Abstract

We report an experimental demonstration of storage of photonic polarization qubit (PPQ) protected by dynamical decoupling (DD). PPQ’s states are stored as a superposition of two spin waves by electromagnetically-induced-transparency (EIT). Carr-Purcell-Meiboom-Gill (CPMG) DD sequences are applied to the spin-wave superposition to suppress its decoherence. Thus, the quantum process fidelity remains better than 0.8 for up to 800μs storage time, which is 3.4-times longer than the corresponding storage time of ~180μs without the CPMG sequences. This work is a key step towards the storage of single-photon polarization qubit protected by the CPMG sequences.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Atomic vapor quantum memory for a photonic polarization qubit

Young-Wook Cho and Yoon-Ho Kim
Opt. Express 18(25) 25786-25793 (2010)

Quantum telecommunication with atomic ensembles

S. D. Jenkins, D. N. Matsukevich, T. Chanelière, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich
J. Opt. Soc. Am. B 24(2) 316-323 (2007)

Entanglement distillation for quantum communication network with atomic-ensemble memories

Tao Li, Guo-Jian Yang, and Fu-Guo Deng
Opt. Express 22(20) 23897-23911 (2014)

References

  • View by:
  • |
  • |
  • |

  1. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
    [Crossref] [PubMed]
  2. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
    [Crossref]
  3. A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
    [Crossref]
  4. Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
    [Crossref]
  5. J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
    [Crossref]
  6. M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
    [Crossref] [PubMed]
  7. T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
    [Crossref] [PubMed]
  8. L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
    [Crossref] [PubMed]
  9. S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
    [Crossref]
  10. B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
    [Crossref]
  11. R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
    [Crossref]
  12. Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
    [Crossref] [PubMed]
  13. Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
    [Crossref] [PubMed]
  14. Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
    [Crossref] [PubMed]
  15. D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
    [Crossref]
  16. S. Yu, P. Xu, X. He, M. Liu, J. Wang, and M. Zhan, “Suppressing phase decoherence of a single atom qubit with Carr-Purcell-Meiboom-Gill sequence,” Opt. Express 21(26), 32130–32140 (2013).
    [Crossref] [PubMed]
  17. G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
    [Crossref] [PubMed]
  18. J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
    [Crossref] [PubMed]
  19. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
    [Crossref] [PubMed]
  20. Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
    [Crossref]
  21. M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
    [Crossref] [PubMed]
  22. G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
    [Crossref] [PubMed]
  23. M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
    [Crossref]
  24. Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
    [Crossref]
  25. T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
    [Crossref] [PubMed]
  26. M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002).
    [Crossref]
  27. J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
    [Crossref]
  28. Y. W. Cho and Y. H. Kim, “Atomic vapor quantum memory for a photonic polarization qubit,” Opt. Express 18(25), 25786–25793 (2010).
    [Crossref] [PubMed]
  29. D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
    [Crossref]
  30. R. Loudon, The Quantum Theory of Light (Oxford University, 2004).
  31. X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
    [Crossref] [PubMed]

2013 (6)

S. Yu, P. Xu, X. He, M. Liu, J. Wang, and M. Zhan, “Suppressing phase decoherence of a single atom qubit with Carr-Purcell-Meiboom-Gill sequence,” Opt. Express 21(26), 32130–32140 (2013).
[Crossref] [PubMed]

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
[Crossref]

M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
[Crossref] [PubMed]

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

2012 (4)

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

2011 (3)

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

2010 (3)

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

Y. W. Cho and Y. H. Kim, “Atomic vapor quantum memory for a photonic polarization qubit,” Opt. Express 18(25), 25786–25793 (2010).
[Crossref] [PubMed]

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

2009 (5)

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

2008 (1)

L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

2007 (2)

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

2005 (1)

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

2004 (1)

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

2002 (2)

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002).
[Crossref]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
[Crossref]

2001 (1)

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

2000 (1)

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
[Crossref] [PubMed]

Bao, X. H.

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Baur, S.

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

Blumoff, J. Z.

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

Bylander, J.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Campbell, C. J.

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Champion, T. F. M.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Chanelière, T.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

Chen, L.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Chen, S.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Chen, Y. A.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Chen, Z. B.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Cho, Y. W.

Chuu, C. S.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Cirac, J. I.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Cory, D. G.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

de Lange, G.

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Dobrovitski, V. V.

