Abstract

A photon echo storage-time extension protocol is presented by using a phase locking method in a three-level backward propagation scheme, where phase locking serves as a conditional stopper of the rephasing process in conventional two-pulse photon echoes. The backward propagation scheme solves the critical problems of extremely low retrieval efficiency and π rephasing pulse-caused spontaneous emission noise in photon echo based quantum memories. The physics of the storage time extension lies in the imminent population transfer from the excited state to an auxiliary spin state by a phase locking control pulse. We numerically demonstrate that the storage time is lengthened by spin dephasing time.

© 2010 OSA

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2009 (4)

B. S. Ham, “Ultralong quantum optical storage using reversible inhomogeneous spin ensembles,” Nat. Photonics 3, 518–522 (2009).
[CrossRef]

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature 457(7231), 859–862 (2009).
[CrossRef] [PubMed]

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79(5), 052329 (2009).
[CrossRef]

J. Ruggiero, J.-L. Le Gouet, C. Simon, and T. Chaneliere, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79(5), 053851 (2009).
[CrossRef]

2008 (8)

I. Novikova, N. B. Philips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78(2), 021802 (2008).
[CrossRef]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-order aberration cancellation in quantum interferometry,” Phys. Rev. Lett. 101(23), 233603 (2008).
[CrossRef] [PubMed]

D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum memory of images: A quantum hologram,” Phys. Rev. A 77(2), 020302 (2008).
[CrossRef]

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for light using two-level atoms,” Phys. Rev. Lett. 100(2), 023601 (2008).
[CrossRef] [PubMed]

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. A. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452(7183), 67–71 (2008).
[CrossRef] [PubMed]

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

2007 (2)

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
[CrossRef] [PubMed]

N. Sangouard, C. Simon, M. Afzelius, and N. Gisin, “Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening,” Phys. Rev. A 75(3), 032327 (2007).
[CrossRef]

2005 (5)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherence media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95(6), 063601 (2005). This demonstration is another version of ref. (19), where rf pulses are used for the rephasing process.
[CrossRef] [PubMed]

M. Nilsson and S. Kroll, “Solid state quantum memory using complete absorption and re-emission of photons by tailored and externally controlled inhomogeneous absorption profiles,” Opt. Commun. 247(4-6), 393–403 (2005).
[CrossRef]

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005).
[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]

2004 (1)

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432(7016), 482–486 (2004).
[CrossRef] [PubMed]

2003 (1)

S. A. Moiseev, V. F. Tarasov, and B. S. Ham, “Quantum memory photon echo-like techniques in solids,” J. Opt. B Quantum Semiclassical Opt. 5(4), S497–S502 (2003).
[CrossRef]

2002 (1)

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[CrossRef] [PubMed]

2001 (2)

S. A. Moiseev and S. Kröll, “Complete reconstruction of the quantum state of a single-photon wave packet absorbed by a Doppler-broadened transition,” Phys. Rev. Lett. 87(17), 173601 (2001).
[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]

1993 (1)

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71(26), 4287–4290 (1993).
[CrossRef] [PubMed]

1987 (1)

1982 (1)

1964 (1)

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon Echo,” Phys. Rev. Lett. 13(19), 567–570 (1964).
[CrossRef]

Abella, I. D.

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon Echo,” Phys. Rev. Lett. 13(19), 567–570 (1964).
[CrossRef]

Afzelius, M.

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79(5), 052329 (2009).
[CrossRef]

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. A. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

N. Sangouard, C. Simon, M. Afzelius, and N. Gisin, “Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening,” Phys. Rev. A 75(3), 032327 (2007).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
[CrossRef] [PubMed]

Akamatsu, D.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Akiba, K.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Alexander, A. L.

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for light using two-level atoms,” Phys. Rev. Lett. 100(2), 023601 (2008).
[CrossRef] [PubMed]

André, A.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005).
[CrossRef] [PubMed]

Arikawa, M.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Bonato, C.

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-order aberration cancellation in quantum interferometry,” Phys. Rev. Lett. 101(23), 233603 (2008).
[CrossRef] [PubMed]

Bonora, S.

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-order aberration cancellation in quantum interferometry,” Phys. Rev. Lett. 101(23), 233603 (2008).
[CrossRef] [PubMed]

Boyer, V.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature 457(7231), 859–862 (2009).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Chaneliere, T.

