Abstract

We propose an adiabatic passage approach to generate two atoms three-dimensional entanglement with the help of quantum Zeno dynamics in a time-dependent interacting field. The atoms are trapped in two spatially separated cavities connected by a fiber, so that the individual addressing is needless. Because the scheme is based on the resonant interaction, the time required to generate entanglement is greatly shortened. Since the fields remain in vacuum state and all the atoms are in the ground states, the losses due to the excitation of photons and the spontaneous transition of atoms are suppressed efficiently compared with the dispersive protocols. Numerical simulation results show that the scheme is robust against the decoherences caused by the cavity decay and atomic spontaneous emission. Additionally, the scheme can be generalized to generate N-atom three-dimensional entanglement and high-dimensional entanglement for two spatially separated atoms.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  50. X. M. Lin, Z. W. Zhou, Y. C. Wu, C. Z. Wang, and G. C. Guo, “Preparation of two-qutrit entangled state in cavity QED,” Chin. Phys. Lett. 22, 1318–1320 (2005).
    [Crossref]

2014 (4)

X. Q. Shao, J. B. You, T. Y. Zheng, C. H. Oh, and S. Zhang, “Stationary three-dimensional entanglement via dissipative Rydberg pumping,” Phys. Rev. A 89, 052313 (2014).
[Crossref]

X. Q. Shao, T. Y. Zheng, C. H. Oh, and S. Zhang, “Dissipative creation of three-dimensional entangled state in optical cavity via spontaneous emission,” Phys. Rev. A 89, 012319 (2014).
[Crossref]

M. Lu, Y. Xia, L. T. Shen, J. Song, and N. B. An, “Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity,” Phys. Rev. A 89, 012326 (2014).
[Crossref]

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

2013 (2)

X. Wu, Z. H. Chen, M. Y. Ye, Y. H. Chen, and X. M. Lin, “Generation of multiparticle three-dimensional entanglement state via adiabatic passage,” Chin. Phys. B 22, 040309 (2013).
[Crossref]

A. del Campo, “Shortcuts to adiabaticity by counter-diabatic driving,” Phys. Rev. Lett. 111, 100502 (2013).
[Crossref]

2012 (4)

A. Walther, F. Ziesel, T. Ruster, S. T. Dawkins, K. Ott, M. Hettrich, K. Singer, F. Schmidt-Kaler, and U. Poschinger, “Controlling fast transport of cold trapped ions,” Phys. Rev. Lett. 109, 080501 (2012).
[Crossref] [PubMed]

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[Crossref]

L. B. Chen, P. Shi, C. H. Zheng, and Y. J. Gu, “Generation of three-dimensional entangled state between a single atom and a Bose-Einstein condensate via adiabatic passage,” Opt. Express 20, 14547–14555 (2012).
[Crossref] [PubMed]

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

2011 (4)

M. Lettner, M. Mücke, S. Riedl, C. Vo, C. Hahn, S. Baur, J. Bochmann, S. Ritter, S. Dürr, and G. Rempe, “Remote entanglement between a single atom and a Bose-Einstein condensate,” Phys. Rev. Lett. 106, 210503 (2011).
[Crossref] [PubMed]

W. A. Li and G. Y. Huang, “Deterministic generation of a three-dimensional entangled state via quantum Zeno dynamics,” Phys. Rev. A 83, 022322 (2011).
[Crossref]

J. F. Schaff, X. L. Song, P. Capuzzi, P. Vignolo, and G. Labeyrie, “Shortcut to adiabaticity for an interacting Bose-Einstein condensate,” Europhys. Lett. 93, 23001 (2011).
[Crossref]

K. H. Hoffmann, P. Salamon, Y. Rezek, and R. Kosloff, “Time-optimal controls for frictionless cooling in harmonic traps,” Europhys. Lett. 96, 60015 (2011).
[Crossref]

2010 (1)

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

2009 (2)

P. Facchi, G. Marmo, and S. Pascazio, “Quantum Zeno dynamics and quantum Zeno subspaces,” J. Phys: Conf. Ser. 196, 012017 (2009).