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Domhan, M.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Dowling, J. P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Du, J.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Duan, L. M.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Dudin, Y. O.

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
[Crossref]

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

Dürr, S.

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

England, D. G.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Ferrier, A.

M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
[Crossref] [PubMed]

Fitch, G.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
[Crossref]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
[Crossref] [PubMed]

Gaebel, T.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Goldner, P.

M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
[Crossref] [PubMed]

Gruber, A.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Gustavsson, S.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Halfmann, T.

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

Hanson, R.

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Harrabi, K.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

He, X.

Heinze, G.

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

Hirayama, Y.

T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

Hubrich, C.

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

Jelezko, F.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Jenkins, S. D.

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

Jin, X. M.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Karpa, L.

L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

Kennedy, T. A. B.

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

Kim, Y. H.

Kok, P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Kolthammer, W. S.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Kuzmich, A.

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
[Crossref]

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

Lan, S. Y.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

Langford, N. K.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Lee, K. C.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Lettner, M.

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

Li, C. M.

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

Li, L.

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
[Crossref]

Li, S.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

Liu, H.

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

Liu, M.

Liu, R. B.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Lovric, M.

M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
[Crossref] [PubMed]

Lu, C. Y.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

Lucas, D. M.

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

Lukin, M. D.

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
[Crossref]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
[Crossref] [PubMed]

Lvovsky, A. I.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

Matsukevich, D. N.

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

Michelberger, P. S.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Milburn, G. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Munro, W. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Nakamura, Y.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Nemoto, K.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Nielsen, M. A.

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002).
[Crossref]

Nunn, J.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Oliver, W. D.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Pan, J. W.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Peng, K.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Popa, I.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Radnaev, A. G.

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

Ralph, T. C.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Reim, K. F.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Rempe, G.

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

Riedl, S.

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

Ristè, D.

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Rong, X.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Sanders, B. C.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

Sasaki, S.

T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

Schmiedmayer, J.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Sprague, M. R.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Steane, A. M.

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

Strassel, T.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Suter, D.

M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
[Crossref] [PubMed]

Szwer, D. J.

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

Tian, L.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Tittel, W.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

Tsai, J. S.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Vewinger, F.

L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

Vo, C.

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

Walmsley, I. A.

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Wang, H.

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Wang, J.

Wang, Y.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Wang, Z. H.

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Webster, S. C.

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

Weinfurter, H.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

Weitz, M.

L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

Wrachtrup, J.

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Wu, Y.

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Xie, C.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Xu, P.

Xu, X. F.

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

Xu, Z.

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Yan, F.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Yan, Z.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Yang, J.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Yoshihara, F.

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Yu, S.

Yuan, Z. S.

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Yuge, T.

T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

Zeilinger, A.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

Zhan, M.

Zhang, Z.

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Zhao, B.

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Zhao, N.

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

Zhao, R.

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

Zoller, P.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Zukowski, M.

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

J. Phys. At. Mol. Opt. Phys. (2)

D. J. Szwer, S. C. Webster, A. M. Steane, and D. M. Lucas, “Keeping a single qubit alive by experimental dynamic decoupling,” J. Phys. At. Mol. Opt. Phys. 44(2), 025501 (2011).
[Crossref]

D. G. England, P. S. Michelberger, T. F. M. Champion, K. F. Reim, K. C. Lee, M. R. Sprague, X. M. Jin, N. K. Langford, W. S. Kolthammer, J. Nunn, and I. A. Walmsley, “High-fidelity polarization storage in a gigahertz bandwidth quantum memory,” J. Phys. At. Mol. Opt. Phys. 45(12), 124008 (2012).
[Crossref]

Nat. Photon. (1)

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photon. 3(12), 706–714 (2009).
[Crossref]

Nat. Phys. (3)

B. Zhao, Y. A. Chen, X. H. Bao, T. Strassel, C. S. Chuu, X. M. Jin, J. Schmiedmayer, Z. S. Yuan, S. Chen, and J. W. Pan, “A millisecond quantum memory for scalable quantum networks,” Nat. Phys. 5(2), 95–99 (2009).
[Crossref]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5(2), 100–104 (2009).
[Crossref]

J. Bylander, S. Gustavsson, F. Yan, F. Yoshihara, K. Harrabi, G. Fitch, D. G. Cory, Y. Nakamura, J. S. Tsai, and W. D. Oliver, “Noise spectroscopy through dynamical decoupling with a superconducting flux qubit,” Nat. Phys. 7(7), 565–570 (2011).
[Crossref]