J. Ruggiero, J.-L. Le Gouet, C. Simon, and T. Chaneliere, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79(5), 053851 (2009).
[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]

Choi, K. S.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452(7183), 67–71 (2008).
[CrossRef] [PubMed]

Cirac, J. I.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432(7016), 482–486 (2004).
[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]

de Riedmatten, H.

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79(5), 052329 (2009).
[CrossRef]

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. A. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
[CrossRef] [PubMed]

Deng, H.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452(7183), 67–71 (2008).
[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]

Eisaman, M. D.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005).
[CrossRef] [PubMed]

Ekert, A. K.

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71(26), 4287–4290 (1993).
[CrossRef] [PubMed]

Fiurásek, J.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432(7016), 482–486 (2004).
[CrossRef] [PubMed]

Fleischhauer, M.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005).
[CrossRef] [PubMed]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherence media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Fraval, E.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95(6), 063601 (2005). This demonstration is another version of ref. (19), where rf pulses are used for the rephasing process.
[CrossRef] [PubMed]

Furusawa, A.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Gisin, N.

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79(5), 052329 (2009).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
[CrossRef] [PubMed]

N. Sangouard, C. Simon, M. Afzelius, and N. Gisin, “Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening,” Phys. Rev. A 75(3), 032327 (2007).
[CrossRef]

Gisin, N. A.

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. A. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

Gorshkov, A. V.

I. Novikova, N. B. Philips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78(2), 021802 (2008).
[CrossRef]

Ham, B. S.

B. S. Ham, “Ultralong quantum optical storage using reversible inhomogeneous spin ensembles,” Nat. Photonics 3, 518–522 (2009).
[CrossRef]

S. A. Moiseev, V. F. Tarasov, and B. S. Ham, “Quantum memory photon echo-like techniques in solids,” J. Opt. B Quantum Semiclassical Opt. 5(4), S497–S502 (2003).
[CrossRef]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[CrossRef] [PubMed]

Hartmann, S. R.

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon Echo,” Phys. Rev. Lett. 13(19), 567–570 (1964).
[CrossRef]

Hemmer, P. R.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[CrossRef] [PubMed]

Hétet, G.

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for light using two-level atoms,” Phys. Rev. Lett. 100(2), 023601 (2008).
[CrossRef] [PubMed]

Honda, K.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Horne, M. A.

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71(26), 4287–4290 (1993).
[CrossRef] [PubMed]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherence media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Jenkins, S. D.

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]

Julsgaard, B.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432(7016), 482–486 (2004).
[CrossRef] [PubMed]

Kachru, R.

Kennedy, T. A. B.

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, M. K.

Kimble, H. J.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452(7183), 67–71 (2008).
[CrossRef] [PubMed]

Kozuma, M.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Kroll, S.

M. Nilsson and S. Kroll, “Solid state quantum memory using complete absorption and re-emission of photons by tailored and externally controlled inhomogeneous absorption profiles,” Opt. Commun. 247(4-6), 393–403 (2005).
[CrossRef]

Kröll, S.

S. A. Moiseev and S. Kröll, “Complete reconstruction of the quantum state of a single-photon wave packet absorbed by a Doppler-broadened transition,” Phys. Rev. Lett. 87(17), 173601 (2001).
[CrossRef] [PubMed]

Kurnit, N. A.

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon Echo,” Phys. Rev. Lett. 13(19), 567–570 (1964).
[CrossRef]

Kuzmich, A.

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]

Lam, P. K.

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for light using two-level atoms,” Phys. Rev. Lett. 100(2), 023601 (2008).
[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]

Laurat, J.

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452(7183), 67–71 (2008).
[CrossRef] [PubMed]

Le Gouet, J.-L.

J. Ruggiero, J.-L. Le Gouet, C. Simon, and T. Chaneliere, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79(5), 053851 (2009).
[CrossRef]

Lett, P. D.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature 457(7231), 859–862 (2009).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Longdell, J. J.

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for light using two-level atoms,” Phys. Rev. Lett. 100(2), 023601 (2008).
[CrossRef] [PubMed]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95(6), 063601 (2005). This demonstration is another version of ref. (19), where rf pulses are used for the rephasing process.
[CrossRef] [PubMed]

Lukin, M. D.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005).
[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]

Manson, N. B.

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95(6), 063601 (2005). This demonstration is another version of ref. (19), where rf pulses are used for the rephasing process.
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherence media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Marino, A. M.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature 457(7231), 859–862 (2009).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Massou, F.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005).
[CrossRef] [PubMed]

Matsukevich, D. N.