B. Weber, H. P. Specht, T. Müller, J. Bochmann, M. Mücke, D. L. Moehring, and G. Rempe, “Photon-photon entanglement with a single trapped atom,” Phys. Rev. Lett. 102, 030501 (2009).
[Crossref] [PubMed]

2007 (2)

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science,  317, 488–490 (2007).
[Crossref] [PubMed]

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79, 53–77 (2007).
[Crossref]

2006 (2)

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[Crossref] [PubMed]

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[Crossref]

2005 (2)

X. M. Lin, Z. W. Zhou, Y. C. Wu, C. Z. Wang, and G. C. Guo, “Preparation of two-qutrit entangled state in cavity QED,” Chin. Phys. Lett. 22, 1318–1320 (2005).
[Crossref]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

2003 (2)

X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled state of two three-level atoms in cavity QED,” Phys. Rev. A 67, 044301 (2003).
[Crossref]

G. Vidal, “Efficient classical simulation of slightly entangled quantum computations,” Phys. Rev. Lett. 91, 147902 (2003).
[Crossref] [PubMed]

2002 (3)

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

P. Facchi and S. Pascazio, “Quantum Zeno Subspaces,” Phys. Rev. Lett. 89, 080401 (2002).
[Crossref] [PubMed]

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. 14, 158 (2002).
[Crossref]

2001 (3)

P. Facchi, S. Pascazio, A. Scardicchio, and L. S. Schulman, “Zeno dynamics yields ordinary constraints,” Phys. Rev. A 65, 012108 (2001).
[Crossref]

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced populstion transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52, 763–809 (2001).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

2000 (4)

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[Crossref] [PubMed]

D. Kaszlikowski, P. Gnacinski, M. Żukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[Crossref] [PubMed]

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature (London) 404, 247–255 (2000).
[Crossref]

P. Facchi, V. Gorini, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Quantum Zeno dynamics,” Phys. Lett. A 275, 12–19 (2000).
[Crossref]

1999 (1)

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

1998 (2)

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

L. Y. Lin, E. L. Goldstein, and R. W. Tkach, “Free-space micromachined optical switches with submillisecond switching time for large-scale optical crossconnects,” IEEE Photon. Technol. Lett. 10, 525–527 (1998).
[Crossref]

1996 (3)

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[Crossref] [PubMed]

H. Nakazato, M. Namiki, and S. Pascazio, “Temporal behavior of quantum mechanical systems,” Int. J. Mod. Phys. B 10, 247–295 (1996).
[Crossref]

1995 (1)

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[Crossref] [PubMed]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

1992 (2)

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

1990 (1)

W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, “Quantum Zeno effect,” Phys. Rev. A 41, 2295–2300 (1990).
[Crossref] [PubMed]

Alonso, D.

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[Crossref]

An, N. B.

M. Lu, Y. Xia, L. T. Shen, J. Song, and N. B. An, “Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity,” Phys. Rev. A 89, 012326 (2014).
[Crossref]

Asano, T.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Baur, S.

M. Lettner, M. Mücke, S. Riedl, C. Vo, C. Hahn, S. Baur, J. Bochmann, S. Ritter, S. Dürr, and G. Rempe, “Remote entanglement between a single atom and a Bose-Einstein condensate,” Phys. Rev. Lett. 106, 210503 (2011).
[Crossref] [PubMed]

Bennett, C. H.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature (London) 404, 247–255 (2000).
[Crossref]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

Bergmann, K.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced populstion transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52, 763–809 (2001).
[Crossref]

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

Berthiaume, A.

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

Bessette, F.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

Bochmann, J.

M. Lettner, M. Mücke, S. Riedl, C. Vo, C. Hahn, S. Baur, J. Bochmann, S. Ritter, S. Dürr, and G. Rempe, “Remote entanglement between a single atom and a Bose-Einstein condensate,” Phys. Rev. Lett. 106, 210503 (2011).
[Crossref] [PubMed]

B. Weber, H. P. Specht, T. Müller, J. Bochmann, M. Mücke, D. L. Moehring, and G. Rempe, “Photon-photon entanglement with a single trapped atom,” Phys. Rev. Lett. 102, 030501 (2009).
[Crossref] [PubMed]

Bollinger, J. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[Crossref] [PubMed]

W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, “Quantum Zeno effect,” Phys. Rev. A 41, 2295–2300 (1990).
[Crossref] [PubMed]

Bose, S.

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[Crossref] [PubMed]

Brandão, F. G. S. L.

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

Bužek, V.

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P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79, 53–77 (2007).
[Crossref]

Shen, L. T.

