field can generate three-color CV entangled beams separated by an octave in frequency through quasi-phase-matched cascaded nonlinear process, which may be very useful for the applications in quantum communication and computation networks.

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(270.0270) Quantum optics : Quantum optics
(270.6570) Quantum optics : Squeezed states

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 7, 2011
Revised Manuscript: March 18, 2011
Manuscript Accepted: June 17, 2011
Published: July 7, 2011

Citation
Y. B. Yu, H. J. Wang, M. Xiao, and S. N. Zhu, "Directly produced three-color entanglement by quasi-phase-matched third-harmonic generation," Opt. Express 19, 13949-13956 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-13949

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References

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008). [CrossRef] [PubMed]
M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988). [CrossRef] [PubMed]
Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992). [CrossRef] [PubMed]
A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, “Generation of bright two-color continuous variable entanglement,” Phys. Rev. Lett. 95, 243603 (2005). [CrossRef] [PubMed]
A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006). [CrossRef] [PubMed]
A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009). [CrossRef] [PubMed]
P. Lodahl, “Einstein-Podolsky-Rosen correlations in second-harmonic generation,” Phys. Rev. A 68, 023806 (2003). [CrossRef]
M. K. Olsen, “Continuous-variable Einstein-Podolsky-Rosen paradox with traveling-wave second-harmonic generation,” Phys. Rev. A 70, 035801 (2004). [CrossRef]
N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006). [CrossRef] [PubMed]
N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008). [CrossRef] [PubMed]
S. Q. Zhai, R. G. Yang, D. H. Fan, J. Guo, K. Liu, J. X. Zhang, and J. R. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78, 014302 (2008). [CrossRef]
S. Q. Zhai, R. G. Yang, K. Liu, H. L. Zhang, J. X. Zhang, and J. R. Gao, “Bright two-color tripartite entanglement with second harmonic generation,” Opt. Express 17, 9851–9857 (2009). [CrossRef] [PubMed]
R. G. Yang, S. Q. Zhai, K. Liu, J. X. Zhang, and J. R. Gao, “Generation of multicolored tripartite entanglement by frequency doubling in a two-port resonator,” J. Opt. Soc. Am. B 27, 2721–2726 (2010). [CrossRef]
J. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]
S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997). [CrossRef]
S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997). [CrossRef]
C. W. Gardiner, Quantum Noise (Springer, 1991).
D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).
M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984). [CrossRef]
R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000). [CrossRef] [PubMed]
A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996). [CrossRef] [PubMed]
M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1–8 (1996). [CrossRef]
R. F. Werner and M. M. Wolf, “Bound entangled Gaussian states,” Phys. Rev. Lett. 86, 3658–3661 (2001). [CrossRef] [PubMed]
G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001). [CrossRef]
S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005). [CrossRef]
A. Serafini, G. Adesso, and F. Illuminati, “Unitarily localizable entanglement of Gaussian states,” Phys. Rev. A 71, 032349 (2005). [CrossRef]

J. Opt. Soc. Am. B

R. G. Yang, S. Q. Zhai, K. Liu, J. X. Zhang, and J. R. Gao, “Generation of multicolored tripartite entanglement by frequency doubling in a two-port resonator,” J. Opt. Soc. Am. B 27, 2721–2726 (2010). [CrossRef]

Nature

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008). [CrossRef] [PubMed]

Opt. Express

S. Q. Zhai, R. G. Yang, K. Liu, H. L. Zhang, J. X. Zhang, and J. R. Gao, “Bright two-color tripartite entanglement with second harmonic generation,” Opt. Express 17, 9851–9857 (2009). [CrossRef] [PubMed]

Phys. Lett. A

M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1–8 (1996). [CrossRef]

Phys. Rev.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]

Phys. Rev. A

S. Q. Zhai, R. G. Yang, D. H. Fan, J. Guo, K. Liu, J. X. Zhang, and J. R. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78, 014302 (2008). [CrossRef]
M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984). [CrossRef]
P. Lodahl, “Einstein-Podolsky-Rosen correlations in second-harmonic generation,” Phys. Rev. A 68, 023806 (2003). [CrossRef]
M. K. Olsen, “Continuous-variable Einstein-Podolsky-Rosen paradox with traveling-wave second-harmonic generation,” Phys. Rev. A 70, 035801 (2004). [CrossRef]
G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001). [CrossRef]
A. Serafini, G. Adesso, and F. Illuminati, “Unitarily localizable entanglement of Gaussian states,” Phys. Rev. A 71, 032349 (2005). [CrossRef]

Phys. Rev. Lett.