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]

Moiseev, S. A.

S. A. Moiseev, V. F. Tarasov, and B. S. Ham, “Quantum memory photon echo-like techniques in solids,” J. Opt. B Quantum Semiclassical Opt. 5(4), S497–S502 (2003).
[CrossRef]

S. A. Moiseev and S. Kröll, “Complete reconstruction of the quantum state of a single-photon wave packet absorbed by a Doppler-broadened transition,” Phys. Rev. Lett. 87(17), 173601 (2001).
[CrossRef] [PubMed]

Mossberg, T. W.

Musser, J. A.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[CrossRef] [PubMed]

Nagatsuka, S.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Nilsson, M.

M. Nilsson and S. Kroll, “Solid state quantum memory using complete absorption and re-emission of photons by tailored and externally controlled inhomogeneous absorption profiles,” Opt. Commun. 247(4-6), 393–403 (2005).
[CrossRef]

Novikova, I.

I. Novikova, N. B. Philips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78(2), 021802 (2008).
[CrossRef]

Philips, N. B.

I. Novikova, N. B. Philips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78(2), 021802 (2008).
[CrossRef]

Polzik, E. S.

D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum memory of images: A quantum hologram,” Phys. Rev. A 77(2), 020302 (2008).
[CrossRef]

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432(7016), 482–486 (2004).
[CrossRef] [PubMed]

Pooser, R. C.

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature 457(7231), 859–862 (2009).
[CrossRef] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Ruggiero, J.

J. Ruggiero, J.-L. Le Gouet, C. Simon, and T. Chaneliere, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79(5), 053851 (2009).
[CrossRef]

Saleh, B. E. A.

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-order aberration cancellation in quantum interferometry,” Phys. Rev. Lett. 101(23), 233603 (2008).
[CrossRef] [PubMed]

Sangouard, N.

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
[CrossRef] [PubMed]

N. Sangouard, C. Simon, M. Afzelius, and N. Gisin, “Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening,” Phys. Rev. A 75(3), 032327 (2007).
[CrossRef]

Sellars, M. J.

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for light using two-level atoms,” Phys. Rev. Lett. 100(2), 023601 (2008).
[CrossRef] [PubMed]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95(6), 063601 (2005). This demonstration is another version of ref. (19), where rf pulses are used for the rephasing process.
[CrossRef] [PubMed]

Sergienko, A. V.

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-order aberration cancellation in quantum interferometry,” Phys. Rev. Lett. 101(23), 233603 (2008).
[CrossRef] [PubMed]

Shahriar, M. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[CrossRef] [PubMed]

Sherson, J.

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432(7016), 482–486 (2004).
[CrossRef] [PubMed]

Simon, C.

J. Ruggiero, J.-L. Le Gouet, C. Simon, and T. Chaneliere, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79(5), 053851 (2009).
[CrossRef]

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79(5), 052329 (2009).
[CrossRef]

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. A. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

N. Sangouard, C. Simon, M. Afzelius, and N. Gisin, “Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening,” Phys. Rev. A 75(3), 032327 (2007).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
[CrossRef] [PubMed]

Sokolov, I. V.

D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum memory of images: A quantum hologram,” Phys. Rev. A 77(2), 020302 (2008).
[CrossRef]

Staudt, M. U.

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. A. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

Sudarshanam, V. S.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[CrossRef] [PubMed]

Tanimura, T.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Tarasov, V. F.

S. A. Moiseev, V. F. Tarasov, and B. S. Ham, “Quantum memory photon echo-like techniques in solids,” J. Opt. B Quantum Semiclassical Opt. 5(4), S497–S502 (2003).
[CrossRef]

Turukhin, A. V.

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[CrossRef] [PubMed]

Vasilyev, D. V.

D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum memory of images: A quantum hologram,” Phys. Rev. A 77(2), 020302 (2008).
[CrossRef]

Villoresi, P.

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-order aberration cancellation in quantum interferometry,” Phys. Rev. Lett. 101(23), 233603 (2008).
[CrossRef] [PubMed]

Yokoi, Y.

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

Zbinden, H.

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
[CrossRef] [PubMed]

Zeilinger, A.

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71(26), 4287–4290 (1993).
[CrossRef] [PubMed]

Zibrov, A. S.

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005).
[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.

