Abstract

We present an alternative scheme for the generation of the entangled microwave radiation with amplification in single triple-Λ five-level molecular magnets driven by two strong control fields and one relative weak pump field. By numerically simulating the dynamics of the system, we show that three fully entangled modes with different frequencies can be obtained in the presence of the relaxations. Our numerical results also show that the entanglement occurs among the three cavity fields with a large number of photons. Physically, the responsible mechanism is quantum coherence. Two strong control fields induce two cavity modes coupled with the strong-driven levels to a quantum beat, and then the relative weak pump field leads to the parametric interaction between such a beat with the third mode coupled with the weak-driven level. The present work provides an efficient approach to achieve tripartite continuous-variable entanglement in the molecular magnets system, which may be necessary for the progress of solid-state quantum information.

© 2012 Optical Society of America

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  4. J. Zhang, C. D. Xie, and K. C. Peng, “Continuous-variable telecloning with phase-conjugate inputs,” Phys. Rev. A 77, 022316 (2008).
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  5. J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
    [CrossRef]
  6. T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
    [CrossRef]
  7. X. L. Su, A. H. Tan, X. J. Jia, J. Zhang, C. D. Xie, and K. C. Peng, “Experimental preparation of quadripartite cluster and Greenberger–Horne–Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
    [CrossRef]
  8. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
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  10. G. Keller, V. D’Auria, N. Treps, T. Coudreau, J. Laurat, and C. Fabre, “Experimental demonstration of frequency-degenerate bright EPR beams with a self-phase-locked OPO,” Opt. Express 16, 9351–9356 (2008).
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  11. M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
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  12. H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuous-variable quadripartite entanglement by intracavity down-conversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
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  21. X. Y. Lü, J. B. Liu, L. G. Si, and X. X. Yang, “Continuous-variable entanglement in a two-mode four-level single-atom laser,” J. Phys. B 41, 035501 (2008).
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  22. X. Y. Lü, J. B. Liu, Yü Tian, P. J. Song, and Z. M. Zhan, “Single molecular magnets as a source of continuous-variable entanglement,” Europhys. Lett. 82, 64003 (2008).
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  23. X. M. Hu, and J. H. Zou, “Quantum-beat lasers as bright sources of entangled sub-Poissonian light,” Phys. Rev. A 78, 045801 (2008).
    [CrossRef]
  24. X. Y. Zhao, Y. H. Ma, and L. Zhou, “Generation of multi-mode-entangled light,” Opt. Commun. 282, 1593–1597 (2009).
    [CrossRef]
  25. X. X. Li and X. M. Hu, “Tripartite entanglement in quantum-beat lasers,” Phys. Rev. A 80, 023815 (2009).
    [CrossRef]
  26. X. Y. Lü, P. Huang, W. X. Yang, and X. X. Yang, “Entanglement via atomic coherence induced by two strong classical fields,” Phys. Rev. A 80, 032305 (2009).
    [CrossRef]
  27. G. X. Li, H. T. Tan, and M. Macovei, “Enhancement of entanglement for two-mode fields generated from four-wave mixing with the help of the auxiliary atomic transition,” Phys. Rev. A 76, 053827 (2007).
    [CrossRef]
  28. Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
    [CrossRef]
  29. S. Pielawa, G. Morigi, D. Vitali, and L. Davidovich, “Generation of Einstein–Podolsky–Rosen-entangled radiation through an atomic reservoir,” Phys. Rev. Lett. 98, 240401 (2007).
    [CrossRef]
  30. S. W. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
    [CrossRef]
  31. G. L. Cheng, X. M. Hu, W. X. Zhong, and Q. Li, “Two-channel interaction of squeeze-transformed modes with dressed atoms: entanglement enhancement in four-wave mixing in three-level systems,” Phys. Rev. A 78, 033811 (2008).
    [CrossRef]
  32. W. X. Shi, X. M. Hu, J. Y. Li, and F. Wang, “Entanglement of three-mode light via six-wave mixing in a four-level Y-type atomic system,” J. Phys. B 43, 155506 (2010).
    [CrossRef]
  33. X. M. Hu, H. Sun, and F. Wang, “Scalable network of quadrangle entanglements via multiple phase-dependent electromagnetically induced transparency,” Phys. Rev. A 82, 045807 (2010).
    [CrossRef]
  34. M. N. Leuenberger and D. Loss, “Quantum computing in molecular magnets,” Nature 410, 789–793 (2001).
    [CrossRef]
  35. A. Ardavan, O. Rival, J. J. L. Morton, S. J. Blundell, A. M. Tyryshkin, G. A. Timco, and R. E. P. Winpenny, “Will spin-relaxation times in molecular magnets permit quantum information processing,” Phys. Rev. Lett. 98, 057201 (2007).
    [CrossRef]
  36. E. M. Chudnovsky, and D. A. Garanin, “Spin tunneling via dislocations in Mn12 acetate crystals,” Phys. Rev. Lett. 87, 187203 (2001).
    [CrossRef]
  37. A. V. Shvetsov, G. A. Vugalter, and A. I. Grebeneva, “Theoretical investigation of electromagnetically induced transparency in a crystal of molecular magnets,” Phys. Rev. B 74, 054416 (2006).
    [CrossRef]
  38. E. M. Chudnovsky and D. A. Garanin, “Phonon superradiance and phonon laser effect in nanomagnets,” Phys. Rev. Lett. 93, 257205 (2004).
    [CrossRef]
  39. I. D. Tokman, G. A. Vugalter, and A. I. Grebeneva, “Parametric interaction of two acoustic waves in a crystal of molecular magnets in the presence of a strong ac magnetic field,” Phys. Rev. B 71, 094431 (2005).
    [CrossRef]
  40. X. T. Xie, W. Li, J. Li, W. X. Yang, A. Yuan, and X. X. Yang, “Transverse acoustic wave in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 75, 184423 (2007).
    [CrossRef]
  41. Y. Wu and X. X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).
    [CrossRef]
  42. Y. Wu and X. X. Yang, “Giant Kerr nonlinearities and solitons in a crystal of molecular magnets,” Appl. Phys. Lett. 91, 094104 (2007).
    [CrossRef]
  43. S. Bertaina, S. Gambarelli, T. Mitra, B. Tsukerblat, A. Mller, and B. Barbara, “Quantum oscillations in a molecular magnet,” Nature 453, 203–206 (2008).
    [CrossRef]
  44. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).
  45. Y. Wu, L. L. Wen, and Y. F. Zhu, “Efficient hyper-Raman scattering in resonant coherent medium,” Opt. Lett. 28, 631–633(2003).
    [CrossRef]
  46. Y. Wu and X. X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70, 053818 (2004).
    [CrossRef]
  47. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1992).
  48. P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
    [CrossRef]