Nature (3)

J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang, and R. B. Liu, “Preserving electron spin coherence in solids by optimal dynamical decoupling,” Nature 461(7268), 1265–1268 (2009).
[Crossref] [PubMed]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S. Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Storage and retrieval of single photons transmitted between remote quantum memories,” Nature 438(7069), 833–836 (2005).
[Crossref] [PubMed]

Opt. Express (2)

Phys. Lett. A (1)

M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303(4), 249–252 (2002).
[Crossref]

Phys. Rev. A (5)

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87(3), 031801 (2013).
[Crossref]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65(2), 022314 (2002).
[Crossref]

Z. Xu, Y. Wu, H. Liu, S. Li, and H. Wang, “Fast manipulation of spin-wave excitations in an atomic ensemble,” Phys. Rev. A 88(1), 013423 (2013).
[Crossref]

S. Riedl, M. Lettner, C. Vo, S. Baur, G. Rempe, and S. Dürr, “Bose-Einstein Condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85(2), 022318 (2012).
[Crossref]

Z. B. Chen, B. Zhao, Y. A. Chen, J. Schmiedmayer, and J. W. Pan, “Fault-tolerant quantum repeater with atomic ensembles and linear optics,” Phys. Rev. A 76(2), 022329 (2007).
[Crossref]

Phys. Rev. Lett. (9)

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84(22), 5094–5097 (2000).
[Crossref] [PubMed]

L. Karpa, F. Vewinger, and M. Weitz, “Resonance beating of light stored using atomic spinor polaritons,” Phys. Rev. Lett. 101(17), 170406 (2008).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93(13), 130501 (2004).
[Crossref] [PubMed]

Y. O. Dudin, S. D. Jenkins, R. Zhao, D. N. Matsukevich, A. Kuzmich, and T. A. B. Kennedy, “Entanglement of a photon and an optical lattice spin wave,” Phys. Rev. Lett. 103(2), 020505 (2009).
[Crossref] [PubMed]

Z. Xu, Y. Wu, L. Tian, L. Chen, Z. Zhang, Z. Yan, S. Li, H. Wang, C. Xie, and K. Peng, “Long lifetime and high-fidelity quantum memory of photonic polarization qubit by lifting zeeman degeneracy,” Phys. Rev. Lett. 111(24), 240503 (2013).
[Crossref] [PubMed]

Y. O. Dudin, A. G. Radnaev, R. Zhao, J. Z. Blumoff, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of light-shift compensated atomic spin waves with telecom light,” Phys. Rev. Lett. 105(26), 260502 (2010).
[Crossref] [PubMed]

T. Yuge, S. Sasaki, and Y. Hirayama, “Measurement of the noise spectrum using a multiple-pulse sequence,” Phys. Rev. Lett. 107(17), 170504 (2011).
[Crossref] [PubMed]

M. Lovrić, D. Suter, A. Ferrier, and P. Goldner, “Faithful solid state optical memory with dynamically decoupled spin wave storage,” Phys. Rev. Lett. 111(2), 020503 (2013).
[Crossref] [PubMed]

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

X. H. Bao, X. F. Xu, C. M. Li, Z. S. Yuan, C. Y. Lu, and J. W. Pan, “Quantum teleportation between remote atomic-ensemble quantum memories,” Proc. Natl. Acad. Sci. U.S.A. 109(50), 20347–20351 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

J. W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Multi-photon entanglement and interferometry,” Rev. Mod. Phys. 84(2), 777–838 (2012).
[Crossref]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

Science (1)

G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski, and R. Hanson, “Universal dynamical decoupling of a single solid-state spin from a spin bath,” Science 330(6000), 60–63 (2010).
[Crossref] [PubMed]

Other (1)