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71(26), 4287–4290 (1993).
[CrossRef] [PubMed]

J. Opt. B Quantum Semiclassical Opt. (1)

S. A. Moiseev, V. F. Tarasov, and B. S. Ham, “Quantum memory photon echo-like techniques in solids,” J. Opt. B Quantum Semiclassical Opt. 5(4), S497–S502 (2003).
[CrossRef]

Nat. Photonics (1)

B. S. Ham, “Ultralong quantum optical storage using reversible inhomogeneous spin ensembles,” Nat. Photonics 3, 518–522 (2009).
[CrossRef]

Nature (7)

A. M. Marino, R. C. Pooser, V. Boyer, and P. D. Lett, “Tunable delay of Einstein-Podolsky-Rosen entanglement,” Nature 457(7231), 859–862 (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]

H. de Riedmatten, M. Afzelius, M. U. Staudt, C. Simon, and N. A. Gisin, “A solid-state light-matter interface at the single-photon level,” Nature 456(7223), 773–777 (2008).
[CrossRef] [PubMed]

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452(7183), 67–71 (2008).
[CrossRef] [PubMed]

M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, “Electromagnetically induced transparency with tunable single-photon pulses,” Nature 438(7069), 837–841 (2005).
[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]

B. Julsgaard, J. Sherson, J. I. Cirac, J. Fiurásek, and E. S. Polzik, “Experimental demonstration of quantum memory for light,” Nature 432(7016), 482–486 (2004).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Nilsson and S. Kroll, “Solid state quantum memory using complete absorption and re-emission of photons by tailored and externally controlled inhomogeneous absorption profiles,” Opt. Commun. 247(4-6), 393–403 (2005).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (5)

N. Sangouard, C. Simon, M. Afzelius, and N. Gisin, “Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening,” Phys. Rev. A 75(3), 032327 (2007).
[CrossRef]

D. V. Vasilyev, I. V. Sokolov, and E. S. Polzik, “Quantum memory of images: A quantum hologram,” Phys. Rev. A 77(2), 020302 (2008).
[CrossRef]

J. Ruggiero, J.-L. Le Gouet, C. Simon, and T. Chaneliere, “Why the two-pulse photon echo is not a good quantum memory protocol,” Phys. Rev. A 79(5), 053851 (2009).
[CrossRef]

I. Novikova, N. B. Philips, and A. V. Gorshkov, “Optimal light storage with full pulse-shape control,” Phys. Rev. A 78(2), 021802 (2008).
[CrossRef]

M. Afzelius, C. Simon, H. de Riedmatten, and N. Gisin, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79(5), 052329 (2009).
[CrossRef]

Phys. Rev. Lett. (9)

S. A. Moiseev and S. Kröll, “Complete reconstruction of the quantum state of a single-photon wave packet absorbed by a Doppler-broadened transition,” Phys. Rev. Lett. 87(17), 173601 (2001).
[CrossRef] [PubMed]

K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura, A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,” Phys. Rev. Lett. 100(9), 093601 (2008).
[CrossRef] [PubMed]

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, “Electro-optic quantum memory for light using two-level atoms,” Phys. Rev. Lett. 100(2), 023601 (2008).
[CrossRef] [PubMed]

J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, “Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid,” Phys. Rev. Lett. 95(6), 063601 (2005). This demonstration is another version of ref. (19), where rf pulses are used for the rephasing process.
[CrossRef] [PubMed]

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, “Observation of ultraslow and stored light pulses in a solid,” Phys. Rev. Lett. 88(2), 023602 (2002).
[CrossRef] [PubMed]

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71(26), 4287–4290 (1993).
[CrossRef] [PubMed]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multimode memories,” Phys. Rev. Lett. 98(19), 190503 (2007).
[CrossRef] [PubMed]

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon Echo,” Phys. Rev. Lett. 13(19), 567–570 (1964).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-order aberration cancellation in quantum interferometry,” Phys. Rev. Lett. 101(23), 233603 (2008).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherence media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[CrossRef]

Science (1)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[CrossRef] [PubMed]

Other (2)

J. Hahn, and B. S. Ham, “Slow light enhanced photon echoes,” arXiv:0909.4992.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics 79–95 (Addison-Wesley, 1974).
[PubMed]

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Figures (6)