M. Lu, Y. Xia, L. T. Shen, J. Song, and N. B. An, “Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity,” Phys. Rev. A 89, 012326 (2014).
[Crossref]

Shi, P.

Shore, B. W.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced populstion transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52, 763–809 (2001).
[Crossref]

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

Singer, K.

A. Walther, F. Ziesel, T. Ruster, S. T. Dawkins, K. Ott, M. Hettrich, K. Singer, F. Schmidt-Kaler, and U. Poschinger, “Controlling fast transport of cold trapped ions,” Phys. Rev. Lett. 109, 080501 (2012).
[Crossref] [PubMed]

Smolin, J.

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

Song, J.

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

M. Lu, Y. Xia, L. T. Shen, J. Song, and N. B. An, “Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity,” Phys. Rev. A 89, 012326 (2014).
[Crossref]

Song, X. L.

J. F. Schaff, X. L. Song, P. Capuzzi, P. Vignolo, and G. Labeyrie, “Shortcut to adiabaticity for an interacting Bose-Einstein condensate,” Europhys. Lett. 93, 23001 (2011).
[Crossref]

Specht, H. P.

B. Weber, H. P. Specht, T. Müller, J. Bochmann, M. Mücke, D. L. Moehring, and G. Rempe, “Photon-photon entanglement with a single trapped atom,” Phys. Rev. Lett. 102, 030501 (2009).
[Crossref] [PubMed]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

Spiller, T.

H. K. Lo, S. Popescu, and T. Spiller, Introduction to Quantum Computation and Information (World Scientific, Singapore, 1997).

Su, S. L.

S. L. Su, X. Q. Shao, H. F. Wang, and S. Zhang, “Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay,” arXiv preprint arXiv:1408.4904, (2014).

Sudarshan, E. C. G.

P. Facchi, V. Gorini, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Quantum Zeno dynamics,” Phys. Lett. A 275, 12–19 (2000).
[Crossref]

Takahashi, Y.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Tanaka, Y.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Thanopulos, I.

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79, 53–77 (2007).
[Crossref]

Theuer, H.

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

Tkach, R. W.

L. Y. Lin, E. L. Goldstein, and R. W. Tkach, “Free-space micromachined optical switches with submillisecond switching time for large-scale optical crossconnects,” IEEE Photon. Technol. Lett. 10, 525–527 (1998).
[Crossref]

Upham, J.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

Vidal, G.

G. Vidal, “Efficient classical simulation of slightly entangled quantum computations,” Phys. Rev. Lett. 91, 147902 (2003).
[Crossref] [PubMed]

Vignolo, P.

J. F. Schaff, X. L. Song, P. Capuzzi, P. Vignolo, and G. Labeyrie, “Shortcut to adiabaticity for an interacting Bose-Einstein condensate,” Europhys. Lett. 93, 23001 (2011).
[Crossref]

Vitanov, N. V.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced populstion transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52, 763–809 (2001).
[Crossref]

Vo, C.

M. Lettner, M. Mücke, S. Riedl, C. Vo, C. Hahn, S. Baur, J. Bochmann, S. Ritter, S. Dürr, and G. Rempe, “Remote entanglement between a single atom and a Bose-Einstein condensate,” Phys. Rev. Lett. 106, 210503 (2011).
[Crossref] [PubMed]

Walther, A.

A. Walther, F. Ziesel, T. Ruster, S. T. Dawkins, K. Ott, M. Hettrich, K. Singer, F. Schmidt-Kaler, and U. Poschinger, “Controlling fast transport of cold trapped ions,” Phys. Rev. Lett. 109, 080501 (2012).
[Crossref] [PubMed]

Wang, C. Z.

X. M. Lin, Z. W. Zhou, Y. C. Wu, C. Z. Wang, and G. C. Guo, “Preparation of two-qutrit entangled state in cavity QED,” Chin. Phys. Lett. 22, 1318–1320 (2005).
[Crossref]

Wang, H. F.

S. L. Su, X. Q. Shao, H. F. Wang, and S. Zhang, “Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay,” arXiv preprint arXiv:1408.4904, (2014).

Weber, B.

B. Weber, H. P. Specht, T. Müller, J. Bochmann, M. Mücke, D. L. Moehring, and G. Rempe, “Photon-photon entanglement with a single trapped atom,” Phys. Rev. Lett. 102, 030501 (2009).
[Crossref] [PubMed]

Webster, S. C.

