Abstract

We investigate the possibility of achieving scalable photonic quantum computing by the giant optical circular birefringence induced by a quantum-dot spin in a double-sided optical microcavity as a result of cavity quantum electrodynamics. We construct a deterministic controlled-not gate on two photonic qubits by two single-photon input-output processes and the readout on an electron-medium spin confined in an optical resonant microcavity. This idea could be applied to multi-qubit gates on photonic qubits and we give the quantum circuit for a three-photon Toffoli gate. High fidelities and high efficiencies could be achieved when the side leakage to the cavity loss rate is low. It is worth pointing out that our devices work in both the strong and the weak coupling regimes.

© 2013 OSA

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2013 (1)

H. R. Wei and F. G. Deng, “Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities,” Phys. Rev. A87, 022305 (2013).
[CrossRef]

2012 (5)

T. J. Wang, S. Y. Song, and G. L. Long, “Quantum repeater based on spatial entanglement of photons and quantum-dot spins in optical microcavities,” Phys. Rev. A85, 062311 (2012).
[CrossRef]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities,” Phys. Rev. A86, 042337 (2012).
[CrossRef]

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett.100, 121116 (2012).
[CrossRef]

B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, “Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities,” Opt. Express20, 24664–24677 (2012).
[CrossRef] [PubMed]

J. Hagemeier, C. Bonato, T. A. Truong, H. Kim, G. J. Beirne, M. Bakker, M. P. van Exter, Y. Q. Luo, P. Petroff, and D. Bouwmeester, “H1 photonic crystal cavities for hybrid quantum information protocols,” Opt. Express20, 24714 (2012).
[CrossRef] [PubMed]

2011 (6)

C. Wang, Y. Zhang, and R. Zhang, “Entanglement purification based on hybrid entangled state using quantum-dot and microcavity coupled system,” Opt. Express19, 25685–25695 (2011).
[CrossRef]

C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A84, 032307 (2011).
[CrossRef]

J. Gudat, C. Bonato, E. van Nieuwenburg, S. Thon, H. Kim, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Permanent tuning of quantum dot transitions to degenerate microcavity resonances,” Appl. Phys. Lett.98, 121111 (2011).
[CrossRef]

C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,” Phys. Rev. B84, 075306 (2011).
[CrossRef]

C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B83, 115303 (2011).
[CrossRef]

A. B. Young, R. Oulton, C. Y. Hu, A. C. T. Thijssen, C. Schneider, S. Reitzenstein, M. Kamp, S. Höfling, L. Worschech, A. Forchel, and J. G. Rarity, “Quantum-dot-induced phase shift in a pillar microcavity,” Phys. Rev. A84, 011803 (2011).
[CrossRef]

2010 (2)

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett.104, 160503 (2010).
[CrossRef] [PubMed]

D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast optical spin echo in a single quantum dot,” Nature Photon.4, 367–370 (2010).
[CrossRef]

2009 (13)

X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature (London)459, 1105–1109 (2009).
[CrossRef]

D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science325, 70–72 (2009).
[CrossRef] [PubMed]

V. V. Shende and I. L. Markov, “On the CNOT-cost of Toffoli gate,” Quantum Inf. Comput.9, 0461–0486 (2009).

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A79, 022301 (2009).
[CrossRef]

Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A80, 042310 (2009).
[CrossRef]

A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nature Phys.5, 262–266 (2009).
[CrossRef]

C. Y. Hu, W. J. Munro, J. L. O’Brien, and J. G. Rarity, “Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity,” Phys. Rev. B80, 205326 (2009).
[CrossRef]

C. Bonato, D. Ding, J. Gudat, S. Thon, H. Kim, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Tuning micropillar cavity birefringence by laser induced surface defects,” Appl. Phys. Lett.95, 251104 (2009).
[CrossRef]

D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science325, 70–72 (2009).
[CrossRef] [PubMed]

R. Ionicioiu, T. P. Spiller, and W. J. Munro, “Generalized Toffoli gates using qudit catalysis,” Phys. Rev. A80, 012312 (2009).
[CrossRef]

W. L. Yang, H. Wei, F. Zhou, and M. Feng, “Generation of multi-atom entangled states and implementation of controlled-phase gating using photonic modules,” J. Phys. B: At. Mol. Opt. Phys.42, 055503 (2009).
[CrossRef]

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-out process with respect to low cavities,” Phy. Rev. A79, 032303 (2009).
[CrossRef]