2011 (1)

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

2010 (2)

W. X. Shi, X. M. Hu, J. Y. Li, and F. Wang, “Entanglement of three-mode light via six-wave mixing in a four-level Y-type atomic system,” J. Phys. B 43, 155506 (2010).
[CrossRef]

X. M. Hu, H. Sun, and F. Wang, “Scalable network of quadrangle entanglements via multiple phase-dependent electromagnetically induced transparency,” Phys. Rev. A 82, 045807 (2010).
[CrossRef]

2009 (4)

X. Y. Zhao, Y. H. Ma, and L. Zhou, “Generation of multi-mode-entangled light,” Opt. Commun. 282, 1593–1597 (2009).
[CrossRef]

X. X. Li and X. M. Hu, “Tripartite entanglement in quantum-beat lasers,” Phys. Rev. A 80, 023815 (2009).
[CrossRef]

X. Y. Lü, P. Huang, W. X. Yang, and X. X. Yang, “Entanglement via atomic coherence induced by two strong classical fields,” Phys. Rev. A 80, 032305 (2009).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuous-variable quadripartite entanglement by intracavity down-conversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

2008 (9)

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. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, “Quantum beat laser as a source of entangled radiation,” Phys. Rev. A 77, 062308 (2008).
[CrossRef]

J. Zhang, C. D. Xie, and K. C. Peng, “Continuous-variable telecloning with phase-conjugate inputs,” Phys. Rev. A 77, 022316 (2008).
[CrossRef]

G. Keller, V. D’Auria, N. Treps, T. Coudreau, J. Laurat, and C. Fabre, “Experimental demonstration of frequency-degenerate bright EPR beams with a self-phase-locked OPO,” Opt. Express 16, 9351–9356 (2008).
[CrossRef]