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science,  317, 488–490 (2007).
[Crossref] [PubMed]

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

Weinfurter, H.

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[Crossref] [PubMed]

Wiesner, S. J.

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

Wilcut, E.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

Wilk, T.

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science,  317, 488–490 (2007).
[Crossref] [PubMed]

Wineland, D. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[Crossref] [PubMed]

W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, “Quantum Zeno effect,” Phys. Rev. A 41, 2295–2300 (1990).
[Crossref] [PubMed]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

Wu, X.

X. Wu, Z. H. Chen, M. Y. Ye, Y. H. Chen, and X. M. Lin, “Generation of multiparticle three-dimensional entanglement state via adiabatic passage,” Chin. Phys. B 22, 040309 (2013).
[Crossref]

Wu, Y. C.

X. M. Lin, Z. W. Zhou, Y. C. Wu, C. Z. Wang, and G. C. Guo, “Preparation of two-qutrit entangled state in cavity QED,” Chin. Phys. Lett. 22, 1318–1320 (2005).
[Crossref]

Xia, Y.

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

M. Lu, Y. Xia, L. T. Shen, J. Song, and N. B. An, “Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity,” Phys. Rev. A 89, 012326 (2014).
[Crossref]

Yan, H.

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. 14, 158 (2002).
[Crossref]

Yang, P.

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. 14, 158 (2002).
[Crossref]

Ye, M. Y.

X. Wu, Z. H. Chen, M. Y. Ye, Y. H. Chen, and X. M. Lin, “Generation of multiparticle three-dimensional entanglement state via adiabatic passage,” Chin. Phys. B 22, 040309 (2013).
[Crossref]

You, J. B.

X. Q. Shao, J. B. You, T. Y. Zheng, C. H. Oh, and S. Zhang, “Stationary three-dimensional entanglement via dissipative Rydberg pumping,” Phys. Rev. A 89, 052313 (2014).
[Crossref]

Zeilinger, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

D. Kaszlikowski, P. Gnacinski, M. Żukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[Crossref] [PubMed]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[Crossref] [PubMed]

Zhang, S.

X. Q. Shao, J. B. You, T. Y. Zheng, C. H. Oh, and S. Zhang, “Stationary three-dimensional entanglement via dissipative Rydberg pumping,” Phys. Rev. A 89, 052313 (2014).
[Crossref]

X. Q. Shao, T. Y. Zheng, C. H. Oh, and S. Zhang, “Dissipative creation of three-dimensional entangled state in optical cavity via spontaneous emission,” Phys. Rev. A 89, 012319 (2014).
[Crossref]

S. L. Su, X. Q. Shao, H. F. Wang, and S. Zhang, “Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay,” arXiv preprint arXiv:1408.4904, (2014).

Zheng, C. H.

Zheng, S. B.

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[Crossref] [PubMed]

Zheng, T. Y.

X. Q. Shao, T. Y. Zheng, C. H. Oh, and S. Zhang, “Dissipative creation of three-dimensional entangled state in optical cavity via spontaneous emission,” Phys. Rev. A 89, 012319 (2014).
[Crossref]

X. Q. Shao, J. B. You, T. Y. Zheng, C. H. Oh, and S. Zhang, “Stationary three-dimensional entanglement via dissipative Rydberg pumping,” Phys. Rev. A 89, 052313 (2014).
[Crossref]

Zhou, Z. W.

X. M. Lin, Z. W. Zhou, Y. C. Wu, C. Z. Wang, and G. C. Guo, “Preparation of two-qutrit entangled state in cavity QED,” Chin. Phys. Lett. 22, 1318–1320 (2005).
[Crossref]

Ziesel, F.

A. Walther, F. Ziesel, T. Ruster, S. T. Dawkins, K. Ott, M. Hettrich, K. Singer, F. Schmidt-Kaler, and U. Poschinger, “Controlling fast transport of cold trapped ions,” Phys. Rev. Lett. 109, 080501 (2012).
[Crossref] [PubMed]

Zou, X. B.

X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled state of two three-level atoms in cavity QED,” Phys. Rev. A 67, 044301 (2003).
[Crossref]

Zukowski, M.