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2008 (6)

B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, S. Seidl, M. Kroner, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature (London)451, 441–444 (2008).
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C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B78, 125318 (2008).
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C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B78, 085307 (2008).
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J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science320, 349–352 (2008).
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D. Press, T. D. Ladd, B. Y. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature (London)456, 218–221 (2008).
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Z. R. Lin, G. P. Guo, T. Tu, F. Y. Zhu, and G. C. Guo, “Generation of quantum-dot cluster states with a superconducting transmission line resonator,” Phys. Rev. Lett.101, 230501 (2008).
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2007 (6)

S. M. Clark, K. M. C. Fu, T. D. Ladd, and Y. Yamamoto, “Quantum computers based on electron spins controlled by ultrafast off-resonant single optical pulses,” Phys. Rev. Lett.99, 040501 (2007).
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A. Greilich, A. Shabaev, D. R. Yakovlev, A. L. Efros, I. A. Yugova, D. Reuter, A. D. Wieck, and M. Bayer, “Nuclei-induced frequency focusing of electron spin coherence,” Science317, 1896–1899 (2007).
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X. D. Xu, Y. W. Wu, B. Sun, Q. Huang, J. Cheng, D. G. Steel, A. S. Bracker, D. Gammon, C. Emary, and L. J. Sham, “Fast spin state initialization in a singly charged InAs-GaAs quantum dot by optical cooling,” Phys. Rev. Lett.99, 097401 (2007).
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S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett.90, 251109 (2007).
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D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J. J. Finley, D. V. Bulaev, and D. Loss, “Observation of extremely slow hole spin relaxation in self-assembled quantum dots,” Phys. Rev. B76, 241306 (2007).
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S. J. Devitt, A. D. Greentree, R. Ionicioiu, J. L. O’Brien, W. J. Munro, and L. C. L. Hollenberg, “Photonic module: An on-demand resource for photonic entanglement,” Phys. Rev. A76, 052312 (2007).
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2006 (4)

M. Atatre, J. Dreiser, A. Badolato, A. Hogele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,” Science312, 551–553 (2006).
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A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,” Science313, 341–345 (2006).
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T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys.8, 30 (2006).
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J. Fiurášek, “Linear-optics quantum Toffoli and Fredkin gates,” Phys. Rev. A73, 062313 (2006).
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2005 (5)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77, 633–673 (2005).
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W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: A new route to optical quantum computation,” New J. Phys.7, 137 (2005).
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D. E. Browne and T. Rudolph, “Resource-efficient linear optical quantum computation,” Phys. Rev. Lett.95, 010501 (2005).
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J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, “Coherent manipulation of coupled electron spins in semiconductor quantum dots,” Science309, 2180–2184 (2005).
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2004 (9)

J. M. Elzerman, R. Hanson, L. H. W. van Beveren, B. Witkamp, L. M. K. Vandersypen, and L. P. Kouwenhoven, “Single-shot read-out of an individual electron spin in a quantum dot,” Nature (London)430, 431–425 (2004).
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M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,” Nature (London)432, 81–84 (2004).
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W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Radiatively limited dephasing in InAs quantum dots,” Phys. Rev. B70, 033301 (2004).
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J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature (London)432, 197–200 (2004).
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T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature (London)432, 200–203 (2004).
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L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interaction,” Phys. Rev. Lett.92, 127902 (2004).
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S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-not gate sufficient for quantum computation,” Phys. Rev. Lett.93, 020504 (2004).
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2003 (5)

Y. Y. Shi, “Both Toffoli and controlled-not need little help to do universal quantum computation,” Quantum Inf. Comput.3, 084–092 (2003).

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J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-not gate,” Nature (London)426, 264–267 (2003).
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T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller, “Spin-based all-optical quantum computation with quantum dots: Understanding and suppressing decoherence,” Phys. Rev. A68, 012310 (2003).
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G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−xGaxAs/GaAs quantum dots,” Phys. Rev. B67, 161306 (2003).
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2002 (4)