X. Y. Lü, J. B. Liu, L. G. Si, and X. X. Yang, “Continuous-variable entanglement in a two-mode four-level single-atom laser,” J. Phys. B 41, 035501 (2008).
[CrossRef]

X. Y. Lü, J. B. Liu, Yü Tian, P. J. Song, and Z. M. Zhan, “Single molecular magnets as a source of continuous-variable entanglement,” Europhys. Lett. 82, 64003 (2008).
[CrossRef]

X. M. Hu, and J. H. Zou, “Quantum-beat lasers as bright sources of entangled sub-Poissonian light,” Phys. Rev. A 78, 045801 (2008).
[CrossRef]

G. L. Cheng, X. M. Hu, W. X. Zhong, and Q. Li, “Two-channel interaction of squeeze-transformed modes with dressed atoms: entanglement enhancement in four-wave mixing in three-level systems,” Phys. Rev. A 78, 033811 (2008).
[CrossRef]

S. Bertaina, S. Gambarelli, T. Mitra, B. Tsukerblat, A. Mller, and B. Barbara, “Quantum oscillations in a molecular magnet,” Nature 453, 203–206 (2008).
[CrossRef]

2007 (11)

X. T. Xie, W. Li, J. Li, W. X. Yang, A. Yuan, and X. X. Yang, “Transverse acoustic wave in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 75, 184423 (2007).
[CrossRef]

Y. Wu and X. X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).
[CrossRef]

Y. Wu and X. X. Yang, “Giant Kerr nonlinearities and solitons in a crystal of molecular magnets,” Appl. Phys. Lett. 91, 094104 (2007).
[CrossRef]

M. Kiffner, M. S. Zubairy, J. Evers, and C. H. Keitel, “Two-mode single-atom laser as a source of entangled light,” Phys. Rev. A 75, 033816 (2007).
[CrossRef]

A. Ardavan, O. Rival, J. J. L. Morton, S. J. Blundell, A. M. Tyryshkin, G. A. Timco, and R. E. P. Winpenny, “Will spin-relaxation times in molecular magnets permit quantum information processing,” Phys. Rev. Lett. 98, 057201 (2007).
[CrossRef]

S. Pielawa, G. Morigi, D. Vitali, and L. Davidovich, “Generation of Einstein–Podolsky–Rosen-entangled radiation through an atomic reservoir,” Phys. Rev. Lett. 98, 240401 (2007).
[CrossRef]

S. W. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
[CrossRef]

G. X. Li, H. T. Tan, and M. Macovei, “Enhancement of entanglement for two-mode fields generated from four-wave mixing with the help of the auxiliary atomic transition,” Phys. Rev. A 76, 053827 (2007).
[CrossRef]

C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

X. L. Su, A. H. Tan, X. J. Jia, J. Zhang, C. D. Xie, and K. C. Peng, “Experimental preparation of quadripartite cluster and Greenberger–Horne–Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

H. T. Tan and G. X. Li, “Macroscopic three-mode squeezed and fully inseparable entangled beams from triply coupled intracavity Kerr nonlinearities,” Phys. Rev. A 75, 063815 (2007).
[CrossRef]

2006 (3)

L. Zhou, H. Xiong, and M. S. Zubairy, “Single atom as a macroscopic entanglement source,” Phys. Rev. A 74, 022321(2006).
[CrossRef]

M. K. Olsen and A. S. Bradley, “Asymmetric polychromatic tripartite entanglement from interlinked χ(2) parametric interactions,” Phys. Rev. A 74, 063809 (2006).
[CrossRef]

A. V. Shvetsov, G. A. Vugalter, and A. I. Grebeneva, “Theoretical investigation of electromagnetically induced transparency in a crystal of molecular magnets,” Phys. Rev. B 74, 054416 (2006).
[CrossRef]

2005 (4)

H. Xiong, M. O. Scully, and M. S. Zubairy, “Correlated spontaneous emission laser as an entanglement amplifier,” Phys. Rev. Lett. 94, 023601 (2005).
[CrossRef]

H. T. Tan, S. Y. Zhu, and M. S. Zubairy, “Continuous-variable entanglement in a correlated spontaneous emission laser,” Phys. Rev. A 72, 022305 (2005).
[CrossRef]