D. Kaszlikowski, P. Gnacinski, M. Żukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[Crossref] [PubMed]

Adv. Mater. (1)

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. 14, 158 (2002).
[Crossref]

Annu. Rev. Phys. Chem. (1)

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced populstion transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52, 763–809 (2001).
[Crossref]

Chin. Phys. B (1)

X. Wu, Z. H. Chen, M. Y. Ye, Y. H. Chen, and X. M. Lin, “Generation of multiparticle three-dimensional entanglement state via adiabatic passage,” Chin. Phys. B 22, 040309 (2013).
[Crossref]

Chin. Phys. Lett. (1)

X. M. Lin, Z. W. Zhou, Y. C. Wu, C. Z. Wang, and G. C. Guo, “Preparation of two-qutrit entangled state in cavity QED,” Chin. Phys. Lett. 22, 1318–1320 (2005).
[Crossref]

Europhys. Lett. (2)

K. H. Hoffmann, P. Salamon, Y. Rezek, and R. Kosloff, “Time-optimal controls for frictionless cooling in harmonic traps,” Europhys. Lett. 96, 60015 (2011).
[Crossref]

J. F. Schaff, X. L. Song, P. Capuzzi, P. Vignolo, and G. Labeyrie, “Shortcut to adiabaticity for an interacting Bose-Einstein condensate,” Europhys. Lett. 93, 23001 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (1)

L. Y. Lin, E. L. Goldstein, and R. W. Tkach, “Free-space micromachined optical switches with submillisecond switching time for large-scale optical crossconnects,” IEEE Photon. Technol. Lett. 10, 525–527 (1998).
[Crossref]

Int. J. Mod. Phys. B (1)

H. Nakazato, M. Namiki, and S. Pascazio, “Temporal behavior of quantum mechanical systems,” Int. J. Mod. Phys. B 10, 247–295 (1996).
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J. Cryptol. (1)

C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

J. Phys: Conf. Ser. (1)

P. Facchi, G. Marmo, and S. Pascazio, “Quantum Zeno dynamics and quantum Zeno subspaces,” J. Phys: Conf. Ser. 196, 012017 (2009).

Nat. Photon. (1)

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photon. 6, 56–61 (2012).
[Crossref]

Nat. Phys. (1)

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[Crossref]

Nature (London) (2)

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature (London) 404, 247–255 (2000).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

New J. Phys. (1)

A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, “Optimally robust shortcuts to population inversion in two-level quantum systems,” New J. Phys. 14, 093040 (2012).
[Crossref]

Opt. Express (1)

Phys. Lett. A (1)

P. Facchi, V. Gorini, G. Marmo, S. Pascazio, and E. C. G. Sudarshan, “Quantum Zeno dynamics,” Phys. Lett. A 275, 12–19 (2000).
[Crossref]

Phys. Rev. A (11)

M. Lu, Y. Xia, L. T. Shen, J. Song, and N. B. An, “Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity,” Phys. Rev. A 89, 012326 (2014).
[Crossref]

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

P. Facchi, S. Pascazio, A. Scardicchio, and L. S. Schulman, “Zeno dynamics yields ordinary constraints,” Phys. Rev. A 65, 012108 (2001).
[Crossref]

W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, “Quantum Zeno effect,” Phys. Rev. A 41, 2295–2300 (1990).
[Crossref] [PubMed]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
[Crossref] [PubMed]

W. A. Li and G. Y. Huang, “Deterministic generation of a three-dimensional entangled state via quantum Zeno dynamics,” Phys. Rev. A 83, 022322 (2011).
[Crossref]

X. Q. Shao, J. B. You, T. Y. Zheng, C. H. Oh, and S. Zhang, “Stationary three-dimensional entanglement via dissipative Rydberg pumping,” Phys. Rev. A 89, 052313 (2014).
[Crossref]

X. Q. Shao, T. Y. Zheng, C. H. Oh, and S. Zhang, “Dissipative creation of three-dimensional entangled state in optical cavity via spontaneous emission,” Phys. Rev. A 89, 012319 (2014).
[Crossref]

M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[Crossref]

X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled state of two three-level atoms in cavity QED,” Phys. Rev. A 67, 044301 (2003).
[Crossref]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[Crossref]

Phys. Rev. Lett. (16)

B. Weber, H. P. Specht, T. Müller, J. Bochmann, M. Mücke, D. L. Moehring, and G. Rempe, “Photon-photon entanglement with a single trapped atom,” Phys. Rev. Lett. 102, 030501 (2009).
[Crossref] [PubMed]

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[Crossref] [PubMed]