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, and A. Forchel, “Fine structure of neutral and charged excitons in self-assembled In(Ga)/As(Al)GaAs quantum dots,” Phys. Rev. B65, 195315 (2002).
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J. J. Finley, D. J. Mowbray, M. S. Skolnick, A. D. Ashmore, C. Baker, and A. F. G. Monte, “Fine structure of charged and neutral excitons in InAs-Al0.6Ga0.4As quantum dots,” Phys. Rev. B66, 153316 (2002).
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C. Piermarocchi, P. C. Chen, L. J. Sham, and D. G. Steel, “Optical RKKY interaction between charged semiconductor quantum dots,” Phys. Rev. Lett.89, 167402 (2002).
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E. Knill, “Quantum gates using linear optics and postselection,” Phys. Rev. A66, 052306 (2002).
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2001 (4)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature (London)409, 46–52 (2001).
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T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A64, 062311 (2001).
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P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
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D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,” Phys. Rev. Lett.87, 227401 (2001).
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1999 (1)

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett.83, 4204–4207 (1999).
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1998 (2)

D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A57, 120–126 (1998).
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C. Y. Hu, W. Ossau, D. R. Yakovlev, G. Landwehr, T. Wojtowicz, G. Karczewski, and J. Kossut, “Optically detected magnetic resonance of excess electrons in type-I quantum wells with a low-density electron gas,” Phys. Rev. B58, R1766–R1769 (1998).
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1997 (1)

R. J. Warburton, C. S. Dürr, K. Karrai, J. P. Kotthaus, G. M. Ribeiro, and P. M. Petroff, “Charged excitons in self-assembled semiconductor quantum dots,” Phys. Rev. Lett.79, 5282–5285 (1997).
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1996 (1)

1995 (1)

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A52, 3457–3457 (1995).
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Abstreiter, G.

D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J. J. Finley, D. V. Bulaev, and D. Loss, “Observation of extremely slow hole spin relaxation in self-assembled quantum dots,” Phys. Rev. B76, 241306 (2007).
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M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,” Nature (London)432, 81–84 (2004).
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Ahmadi, E. D.

I. J. Luxmoore, E. D. Ahmadi, B. J. Luxmoore, N. A. Wasley, A. I. Tartakovskii, M. Hugues, M. S. Skolnick, and A. M. Fox, “Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning,” Appl. Phys. Lett.100, 121116 (2012).
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An, J. H.

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-out process with respect to low cavities,” Phy. Rev. A79, 032303 (2009).
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Ashmore, A. D.

J. J. Finley, D. J. Mowbray, M. S. Skolnick, A. D. Ashmore, C. Baker, and A. F. G. Monte, “Fine structure of charged and neutral excitons in InAs-Al0.6Ga0.4As quantum dots,” Phys. Rev. B66, 153316 (2002).
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Atatre, M.

M. Atatre, J. Dreiser, A. Badolato, A. Hogele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,” Science312, 551–553 (2006).
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Awschalom, D. D.

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science320, 349–352 (2008).
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A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett.83, 4204–4207 (1999).
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Badolato, A.

M. Atatre, J. Dreiser, A. Badolato, A. Hogele, K. Karrai, and A. Imamoglu, “Quantum-dot spin-state preparation with near-unity fidelity,” Science312, 551–553 (2006).
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Baker, C.

J. J. Finley, D. J. Mowbray, M. S. Skolnick, A. D. Ashmore, C. Baker, and A. F. G. Monte, “Fine structure of charged and neutral excitons in InAs-Al0.6Ga0.4As quantum dots,” Phys. Rev. B66, 153316 (2002).
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Bakker, M.

Barenco, A.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A52, 3457–3457 (1995).
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Bayer, M.

A. Greilich, S. E. Economou, S. Spatzek, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer, “Ultrafast optical rotations of electron spins in quantum dots,” Nature Phys.5, 262–266 (2009).
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A. Greilich, A. Shabaev, D. R. Yakovlev, A. L. Efros, I. A. Yugova, D. Reuter, A. D. Wieck, and M. Bayer, “Nuclei-induced frequency focusing of electron spin coherence,” Science317, 1896–1899 (2007).
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A. Greilich, D. R. Yakovlev, A. Shabaev, A. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, and M. Bayer, “Mode locking of electron spin coherences in singly charged quantum dots,” Science313, 341–345 (2006).
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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, and A. Forchel, “Fine structure of neutral and charged excitons in self-assembled In(Ga)/As(Al)GaAs quantum dots,” Phys. Rev. B65, 195315 (2002).
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Beirne, G. J.

Bennett, C. H.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A52, 3457–3457 (1995).
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Berezovsky, J.