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

I. D. Tokman, G. A. Vugalter, and A. I. Grebeneva, “Parametric interaction of two acoustic waves in a crystal of molecular magnets in the presence of a strong ac magnetic field,” Phys. Rev. B 71, 094431 (2005).
[CrossRef]

2004 (3)

Y. Wu and X. X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70, 053818 (2004).
[CrossRef]

E. M. Chudnovsky and D. A. Garanin, “Phonon superradiance and phonon laser effect in nanomagnets,” Phys. Rev. Lett. 93, 257205 (2004).
[CrossRef]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
[CrossRef]

2003 (4)

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[CrossRef]

Y. Wu, L. L. Wen, and Y. F. Zhu, “Efficient hyper-Raman scattering in resonant coherent medium,” Opt. Lett. 28, 631–633(2003).
[CrossRef]

2001 (2)

E. M. Chudnovsky, and D. A. Garanin, “Spin tunneling via dislocations in Mn12 acetate crystals,” Phys. Rev. Lett. 87, 187203 (2001).
[CrossRef]

M. N. Leuenberger and D. Loss, “Quantum computing in molecular magnets,” Nature 410, 789–793 (2001).
[CrossRef]

2000 (1)

P. van Loock, P. van Loock, and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[CrossRef]

1998 (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Aoki, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

Ardavan, A.

A. Ardavan, O. Rival, J. J. L. Morton, S. J. Blundell, A. M. Tyryshkin, G. A. Timco, and R. E. P. Winpenny, “Will spin-relaxation times in molecular magnets permit quantum information processing,” Phys. Rev. Lett. 98, 057201 (2007).
[CrossRef]

Barbara, B.

S. Bertaina, S. Gambarelli, T. Mitra, B. Tsukerblat, A. Mller, and B. Barbara, “Quantum oscillations in a molecular magnet,” Nature 453, 203–206 (2008).
[CrossRef]

Bertaina, S.

S. Bertaina, S. Gambarelli, T. Mitra, B. Tsukerblat, A. Mller, and B. Barbara, “Quantum oscillations in a molecular magnet,” Nature 453, 203–206 (2008).
[CrossRef]

Bloomer, R.

M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

Blundell, S. J.

A. Ardavan, O. Rival, J. J. L. Morton, S. J. Blundell, A. M. Tyryshkin, G. A. Timco, and R. E. P. Winpenny, “Will spin-relaxation times in molecular magnets permit quantum information processing,” Phys. Rev. Lett. 98, 057201 (2007).
[CrossRef]

Bradley, A. S.

C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

M. K. Olsen and A. S. Bradley, “Asymmetric polychromatic tripartite entanglement from interlinked χ(2) parametric interactions,” Phys. Rev. A 74, 063809 (2006).
[CrossRef]

Braunstein, S. L.

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

P. van Loock, P. van Loock, and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[CrossRef]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Cheng, G. L.

G. L. Cheng, X. M. Hu, W. X. Zhong, and Q. Li, “Two-channel interaction of squeeze-transformed modes with dressed atoms: entanglement enhancement in four-wave mixing in three-level systems,” Phys. Rev. A 78, 033811 (2008).
[CrossRef]

Chuang, I.

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Chudnovsky, E. M.

E. M. Chudnovsky and D. A. Garanin, “Phonon superradiance and phonon laser effect in nanomagnets,” Phys. Rev. Lett. 93, 257205 (2004).
[CrossRef]

E. M. Chudnovsky, and D. A. Garanin, “Spin tunneling via dislocations in Mn12 acetate crystals,” Phys. Rev. Lett. 87, 187203 (2001).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1992).

Coudreau, T.

D’Auria, V.

Davidovich, L.

S. Pielawa, G. Morigi, D. Vitali, and L. Davidovich, “Generation of Einstein–Podolsky–Rosen-entangled radiation through an atomic reservoir,” Phys. Rev. Lett. 98, 240401 (2007).
[CrossRef]

Deng, L.

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
[CrossRef]

Du, S. W.

S. W. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
[CrossRef]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1992).

Evers, J.