R. Loudon, The Quantum Theory of Light (Oxford University, 2004).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 The atomic level schemes of R 87 b for EIT storages (a) and Raman π rotations (b), respectively. σ + and σ + are the right- and left-circularly-polarized signal fields, respectively. W / R is the left-circularly-polarized writing/reading field. Δ R denotes the detuning of the Raman laser from the transition | a | e .
Fig. 2
Fig. 2 (a) CPMG π pulse sequence. (b) The illustration of function f ( t ' ) (n: even).
Fig. 3
Fig. 3 (a) The experimental setup. HWP: half-wave plate; QWP: quarter-wave plate; PBS: polarizing beam splitter; BS: polarization-insensitive beam splitter; D1, 2: Photon detectors. (b) The involved atomic level scheme of R 87 b for optical pumping.
Fig. 4
Fig. 4 The retrieval efficiencies as the function of the storage time. The square dots in curve ( Ι ) and circle dots in curve ( Ι Ι ) are the measured results for σ + -polarized and σ -polarized fields, respectively.
Fig. 5
Fig. 5 (a) and (b) The applied CPMG sequences for F d d = 5 k H z and F d d = 10 k H z , respectively. π i ( i = 1 , 2 , 3 , 4 ) is the i-th π pulse. (c) The quantum process fidelities F p as the function of the storage time. The square dots are the results without the CPMG sequence. The circle and triangle dots are the results with CPMG sequences of 5- k H z and 10- k H z frequencies, respectively. The horizontal dashed (red) line is the boundary of 1/2.
Fig. 6
Fig. 6 Quantum process fidelity F p at storage time of 800μs as the function of the number of π-pulses n (lower) and the frequency F d d (upper).

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

ε ( t ) = ε R ( t ) + ε L ( t ) = | ε ( t ) | ( α | R + β e i φ | L ) ,
( S 0 i n S 1 i n S 2 i n S 3 i n ) = | ε ( t ) | 2 ( 1 2 α β sin θ α 2 β 2 2 α β cos θ )
S ^ ± ( z , t ) = ( N z ) 1 z j N z | a m F = ± 1 j j b m F = 1 | e i ω a b t ,
S ( z , t 1 ) = S ^ ( z , t 1 ) + S ^ + ( z , t 1 ) = | S ( z , t 1 ) | ( α s + + β e i φ s ) .
S ( z , t ) = | S ^ ( z , 0 ) | e t / 2 τ d i ω a b t ( α e t / 2 τ + i Ω + t i 0 t ω + ( t ) d t ' s + + e i φ β s e t / 2 τ i Ω t i 0 t ω ( t ) d t ) ,
ε o u t ( t ) = R S ( z , t ) R e t / 2 τ d i ω a b t ( α e t / 2 τ + | R + e i φ β e t / 2 τ i Ω t i 0 t δ ω ( t ) d t | L ) ,
( S 0 o u t S 1 o u t S 2 o u t S 3 o u t ) = R e t / τ d ( α 2 e t / τ + + β 2 e t / τ 2 α β e t ( 1 / 2 τ + + 1 / 2 τ ) W ( t ) sin ( Ω t + φ ) α 2 e t / τ + β 2 e t / τ 2 α β e t ( 1 / 2 τ + + 1 / 2 τ ) W ( t ) cos ( Ω t + φ ) ) ,
W ( t ) = e t / T 0 ,
F s t = T r ( ρ i n ρ o u t ) .
F s t ( X ) 1 2 + e t ( 1 / 2 τ + + 1 / 2 τ ) W ( t ) cos Ω t e t / τ + + e t / τ ,
F s t ( X ) = 1 ,
F p 3 F st ¯ 1 2 ,
F s t ( X ) 1 2 + e t ( 1 / 2 τ + + 1 / 2 τ ) W ( t ) cos Ω t e t / τ + + e t / τ ,
α s + β e i φ s + α s + + β e i φ s .
S ( z , t ) = S ^ + ( z , t ) + S ^ ( z , t ) = | S ( z , t 0 ) | H ( t ) ( α e δ t 2 τ + s + + e i φ β W ( τ ) e δ t 2 τ i Ω δ t i τ τ + δ t δ ω ( t ) d t s ) ,
f ( t ' ) = 0 f o r t ' < 0 o r t ' > τ , f ( t ' ) = ( 1 ) l f o r t k < t ' < t k + 1 , k = 0 , 1 , 2 , 3 2 m .
S ( z , t ) = | S ( z , t 0 ) | H ( t ) ( α s + ( z , t ) + β e i φ i Ω δ t s ( z , t ) ) .
F p 1 + cos ϑ 2 .
S ( z , t ) = | S ( z , t 0 ) | H ( t ) ( α s ( z , t ) + β e i φ i ϑ s + ( z , t ) ) ,

Metrics