J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, “Picosecond coherent optical manipulation of a single electron spin in a quantum dot,” Science320, 349–352 (2008).
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M. V. G. Dutt, J. Cheng, B. Li, X. D. Xu, X. Q. Li, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, S. E. Economou, R. B. Liu, and L. J. Sham, “Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots,” Phys. Rev. Lett.94, 227403 (2005).
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G. Bester, S. Nair, and A. Zunger, “Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled In1−xGaxAs/GaAs quantum dots,” Phys. Rev. B67, 161306 (2003).
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Bichler, M.

D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J. J. Finley, D. V. Bulaev, and D. Loss, “Observation of extremely slow hole spin relaxation in self-assembled quantum dots,” Phys. Rev. B76, 241306 (2007).
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M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, “Optically programmable electron spin memory using semiconductor quantum dots,” Nature (London)432, 81–84 (2004).
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Bimberg, D.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
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D. Birkedal, K. Leosson, and J. M. Hvam, “Long lived coherence in self-assembled quantum dots,” Phys. Rev. Lett.87, 227401 (2001).
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J. Hagemeier, C. Bonato, T. A. Truong, H. Kim, G. J. Beirne, M. Bakker, M. P. van Exter, Y. Q. Luo, P. Petroff, and D. Bouwmeester, “H1 photonic crystal cavities for hybrid quantum information protocols,” Opt. Express20, 24714 (2012).
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J. Gudat, C. Bonato, E. van Nieuwenburg, S. Thon, H. Kim, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Permanent tuning of quantum dot transitions to degenerate microcavity resonances,” Appl. Phys. Lett.98, 121111 (2011).
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C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,” Phys. Rev. B84, 075306 (2011).
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C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett.104, 160503 (2010).
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C. Bonato, D. Ding, J. Gudat, S. Thon, H. Kim, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Tuning micropillar cavity birefringence by laser induced surface defects,” Appl. Phys. Lett.95, 251104 (2009).
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Borri, P.

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Radiatively limited dephasing in InAs quantum dots,” Phys. Rev. B70, 033301 (2004).
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P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong dephasing time in InGaAs quantum dots,” Phys. Rev. Lett.87, 157401 (2001).
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Bose, R.

C. W. Wong, J. Gao, J. F. McMillan, F.W. Sun, and R. Bose, “Quantum information processing through quantum dots in slow-light photonic crystal waveguides,” Photonics and Nanostructures-Fundamentals and Applications7, 47 (2009).
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Bouwmeester, D.

J. Hagemeier, C. Bonato, T. A. Truong, H. Kim, G. J. Beirne, M. Bakker, M. P. van Exter, Y. Q. Luo, P. Petroff, and D. Bouwmeester, “H1 photonic crystal cavities for hybrid quantum information protocols,” Opt. Express20, 24714 (2012).
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J. Gudat, C. Bonato, E. van Nieuwenburg, S. Thon, H. Kim, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Permanent tuning of quantum dot transitions to degenerate microcavity resonances,” Appl. Phys. Lett.98, 121111 (2011).
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C. Bonato, E. van Nieuwenburg, J. Gudat, S. Thon, H. Kim, M. P. van Exter, and D. Bouwmeester, “Strain tuning of quantum dot optical transitions via laser-induced surface defects,” Phys. Rev. B84, 075306 (2011).
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C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett.104, 160503 (2010).
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C. Bonato, D. Ding, J. Gudat, S. Thon, H. Kim, P. M. Petroff, M. P. van Exter, and D. Bouwmeester, “Tuning micropillar cavity birefringence by laser induced surface defects,” Appl. Phys. Lett.95, 251104 (2009).
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Bracker, A. S.

X. D. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Optically controlled locking of the nuclear field via coherent dark-state spectroscopy,” Nature (London)459, 1105–1109 (2009).
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X. D. Xu, Y. W. Wu, B. Sun, Q. Huang, J. Cheng, D. G. Steel, A. S. Bracker, D. Gammon, C. Emary, and L. J. Sham, “Fast spin state initialization in a singly charged InAs-GaAs quantum dot by optical cooling,” Phys. Rev. Lett.99, 097401 (2007).
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M. V. G. Dutt, J. Cheng, B. Li, X. D. Xu, X. Q. Li, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, S. E. Economou, R. B. Liu, and L. J. Sham, “Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots,” Phys. Rev. Lett.94, 227403 (2005).
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Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-not gate,” Nature (London)426, 264–267 (2003).
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Braunstein, S. L.

T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. van Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys.8, 30 (2006).
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Browne, D. E.