M. Lettner, M. Mücke, S. Riedl, C. Vo, C. Hahn, S. Baur, J. Bochmann, S. Ritter, S. Dürr, and G. Rempe, “Remote entanglement between a single atom and a Bose-Einstein condensate,” Phys. Rev. Lett. 106, 210503 (2011).
[Crossref] [PubMed]

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[Crossref] [PubMed]

G. Vidal, “Efficient classical simulation of slightly entangled quantum computations,” Phys. Rev. Lett. 91, 147902 (2003).
[Crossref] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[Crossref] [PubMed]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[Crossref] [PubMed]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[Crossref] [PubMed]

D. Kaszlikowski, P. Gnacinski, M. Żukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[Crossref] [PubMed]

P. Kwiat, H. Weinfurter, T. Herzog, A. Zeilinger, and M. A. Kasevich, “Interaction-free measurement,” Phys. Rev. Lett. 74, 4763–4766 (1995).
[Crossref] [PubMed]

A. Walther, F. Ziesel, T. Ruster, S. T. Dawkins, K. Ott, M. Hettrich, K. Singer, F. Schmidt-Kaler, and U. Poschinger, “Controlling fast transport of cold trapped ions,” Phys. Rev. Lett. 109, 080501 (2012).
[Crossref] [PubMed]

P. Facchi and S. Pascazio, “Quantum Zeno Subspaces,” Phys. Rev. Lett. 89, 080401 (2002).
[Crossref] [PubMed]

X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, “Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity,” Phys. Rev. Lett. 104, 063002 (2010).
[Crossref] [PubMed]

A. del Campo, “Shortcuts to adiabaticity by counter-diabatic driving,” Phys. Rev. Lett. 111, 100502 (2013).
[Crossref]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[Crossref]

P. Král, I. Thanopulos, and M. Shapiro, “Colloquium: Coherently controlled adiabatic passage,” Rev. Mod. Phys. 79, 53–77 (2007).
[Crossref]

Science (1)

T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science,  317, 488–490 (2007).
[Crossref] [PubMed]

Other (3)

S. L. Su, X. Q. Shao, H. F. Wang, and S. Zhang, “Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay,” arXiv preprint arXiv:1408.4904, (2014).

H. K. Lo, S. Popescu, and T. Spiller, Introduction to Quantum Computation and Information (World Scientific, Singapore, 1997).

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

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Figures (7)

Fig. 1
Fig. 1 The schematic setup for generating two atoms three-dimensional entanglement. The two atoms are trapped in two spatially separated optical cavities connected by a fiber.
Fig. 2
Fig. 2 The level configurations of atom A and B.
Fig. 3
Fig. 3 The time dependence of the laser fields ΩA(t) corresponding to solid line and ΩB(t) corresponding to dashed line with t 0 = Ω 0 1 and τ = 5.27t0.
Fig. 4
Fig. 4 Time evolutions of the populations of corresponding system states, controlled by the effective Hamiltonian of Eq. (11) (blue line) and the initial Hamiltonian of Eq. (1) (red line). The subgraph is the partially enlarged view.
Fig. 5
Fig. 5 The fidelity corresponding to the target state versus κ/g and γ/g, with g = 20Ω0, η = 100g, t 0 = Ω 0 1 and τ= 5.27t0.
Fig. 6
Fig. 6 Schematic setup for generation of N-atom three-dimensional entanglement.
Fig. 7
Fig. 7 The potential atomic levels configuration for atom A and B.

Equations (40)