M. Kiffner, M. S. Zubairy, J. Evers, and C. H. Keitel, “Two-mode single-atom laser as a source of entangled light,” Phys. Rev. A 75, 033816 (2007).
[CrossRef]

Fabre, C.

Fan, D. H.

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]

Fuchs, C. A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Furusawa, A.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[CrossRef]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

Gambarelli, S.

S. Bertaina, S. Gambarelli, T. Mitra, B. Tsukerblat, A. Mller, and B. Barbara, “Quantum oscillations in a molecular magnet,” Nature 453, 203–206 (2008).
[CrossRef]

Gao, J. R.

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]

Garanin, D. A.

E. M. Chudnovsky and D. A. Garanin, “Phonon superradiance and phonon laser effect in nanomagnets,” Phys. Rev. Lett. 93, 257205 (2004).
[CrossRef]

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Y. Wu and X. X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).
[CrossRef]

Y. Wu and X. X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70, 053818 (2004).
[CrossRef]

Yonezawa, H.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

Yu, X. Q.

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuous-variable quadripartite entanglement by intracavity down-conversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Yu, Y. B.

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuous-variable quadripartite entanglement by intracavity down-conversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Yuan, A.

X. T. Xie, W. Li, J. Li, W. X. Yang, A. Yuan, and X. X. Yang, “Transverse acoustic wave in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 75, 184423 (2007).
[CrossRef]

Zhai, S. Q.

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]

Zhan, Z. M.

X. Y. Lü, J. B. Liu, Yü Tian, P. J. Song, and Z. M. Zhan, “Single molecular magnets as a source of continuous-variable entanglement,” Europhys. Lett. 82, 64003 (2008).
[CrossRef]

Zhang, J.

J. Zhang, C. D. Xie, and K. C. Peng, “Continuous-variable telecloning with phase-conjugate inputs,” Phys. Rev. A 77, 022316 (2008).
[CrossRef]

X. L. Su, A. H. Tan, X. J. Jia, J. Zhang, C. D. Xie, and K. C. Peng, “Experimental preparation of quadripartite cluster and Greenberger–Horne–Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

Zhang, J. X.

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]

Zhao, F. G.

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

Zhao, J. S.

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuous-variable quadripartite entanglement by intracavity down-conversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Zhao, X. Y.

X. Y. Zhao, Y. H. Ma, and L. Zhou, “Generation of multi-mode-entangled light,” Opt. Commun. 282, 1593–1597 (2009).
[CrossRef]

Zhong, W. X.

G. L. Cheng, X. M. Hu, W. X. Zhong, and Q. Li, “Two-channel interaction of squeeze-transformed modes with dressed atoms: entanglement enhancement in four-wave mixing in three-level systems,” Phys. Rev. A 78, 033811 (2008).
[CrossRef]

Zhou, L.

X. Y. Zhao, Y. H. Ma, and L. Zhou, “Generation of multi-mode-entangled light,” Opt. Commun. 282, 1593–1597 (2009).
[CrossRef]

L. Zhou, H. Xiong, and M. S. Zubairy, “Single atom as a macroscopic entanglement source,” Phys. Rev. A 74, 022321(2006).
[CrossRef]

Zhu, S. N.

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuous-variable quadripartite entanglement by intracavity down-conversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Zhu, S. Y.

H. T. Tan, S. Y. Zhu, and M. S. Zubairy, “Continuous-variable entanglement in a correlated spontaneous emission laser,” Phys. Rev. A 72, 022305 (2005).
[CrossRef]

Zhu, Y. F.

Zou, J. H.

X. M. Hu, and J. H. Zou, “Quantum-beat lasers as bright sources of entangled sub-Poissonian light,” Phys. Rev. A 78, 045801 (2008).
[CrossRef]

Zubairy, M. S.

S. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, “Quantum beat laser as a source of entangled radiation,” Phys. Rev. A 77, 062308 (2008).
[CrossRef]

M. Kiffner, M. S. Zubairy, J. Evers, and C. H. Keitel, “Two-mode single-atom laser as a source of entangled light,” Phys. Rev. A 75, 033816 (2007).
[CrossRef]

L. Zhou, H. Xiong, and M. S. Zubairy, “Single atom as a macroscopic entanglement source,” Phys. Rev. A 74, 022321(2006).
[CrossRef]

H. T. Tan, S. Y. Zhu, and M. S. Zubairy, “Continuous-variable entanglement in a correlated spontaneous emission laser,” Phys. Rev. A 72, 022305 (2005).
[CrossRef]

H. Xiong, M. O. Scully, and M. S. Zubairy, “Correlated spontaneous emission laser as an entanglement amplifier,” Phys. Rev. Lett. 94, 023601 (2005).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Appl. Phys. Lett. (1)

Y. Wu and X. X. Yang, “Giant Kerr nonlinearities and solitons in a crystal of molecular magnets,” Appl. Phys. Lett. 91, 094104 (2007).
[CrossRef]

Europhys. Lett. (1)

X. Y. Lü, J. B. Liu, Yü Tian, P. J. Song, and Z. M. Zhan, “Single molecular magnets as a source of continuous-variable entanglement,” Europhys. Lett. 82, 64003 (2008).
[CrossRef]

J. Phys. B (2)

W. X. Shi, X. M. Hu, J. Y. Li, and F. Wang, “Entanglement of three-mode light via six-wave mixing in a four-level Y-type atomic system,” J. Phys. B 43, 155506 (2010).
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X. Y. Lü, J. B. Liu, L. G. Si, and X. X. Yang, “Continuous-variable entanglement in a two-mode four-level single-atom laser,” J. Phys. B 41, 035501 (2008).
[CrossRef]

Nature (2)

S. Bertaina, S. Gambarelli, T. Mitra, B. Tsukerblat, A. Mller, and B. Barbara, “Quantum oscillations in a molecular magnet,” Nature 453, 203–206 (2008).
[CrossRef]

M. N. Leuenberger and D. Loss, “Quantum computing in molecular magnets,” Nature 410, 789–793 (2001).
[CrossRef]

Opt. Commun. (1)

X. Y. Zhao, Y. H. Ma, and L. Zhou, “Generation of multi-mode-entangled light,” Opt. Commun. 282, 1593–1597 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (20)

Y. Wu and X. X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70, 053818 (2004).
[CrossRef]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[CrossRef]

X. M. Hu, and J. H. Zou, “Quantum-beat lasers as bright sources of entangled sub-Poissonian light,” Phys. Rev. A 78, 045801 (2008).
[CrossRef]

X. X. Li and X. M. Hu, “Tripartite entanglement in quantum-beat lasers,” Phys. Rev. A 80, 023815 (2009).
[CrossRef]

X. Y. Lü, P. Huang, W. X. Yang, and X. X. Yang, “Entanglement via atomic coherence induced by two strong classical fields,” Phys. Rev. A 80, 032305 (2009).
[CrossRef]

G. X. Li, H. T. Tan, and M. Macovei, “Enhancement of entanglement for two-mode fields generated from four-wave mixing with the help of the auxiliary atomic transition,” Phys. Rev. A 76, 053827 (2007).
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Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
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X. M. Hu, H. Sun, and F. Wang, “Scalable network of quadrangle entanglements via multiple phase-dependent electromagnetically induced transparency,” Phys. Rev. A 82, 045807 (2010).
[CrossRef]

S. W. Du, E. Oh, J. M. Wen, and M. H. Rubin, “Four-wave mixing in three-level systems: interference and entanglement,” Phys. Rev. A 76, 013803 (2007).
[CrossRef]

G. L. Cheng, X. M. Hu, W. X. Zhong, and Q. Li, “Two-channel interaction of squeeze-transformed modes with dressed atoms: entanglement enhancement in four-wave mixing in three-level systems,” Phys. Rev. A 78, 033811 (2008).
[CrossRef]

J. Zhang, C. D. Xie, and K. C. Peng, “Continuous-variable telecloning with phase-conjugate inputs,” Phys. Rev. A 77, 022316 (2008).
[CrossRef]

C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity down-conversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuous-variable quadripartite entanglement by intracavity down-conversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

M. K. Olsen and A. S. Bradley, “Asymmetric polychromatic tripartite entanglement from interlinked χ(2) parametric interactions,” Phys. Rev. A 74, 063809 (2006).
[CrossRef]

H. T. Tan and G. X. Li, “Macroscopic three-mode squeezed and fully inseparable entangled beams from triply coupled intracavity Kerr nonlinearities,” Phys. Rev. A 75, 063815 (2007).
[CrossRef]