D. E. Browne and T. Rudolph, “Resource-efficient linear optical quantum computation,” Phys. Rev. Lett.95, 010501 (2005).
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Brunner, D.

D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science325, 70–72 (2009).
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D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “A coherent single-hole spin in a semiconductor,” Science325, 70–72 (2009).
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B. D. Gerardot, D. Brunner, P. A. Dalgarno, P. Öhberg, S. Seidl, M. Kroner, K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, “Optical pumping of a single hole spin in a quantum dot,” Nature (London)451, 441–444 (2008).
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Bulaev, D. V.

D. Heiss, S. Schaeck, H. Huebl, M. Bichler, G. Abstreiter, J. J. Finley, D. V. Bulaev, and D. Loss, “Observation of extremely slow hole spin relaxation in self-assembled quantum dots,” Phys. Rev. B76, 241306 (2007).
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Burkard, G.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett.83, 4204–4207 (1999).
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T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller, “Spin-based all-optical quantum computation with quantum dots: Understanding and suppressing decoherence,” Phys. Rev. A68, 012310 (2003).
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C. Piermarocchi, P. C. Chen, L. J. Sham, and D. G. Steel, “Optical RKKY interaction between charged semiconductor quantum dots,” Phys. Rev. Lett.89, 167402 (2002).
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Cheng, J.

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Photonics and Nanostructures-Fundamentals and Applications (1)

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Phys. Rev. B (11)

C. Y. Hu, A. Young, J. L. O’Brien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B78, 085307 (2008).
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Science (7)

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Other (4)

H. J. Kimble, Cavity Quantum Electrodynamics (Academic, San Diego, 1994).

By taking g/(κ+ κs) = 1.0,κs/κ= 0.7 and γ= 0.1κfor a micropillar microcavitr with diameter d= 1.5μm, Q= 1.7 × 104, one can get n0= 2 × 10−3, τ= 9 ps, and τ/n0= 4.5 ns.

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity,” Laser Phys. Lett. (accepted); arXiv:1303.0056.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic diagram for a spin-QD-double-side-cavity unit. (b) Energy levels and optical property of a negatively charged exciton X in a GaAs/InAs QD or GaAs interface QD confined in an optical resonant microcavity with two partially reflective mirrors.

Fig. 2
Fig. 2

Quantum circuit for implementing a deterministic photonic two-qubit CNOT gate without additional photonic qubits via a spin-QD-double-side-cavity system. PBSi (i = 1, 2, 3, 4) transmits the photon in the right-circularly-polarized state |R〉 and reflects the photon in the left-circularly-polarized state |L〉, respectively. HWPj (j = 1, 2) is used to perform a Hadamard operation on the polarization of photons, that is, | R 1 2 ( | R + | L ) and | L 1 2 ( | R | L ). DL is the time-delay device for making the photons from spatial modes 5 and 1 reach PBS3 simultaneously, that is, fiber loops for the storage of the photon for the time needed by the interaction between the single photon and the QD.

Fig. 3
Fig. 3

Schematic diagram for implementing a deterministic photonic three-qubit Toffoli gate. The implementation of the Toffoli gate is divided into two processes shown in (a) and (b), and the cavity is just the same one for the first and the second control qubits to interact with the spin in sequence. Pπ is a phase shifter that contributes a π phase shift to the photon passing through it. The working states of the optical switches S1 and S2 shown in (c) and (d) can be controlled accurately by a computer. S1 leads the photon emitting from spatial mode 11 to 12 until t = T0 + 2T1 + T2, and then leads the photon emitting from spatial mode 11 to 14 from t = T0 + 2T1 + T2 to t = T0 + 3T1 + T2 + T3. When T0 + 3T1 + T2 + T3 < t < T0 + 4T1 + 2T2 + T3, S1 turns back to spatial mode 12 again. T0 is the time for the single-photon process PBS4-S2, while T1 for S2-PBS5-cavity-PBS5-S1, T2 for S1-HWP3-S2, and T3 for S2-S1. DL in (a) is used for the storage of the photon for the time needed by the interaction between the single photon and the QD, while DL in (b) is four times of (a).

Fig. 4
Fig. 4

The fidelities of the present quantum gates as a function of the coupling strength g/κ and the side leakage rate κs. (a) The fidelity of the CNOT gate FCT ; (b) The fidelity of the Toffoli gate FT.