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H total = H a - l + H a - c - f ,
H a - l = Ω A ( t ) ( | e L A 1 | + | e R A 0 | ) + Ω B ( t ) ( | e L B L | + e R | B R | ) + H . c . ,
H a - c - f = g A L a A L | e L A L | + g A R a A R | e R A R | + g B L a B L | e L B g | + g B R a B R | e R B g | + η b L ( a A L + a B L ) + η b R ( a A R | a B R ) + H . c . ,
| Ψ = 1 3 ( | R A | R B + | L A | L B + | g A | g B ) ,
| Ψ A = 1 3 ( | 1 A + | 0 A + | g A ) ,
| ϕ 1 = | 0 A | g B | 0 AC | 0 BC | 0 f , | ϕ 2 = | e R A | g B | 0 AC | 0 BC | 0 f , | ϕ 3 = | R A | g B | 1 R AC | 0 BC | 0 f , | ϕ 4 = | R A | g B | 0 AC | 0 BC | 1 R f , | ϕ 5 = | R A | g B | 0 AC | 1 R BC | 0 f , | ϕ 6 = | R A | e R B | 0 AC | 0 BC | 0 f , | ϕ 7 = | R A | R B | 0 AC | 0 BC | 0 f .
Γ P 1 = { | ϕ 1 , | ϕ 7 , | ψ 1 } , Γ P 2 = { | ψ 2 } , Γ P 3 = { | ψ 3 } , Γ P 4 = { | ψ 4 } , Γ P 5 = { | ψ 5 } ,
| ψ 1 = 1 ε ( η | ϕ 2 g | ϕ 4 + η | ϕ 6 ) , | ψ 2 = 1 2 ( | ϕ 2 + | ϕ 3 | ϕ 5 + | ϕ 6 ) , | ψ 3 = 1 2 ( | ϕ 2 | ϕ 3 + | ϕ 5 + | ϕ 6 ) , | ψ 4 = 1 2 ε ( g | ϕ 2 ε | ϕ 3 + 2 η | ϕ 4 ) ε | ϕ 5 + g | ϕ 6 , | ψ 5 = 1 2 ε ( g | ϕ 2 + ε | ϕ 3 + 2 η | ϕ 4 ) + ε | ϕ 5 + g | ϕ 6 ,
P i α = | α α | , ( | α Γ P i ) .
H total i , α , β ( λ i P i α + P i α H a - l P i β ) = g | ψ 2 ψ 2 | + g | ψ 3 ψ 3 | ε | ψ 4 ψ 4 | + ε | ψ 5 ψ 5 | + 1 ε η ( Ω A ( t ) | ψ 1 | ϕ 1 + Ω B ( t ) | ψ 1 | ϕ 7 + H . c . ) .
H eff = Ω A 1 ( t ) | ψ 1 | ϕ 1 + Ω B 1 ( t ) | ψ 1 | ϕ 7 + H . c . ,
| ψ D 1 = 1 Ω A 1 ( t ) 2 + Ω B 1 ( t ) 2 ( Ω B 1 ( t ) | ϕ 1 + Ω A 1 ( t ) | ϕ 7 ) .
lim t Ω A 1 ( t ) Ω B 1 ( t ) = 0 , lim t + Ω A 1 ( t ) Ω B 1 ( t ) = ,
| ϕ 1 = | 1 A | g B | 0 AC | 0 BC | 0 f , | ϕ 2 = | e L A | g B | 0 AC | 0 BC | 0 f , | ϕ 3 = | L A | g B | 1 L AC | 0 BC | 0 f , | ϕ 4 = | L A | g B | 0 AC | 0 BC | 1 L f , | ϕ 5 = | L A | g B | 0 AC | 1 L BC | 0 f , | ϕ 6 = | L A | e L B | 0 AC | 0 BC | 0 f , | ϕ 7 = | L A | L B | 0 AC | 0 BC | 0 f .
H eff = Ω A 1 ( t ) | ψ 1 ϕ 1 | + Ω B 1 ( t ) | ψ 1 ϕ 7 | + H . c . ,
| ψ D 2 = 1 Ω A 1 ( t ) 2 + Ω B 1 ( t ) 2 ( Ω B 1 ( t ) | ϕ 1 + Ω A 1 ( t ) | ϕ 7 ) .
| Ψ ( 0 ) = 1 3 ( | 0 A + | 1 A + | g A ) | g B | 0 AC | 0 BC | 0 f
| Ψ final = 1 3 ( | R A | R B + | L A | L B + | g A | g B ) | 0 AC | 0 BC | 0 f ,
Ω A ( t ) = Ω 0 sin 4 [ π ( t τ ) / 31 t 0 ]
Ω B ( t ) = Ω 0 sin 4 ( π t / 31 t 0 ) .
ρ ( t ˙ ) = i [ H total , ρ ( t ) ] j = L , R κ f 2 [ b j + b j ρ ( t ) 2 b j ρ ( t ) b j + + ρ ( t ) b j + b j ] j = L , R i = A , B κ j 2 [ a i j + a i j ρ ( t ) 2 a i j ρ ( t ) a i j + + ρ ( t ) a i j + a i j ] γ A 2 { h = L , 1 [ σ e L , e L A ρ ( t ) 2 σ h , e L A ρ ( t ) σ e L , h A + ρ ( t ) σ e L , e L A ] + k = R , 0 [ σ e R , e R A ρ ( t ) 2 σ k , e R A ρ ( t ) σ e R , k A + ρ ( t ) σ e R , e R A ] } j = L , R l = j , g γ B 2 [ σ e j , e j B ρ ( t ) 2 σ l , e j B ρ ( t ) σ e j , l B + ρ ( t ) σ e j B σ e j B ] ,