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. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, “Quantum beat laser as a source of entangled radiation,” Phys. Rev. A 77, 062308 (2008).
[CrossRef]

H. T. Tan, S. Y. Zhu, and M. S. Zubairy, “Continuous-variable entanglement in a correlated spontaneous emission laser,” Phys. Rev. A 72, 022305 (2005).
[CrossRef]

L. Zhou, H. Xiong, and M. S. Zubairy, “Single atom as a macroscopic entanglement source,” Phys. Rev. A 74, 022321(2006).
[CrossRef]

M. Kiffner, M. S. Zubairy, J. Evers, and C. H. Keitel, “Two-mode single-atom laser as a source of entangled light,” Phys. Rev. A 75, 033816 (2007).
[CrossRef]

Phys. Rev. B (4)

A. V. Shvetsov, G. A. Vugalter, and A. I. Grebeneva, “Theoretical investigation of electromagnetically induced transparency in a crystal of molecular magnets,” Phys. Rev. B 74, 054416 (2006).
[CrossRef]

I. D. Tokman, G. A. Vugalter, and A. I. Grebeneva, “Parametric interaction of two acoustic waves in a crystal of molecular magnets in the presence of a strong ac magnetic field,” Phys. Rev. B 71, 094431 (2005).
[CrossRef]

X. T. Xie, W. Li, J. Li, W. X. Yang, A. Yuan, and X. X. Yang, “Transverse acoustic wave in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 75, 184423 (2007).
[CrossRef]

Y. Wu and X. X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).
[CrossRef]

Phys. Rev. Lett. (10)

E. M. Chudnovsky and D. A. Garanin, “Phonon superradiance and phonon laser effect in nanomagnets,” Phys. Rev. Lett. 93, 257205 (2004).
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A. Ardavan, O. Rival, J. J. L. Morton, S. J. Blundell, A. M. Tyryshkin, G. A. Timco, and R. E. P. Winpenny, “Will spin-relaxation times in molecular magnets permit quantum information processing,” Phys. Rev. Lett. 98, 057201 (2007).
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E. M. Chudnovsky, and D. A. Garanin, “Spin tunneling via dislocations in Mn12 acetate crystals,” Phys. Rev. Lett. 87, 187203 (2001).
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S. Pielawa, G. Morigi, D. Vitali, and L. Davidovich, “Generation of Einstein–Podolsky–Rosen-entangled radiation through an atomic reservoir,” Phys. Rev. Lett. 98, 240401 (2007).
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M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, and O. Pfister, “Parallel generation of quadripartite cluster entanglement in the optical frequency comb,” Phys. Rev. Lett. 107, 030505 (2011).
[CrossRef]

H. Xiong, M. O. Scully, and M. S. Zubairy, “Correlated spontaneous emission laser as an entanglement amplifier,” Phys. Rev. Lett. 94, 023601 (2005).
[CrossRef]

P. van Loock, P. van Loock, and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
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J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

X. L. Su, A. H. Tan, X. J. Jia, J. Zhang, C. D. Xie, and K. C. Peng, “Experimental preparation of quadripartite cluster and Greenberger–Horne–Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef]

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Science (1)

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M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

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Figures (4)

Fig. 1.
Fig. 1.

(a) A magnetic molecule (M) with the easy anisotropy axis z in a dc magnetic field H0 parallel to the x axis. All the magnetic fields propagate along the z axis, and Hp, Hc1, U3 are polarized along the x axis and Hc2, U1, U2 are polarized along the y axis. (b) The full-resonant five-level molecular system. Three classical electromagnetic fields with frequencies ωp, ωc1, ωc2 are, respectively, applied to the molecular transitions |0|2, |1|3, and |1|4, and three cavity modes with frequencies ν1, ν2, and ν3 are coupled with the transitions |1|2, |0|3, and |0|4, respectively.

Fig. 2.
Fig. 2.

The correlation spectra V12, V13, V23 (a), and the average photon numbers Nl (l=13) of every cavity mode (b) as functions of the time evolution γt, when three cavity modes are initially in the coherent state |10,10,10. The parameters are chosen as κ=0.001, g=1, Ωp=2.5, Ωc1=25, and Ωc2=20.