Fig. 5
Fig. 5

The efficiencies of the present deterministic photon-qubit gates as a function of g/κ and κs. (a) The efficiency of the CNOT gate ηCT ; (b) The efficiency of the Toffoli gate ηT.

Equations (32)

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| R | L , | L | R , | R | L , | L | R , | R | R , | L | L , | R | R , | L | L .
| ψ c p = α c | R c + β c | L c , | ψ t p = α t | R t + β t | L t , | ψ e = | ,
| Ω 0 = | ψ c p | ψ t p | ψ e ,
| Ω 1 = ( α c α t | R c , 2 | R t + α c β t | R c , 2 | L t + β c α t | L c , 1 | R t + β c β t | L c , 1 | L t ) | .
| R H p 1 2 ( | R + | L ) , | L H p 1 2 ( | R | L ) ,
| H e | 1 2 ( | + | ) , | H e | 1 2 ( | | ) .
| Ω 2 = 1 2 α c α t ( | R c , 3 + | L c , 4 ) | R t ( | + | ) 1 2 α c β t ( | R c , 3 + | L c , 4 ) | L t ( | + | ) + ( β c α t | L c , 1 | R t + β c β t | L c , 1 | L t ) | .
| Ω 3 = α c α t | R c , 6 | R t | α c β t | R c , 6 | L t | + β c α t | L c , 6 | R t | + β c β t | L c , 6 | L t | .
| Ω 4 = ( α c α t | R c , 6 | R t , 9 + α c β t | R c , 6 | L t , 9 ) | + ( β c α t | L c , 6 | L t , 9 + β c β t | L c , 6 | R t , 9 ) | .
| ψ c t = α c α t | R c , 6 | R t , 9 + α c β t | R c , 6 | L t , 9 + β c α t | L c , 6 | L t , 9 + β c β t | L c , 6 | R t , 9 .
| ψ c 1 p = α c 1 | R c 1 + β c 1 | L c 1 , | ψ c 2 p = α c 2 | R c 2 + β c 2 | L c 2 , | ψ t p = α t | R t + β t | L t .
| Ξ 0 = | ψ c 1 p | ψ c 2 p | ψ t p | .
| Ξ 1 = [ ( α c 1 α c 2 | R c 1 , 6 | R c 2 α c 1 β c 2 | R c 1 , 6 | L c 2 ) | + ( β c 1 α c 2 | L c 1 , 6 | R c 2 + β c 1 β c 2 | L c 1 , 6 | L c 2 ) | ] ( α t | R t + β t | L t ) .
| Ξ 2 = [ ( α c 1 α c 2 | R c 1 , 6 | L c 2 , 11 α c 1 β c 2 | R c 1 , 6 | L c 2 , 8 ) | + ( β c 1 α c 2 | L c 1 , 6 | R c 2 , 11 + β c 1 β c 2 | L c 1 , 6 | L c 2 , 8 ) | ] ( α t | R t + β t | L t ) .
| Ξ 3 = [ α c 1 α c 2 2 | R c 1 , 6 ( | R c 2 , 11 | L c 2 , 11 ) ( | | ) α c 1 β c 2 | R c 1 , 6 | L c 2 , 8 | + β c 1 α c 2 2 | L c 1 , 6 ( | R c 2 , 11 + | L c 2 , 11 ) ( | | ) + β c 1 β c 2 | L c 1 , 6 | L c 2 , 8 | ] ( α t | R t + β t | L t ) .
| Ξ 4 = [ α c 1 α c 2 2 | R c 1 , 6 ( | R c 2 , 11 | L c 2 , 11 ) | α c 1 β c 2 | R c 1 , 6 | L c 2 , 8 | ] + β c 1 α c 2 2 | L c 1 , 6 ( | R c 2 , 11 + | L c 2 , 11 ) | + β c 1 β c 2 | L c 1 , 6 | L c 2 , 8 | ( α t | R t + β t | L t ) .
| Ξ 5 = α c 1 α c 2 2 | R c 1 , 6 ( | R c 2 , 11 | L c 2 , 11 ( α t | L t , 21 + β t | R t , 21 ) | | ) α c 1 β c 2 | R c 1 , 6 | L c 2 , 8 ( α t | L t , 21 + β t | R t , 21 ) | β c 1 α c 2 2 | L c 1 , 6 ( | R c 2 , 11 + | L c 2 , 11 ( α t | L t , 21 + β t | R t , 21 ) | + | ) + β c 1 β c 2 | L c 1 , 6 | L c 2 , 8 ( α t | R t , 21 + β t | L t , 21 ) | .