H total n = H a - l n + H a - c - f n ,
H a - l n = Ω A ( t ) ( | e L 1 1 | + | e R 1 0 | ) + Ω B ( t ) ( | e L n L | + | e R n R | ) + H . c . ,
H a - c - f n = g 1 L a 1 L | e L 1 L | + g 1 R a 1 R | e R 1 R | + g n L a n L | e L n g | + g n R a n R | e R n g | + η b L ( a 1 L + a n L ) + η b R ( a 1 R + a n R ) + H . c . ,
| φ N = 1 3 ( | R 1 | R 2 | R N + | L 1 | L 2 | L N + | g 1 | g 2 | g N ) ,
| φ 1 = 1 3 ( | 0 1 + | 1 1 + | g 1 ) | g 2 | g 3 | g N | 0 1 C | 0 2 C | 0 N C | 0 f .
| ϕ 2 = 1 3 ( | 0 1 | R 2 + | 1 1 | L 2 + | g 1 | g 2 ) | g 3 | g 4 | g N | 0 1 C | 0 2 C | 0 N C | 0 f .
| φ 3 = 1 3 ( | R 1 | R 2 | R n + | L 1 | L 2 | L n + | g 1 | g 2 | g n ) | g n + 1 | g n + 2 | g N | 0 1 C | 0 2 C | 0 N C | 0 f .
| φ 4 = 1 3 ( | R 1 | R 2 | R N + | L 1 | L 2 | L N + | g 1 | g 2 | g N ) | 0 1 C | 0 2 C | 0 N C | 0 f .
total = a - l + a - c - f ,
a - l = Ω A ( t ) ( | e L A 1 | + | e R A 0 | ) + Ω B ( t ) i = 1 N ( | e Li B L i | + | e Ri B R i | ) + H . c . ,
H a - c - f = i = 1 N [ ( g ALi a ALi | e L A L i | + g ARi a ARi | e R A R i | ) + g BLi a BLi | e Li B g | + g BRi a BRi | e Ri B g | + η b Li ( a ALi + a BLi ) + η b Ri ( a ARi + a BRi ) + H . c . ] .
Γ = { | ζ 1 = | 1 A | g B | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f , | ζ 2 = | e L A | g B | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f , | ζ 2 + i = | L i A | g B | 1 i AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f , | ζ 2 + N + i = | L i A | g B | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 1 i f , | ζ 2 + 2 N + i = | L i A | g B | 0 1 0 2 0 N AC | 1 i BC | 0 1 0 2 0 N f , | ζ 2 + 3 N + i = | L i A | e Li B | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f , | ζ 2 + 4 N + i = | L i A | L i B | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f . } ,
eff = 1 N + 1 ( Ω A 1 ( t ) | X 1 ζ 1 | + Ω B 1 ( t ) j = 4 N + 3 5 N + 2 | X 1 ζ j | + H . c . ) ,
| X 1 = 1 ε 2 N + 1 ( η | ζ 2 g j = N + 3 2 N + 2 | ζ j + η k = 3 N + 3 4 N + 2 | ζ k ) .
| X D = 1 ( N + 1 ) ( Ω A 1 ( t ) 2 + Ω B 1 ( t ) 2 ) ( Ω B 1 ( t ) | ζ 1 + Ω A 1 ( t ) j = 4 N + 3 5 N + 2 | ζ j ) .
| ν = 1 N j = 4 N + 3 5 N + 2 | ζ j = 1 N m = 1 N | L m A | L m B | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f ,
| ν 1 = 1 N k = 1 N | R k A | R k B | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f .
| ν 0 = 1 3 ( | 1 A + | 0 A + | g A ) | g B | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f ,
| β = 1 2 N + 1 [ m = 1 N | L m A | L m B + k = 1 N | R k A | R k B + | g A | g B ] | 0 1 0 2 0 N AC | 0 1 0 2 0 N BC | 0 1 0 2 0 N f .

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