Fig. 3.
Fig. 3.

The time evolution of correlation spectra V12, V13, V23 (a), and the average photon numbers Nl (l=13) of every cavity mode (b) when the mode 1 is initially in the squeezed vacuum state S(r)|0, the mode 2 is in the coherent state |10, and the mode 3 is in the vacuum state |0. The parameters are given by κ=0.001, g=1, r=1, Ωp=2, Ωc1=20, and Ωc2=25.

Fig. 4.
Fig. 4.

The correlation spectra V12, V13, V23 (a), and the average photon numbers Nl (l=13) of every cavity mode (b) as functions of the time evolution γt, when three cavity modes are initially in the coherent state |10,10,10. The parameters are the same as in Fig. 2 except for Ωp=3.5.

Equations (29)

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H^=H^0S+H^0F+V^D+V^C,
H^0S=DS^z2+H^trgμBS^xH0,
H^0F=l=13νlalal,
V^D=gBμB2j=p,c1,c2S^·Hjeiωjt+H.c.,
V^C=gBμB2l=13S^·Ulal+H.c.,
H^D=Ωpσ20Ωc1σ31Ωc2σ41+H.c.,
H^C=g1a1σ21+g2a2σ30+g3a3σ40+H.c.,
|+=12(cosθ|3+sinθ|4+|1),|=12(cosθ|3+sinθ|4|1),|0=sinθ|3+cosθ|4,
H^C=g1a1(σ2+σ2)/2+(g2a2cosθ+g3a3sinθ)(σ+0+σ0)/2+(g2a2sinθ+g3a3cosθ)σ00/2+H.c..
ρ˙f=l=1,2,3[αll(alρfalρfalal)+(βll+κl/2)(alρfalalalρf)]+l=2,3[α1l(a1ρfalρfala1)β1l(a1alρfalρfa1)]+l=2,3[αl1(alρfa1ρfa1al)βl1(ala1ρfa1ρfal)]+l,m=2,3;lm[αlm(alρfamρfamal)βlm(alamρfamρfal)]+.H.c.
V12=V(X1X2)+V(Y1+Y2+Y3)<4,V13=V(X1X3)+V(Y1+Y2+Y3)<4,V23=V(X2X3)+V(Y1+Y2+Y3)<4.
α11=g122D[(γ2+iΩc)ρ22(0)iΩpρ02(0)]+c.c,
β11=g122D(γ2+iΩc)ρ(0)+c.c,
α22=g22cos2θ2D(3γ2+iΩc)ρ++(0)+c.c,
β22=g22cos2θ2D[(3γ2+iΩc2Dsin2θγcos2θ)ρ00(0)+iΩpρ02(0)]+c.c,
α33=g32sin2θ2D(3γ2+iΩc)ρ++(0)+c.c,
β33=g32sin2θ2D[(3γ2+iΩc2Dcos2θγsin2θ)ρ00(0)+iΩpρ02(0)]+c.c,
α12=g1g2cosθ2D[(γ2+iΩc)ρ20(0)+iΩpρ00(0)]+c.c,
β12=g1g2cosθ2DiΩpρ(0)+c.c,
α13=g1g3sinθ2D[(γ2+iΩc)ρ20(0)+iΩpρ00(0)]+c.c,
β13=g1g3sinθ2DiΩpρ(0)+c.c,
α21=g1g2cosθ2DiΩpρ++(0)+c.c,
β21=g1g2cosθ2D[(3γ2+iΩc)ρ20(0)+iΩpρ22(0)]+c.c,
α31=g1g3sinθ2DiΩpρ++(0)+c.c,
β31=g1g3sinθ2D[(3γ2+iΩc)ρ20(0)+iΩpρ22(0)]+c.c,
α23=g2g3cosθ2D(3γ2+iΩc)ρ++(0)+c.c,
β23=g2g3cosθsinθ2D[(3γ2+iΩc2Dγ)ρ00(0)+iΩpρ02(0)]+c.c,
α32=g2g3cosθ2D(3γ2+iΩc)ρ++(0)+c.c,
β32=g2g3cosθsinθ2D[(3γ2+iΩc2Dγ)ρ00(0)+iΩpρ02(0)]+c.c,

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