| Ξ 6 = α c 1 α c 2 | R c 1 , 6 | R c 2 , 16 ( α t | L t , 21 + β t | R t , 21 ) | α c 1 β c 2 | R c 1 , 6 | L c 2 , 8 ( α t | L t , 21 + β t | R t , 21 ) | + β c 1 α c 2 | L c 1 , 6 | R c 2 , 16 ( α t | L t , 21 + β t | R t , 21 ) | + β c 1 β c 2 | L c 1 , 6 | L c 2 , 8 ( α t | R t , 21 + β t | L t , 21 ) | .
| Ξ 7 = α c 1 α c 2 | R c 1 , 6 | R c 2 , 17 ( α t | L t , 21 + β t | R t , 21 ) | α c 1 β c 2 | R c 1 , 6 | L c 2 , 17 ( α t | L t , 21 + β t | R t , 21 ) | + β c 1 α c 2 | L c 1 , 6 | R c 2 , 17 ( α t | L t , 21 + β t | R t , 21 ) | + β c 1 β c 2 | L c 1 , 6 | L c 2 , 17 ( α t | R t , 21 + β t | L t , 21 ) | .
| ψ T = α c 1 α c 2 | R c 1 , 6 | R c 2 , 17 ( α t | R t , 21 + β t | L t , 21 ) + α c 1 β c 2 | R c 1 , 6 | L c 2 , 17 ( α t | R t , 21 + β t | L t , 21 ) + β c 1 α c 2 | L c 1 , 6 | R c 2 , 17 ( α t | R t , 21 + β t | L t , 21 ) + β c 1 β c 2 | L c 1 , 6 | L c 2 , 17 ( α t | L t , 21 + β t | R t , 21 ) .
d a ^ d t = [ i ( ω c ω ) + κ + κ s 2 ] a ^ g σ κ a ^ in κ a ^ in + H ^ , d σ d t = [ i ( ω X ω ) + γ 2 ] σ g σ z a ^ + G ^ ,
a ^ r = a ^ in + κ a ^ , a ^ t = a ^ in + κ a ^ ,
t ( ω ) = κ [ i ( ω X ω ) + γ 2 ] [ i ( ω X ω ) + γ 2 ] [ i ( ω c ω ) + κ + κ s 2 ] + g 2 , r ( ω ) = 1 + t ( ω ) .
r = 1 + t , t = κ γ 2 γ 2 [ κ + κ s 2 ] + g 2 .
r 0 = κ s 2 κ + κ s 2 , t 0 = κ κ + κ s 2 .
| R | r | | L + | t | | R , | L | r | | R + | t | | L , | R | r | | L + | t | | R , | L | r | | R + | t | | L , | R | t 0 | | R | r 0 | | L , | L | t 0 | | L | r 0 | | R , | R | t 0 | | R | r 0 | | L , | L | t 0 | | L | r 0 | | R .
F CT = [ | t 0 | + | r | 2 ] 2 , F T = [ ξ 1 + 2 ξ 2 ξ 3 32 ] 2 ,
ξ 1 = ( | t 0 | | r 0 | | t | + | r | ) × [ | r 0 | ( | t 0 | | r 0 | ) ( | t 0 | | r 0 | + | r | | t | ) 2 + | r 0 | ( | r | | t | ) ( | t 0 | | r 0 | | r | + | t | ) 2 + 4 | t 0 | ( | r | | t | ) + 4 ( | t 0 | | r 0 | ) ] , ξ 2 = | r | ( | t 0 | | r 0 | ) ( | t 0 | | r 0 | | r | + | t | ) 2 + | r | ( | r | | t | ) ( | t 0 | | r 0 | + | r | | t | ) 2 + 4 | t | ( | t 0 | | r 0 | ) + 4 ( | r | | t | ) , ξ 3 = | r 0 | ( | t 0 | | r 0 | + | r | | t | ) 2 ( | t 0 | | r 0 | | r | + | t | ) 2 .
η CT = 1 3 [ 1 2 + 5 ζ 4 ] , η T = 1 4 [ 1 + 5 ζ 4 + ζ 4 32 ] .
[ 1 + exp ( Δ t / T 2 e ) ] / 2 .
[ 1 exp ( τ / T 2 ) ] .
ρ e ( t ) = 1 2 ( 1 e t / 2 T 2 e t / 2 T 2 1 ) ,

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