R. F. Werner and M. M. Wolf, “Bound entangled Gaussian states,” Phys. Rev. Lett. 86, 3658–3661 (2001). [CrossRef] [PubMed]
N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006). [CrossRef] [PubMed]
N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008). [CrossRef] [PubMed]
M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988). [CrossRef] [PubMed]
Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992). [CrossRef] [PubMed]
A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, “Generation of bright two-color continuous variable entanglement,” Phys. Rev. Lett. 95, 243603 (2005). [CrossRef] [PubMed]
A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006). [CrossRef] [PubMed]
R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000). [CrossRef] [PubMed]
A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996). [CrossRef] [PubMed]
S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997). [CrossRef]

Rev. Mod. Phys.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005). [CrossRef]

Science

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997). [CrossRef]
A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009). [CrossRef] [PubMed]

Other

C. W. Gardiner, Quantum Noise (Springer, 1991).
D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

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[1] H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008). [CrossRef] [PubMed]

[2] M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988). [CrossRef] [PubMed]

[3] Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992). [CrossRef] [PubMed]

[4] A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, “Generation of bright two-color continuous variable entanglement,” Phys. Rev. Lett. 95, 243603 (2005). [CrossRef] [PubMed]

[5] A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006). [CrossRef] [PubMed]

[6] A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009). [CrossRef] [PubMed]

[7] P. Lodahl, “Einstein-Podolsky-Rosen correlations in second-harmonic generation,” Phys. Rev. A 68, 023806 (2003). [CrossRef]

[8] M. K. Olsen, “Continuous-variable Einstein-Podolsky-Rosen paradox with traveling-wave second-harmonic generation,” Phys. Rev. A 70, 035801 (2004). [CrossRef]

[9] N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006). [CrossRef] [PubMed]

[10] N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008). [CrossRef] [PubMed]

[11] S. Q. Zhai, R. G. Yang, D. H. Fan, J. Guo, K. Liu, J. X. Zhang, and J. R. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78, 014302 (2008). [CrossRef]

[12] S. Q. Zhai, R. G. Yang, K. Liu, H. L. Zhang, J. X. Zhang, and J. R. Gao, “Bright two-color tripartite entanglement with second harmonic generation,” Opt. Express 17, 9851–9857 (2009). [CrossRef] [PubMed]

[13] R. G. Yang, S. Q. Zhai, K. Liu, J. X. Zhang, and J. R. Gao, “Generation of multicolored tripartite entanglement by frequency doubling in a two-port resonator,” J. Opt. Soc. Am. B 27, 2721–2726 (2010). [CrossRef]

[14] J. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]

[15] S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752–2755 (1997). [CrossRef]

[16] S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997). [CrossRef]

[17] C. W. Gardiner, Quantum Noise (Springer, 1991).

[18] D. F. Walls and G. J. Milburn, Quantum Optics (Springer, 1994).

[19] M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984). [CrossRef]

[20] R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000). [CrossRef] [PubMed]

[21] A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett. 77, 1413–1415 (1996). [CrossRef] [PubMed]

[22] M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,” Phys. Lett. A 223, 1–8 (1996). [CrossRef]

[23] R. F. Werner and M. M. Wolf, “Bound entangled Gaussian states,” Phys. Rev. Lett. 86, 3658–3661 (2001). [CrossRef] [PubMed]

[24] G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001). [CrossRef]

[25] S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005). [CrossRef]

[26] A. Serafini, G. Adesso, and F. Illuminati, “Unitarily localizable entanglement of Gaussian states,” Phys. Rev. A 71, 032349 (2005). [CrossRef]

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Directly produced three-color entanglement by quasi-phase-matched third-harmonic generation

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J. Opt. Soc. Am. B

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