Fig. 1
Fig. 1

Phase locked echo. (a) Energy level diagram interacting with light pulses. B1, B2, D, E, and R stand for locking, unlocking, data, photon echo, and rephasing pulses. The pulse areas of D, R, B1, and B2 are π/2, π, π, and 3π, respectively. Δinh (680 kHz at full width at half maximum) is an optical inhomogeneous width with Gaussian distribution. (b) Pulse sequence. (c) Programed pulse sequence. TD = 5; TR = 10; TB1 = 10.1;TB2 = 55 μs. (d) Numerical simulations for (c). Marks 1, 2, and 3 represent conventional photon echoes without B1 and B2 for TR = 10, 20, and 30 μs, respectively. Marks β, δ, and γ respectively represent phase locked photon echoes with B1 (π) and B2 for B2 = 3π, 2π, and π in pulse area. The pulse area is defined by Ω d t . Γ12 = γ12 = 0; Γ13 = Γ23 = 5 kHz; γ13 = γ23 = 10 kHz. ΩD = ΩR = ΩB1 = ΩB2 = 5 MHz.

Fig. 2
Fig. 2

(a) D-pulse area independent photon echo efficiency using phase locking. ΦD stands for pulse area of the data pulse D. This linear relationship between efficiency and pulse area sustains up to ΦD = π/10. The data D pulse magnitude decreases by a factor of (i) 10 (green), (ii) 100 (blue), and (iii) 1000 (red), compared with that in Fig. 1. For comparison, the green (red) curve is multiplied (divided) by 10, while the blue curve shows no change. (b) B1 delay invariant phase locked echo. TB1 in Fig. 1 and Eq. (1) is varied. The B1 delay from R is (c) 7 μs, and (d) 15 μs, while R delay from D is 10 μs. All other parameters are the same as in Fig. 1 except for γ12 = Γ13 = 2 kHz in (a) and the inset of (b).

Fig. 5
Fig. 5

Rephasing control by using B pulses. (a) and (b) Population evolution with R, B1, and B2 for symmetrically detuned atoms. (c) and (d) Coherence evolution with R, B1, and B2 for symmetrically detuned atoms. (e) and (f) Bloch vector evolution for (c) and (d), respectively. All parameters are the same as in Fig. 4, unless otherwise indicated.

Fig. 3
Fig. 3

Storage time versus spin phase decay. D(π/2), R(π), and B1(π) fall at t = 5, 15, and 20 μs. B2 (3π) position at T = 15 (Blue), 30 (Green), 45 (Red), 60 (Black), and 90 μs (last black peak). All other parameters are the same as in Fig. 1.

Fig. 4
Fig. 4

(a) and (c) Conventional two-pulse photon echo. D (R) turns on at t = 5 (10) μs. δ = 40 kHz. (b) and (d) Phase locked photon echo using B1 (π) and B2 (3π). Here, 161 groups of atoms are considered for 1.6 MHz optical inhomogeneous broadening. All parameters are the same as in Fig. 1.

Fig. 6
Fig. 6

Function of phase locking and unlocking pulses. (a) Pulse sequence of D(π/2)-R(π)-B1(π)-B2(7π). (b) Photon echo for (a). (c) and (d) Coherence evolution for symmetrically detuned atoms with R, B1, and B2. Red: Reρ 13(−δ), Blue: Reρ 13( + δ), Green: Imρ 13( ± δ), Cyan: ρ 11, Dotted: ρ 22, and Magenta: ρ 33. (e) Coherence evolution of Reρ 13 versus detuning for B2. (f) Coherence evolution of Imρ 13 versus detuning for B2. Parameters are the same as in Fig. 3. ΩR = ΩB1 = ΩB2 = 5 MHz.

Equations (11)

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T E = T B 2 + ( T R T D ) ( T B 1 T R ) .
d ρ d t = i [ H , ρ ] 1 2 { Γ , ρ } ,
d ρ 13 d t = i Ω 13 ( ρ 33 ρ 11 ) i Ω 23 ρ 12 i ( δ 1 + γ 13 ) ρ 13 ,
d ρ 23 d t = i Ω 23 ( ρ 33 ρ 22 ) i Ω 13 ρ 21 i ( δ 1 + γ 23 ) ρ 23 ,
d ρ 12 d t = i Ω 13 ρ 32 i Ω 23 ρ 13 i ( δ 1 δ 2 ) ρ 12 γ 12 ρ 12 ,
Φ R = ( 2 n 1 ) π ,
Φ B 2 = ( 4 n 1 ) π ,
Φ B 1 = ( 4 n 3 ) π ,
Φ B 2 = ( 4 n 3 ) π ,
Φ B 1 = ( 4 n 1 ) π ,
Φ B 1 + B 2 = 4 n π ,

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