Abstract

Optical locking applied to rephased atoms in photon echoes is analyzed for on-demand photon storage time extension, where the storage time extension is confined by the inverse of spin inhomogeneous broadening. Both optical locking and photon storage mechanisms in atomic frequency comb echoes are discussed and compared with those in two-pulse photon echo-based phase-locked echoes and three-pulse photon echoes.

© 2011 Optical Society of America

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  1. N. A. Kurnit, I. D. Abella, and S. R. Hartmann, “Observation of a photon echo,” Phys. Rev. Lett. 13, 567–570 (1964).
    [CrossRef]
  2. T. W. Mossberg, “Time-domain frequency-selective optical data storage,” Opt. Lett. 7, 77–79 (1982).
    [CrossRef]
  3. M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
    [CrossRef]
  4. B. S. Ham and J. Hahn, “Atomic coherence swing in a double L-type system using ultraslow light,” Opt. Lett. 34, 776–778(2009).
    [CrossRef]
  5. V. Boyer, D. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
    [CrossRef]
  6. B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient phase conjugation via two-photon coherence in an optically dense crystal,” Phys. Rev. A 59, R2583–R2586 (1999).
    [CrossRef]
  7. N. W. Carlson, W. R. Babbitt, and T. W. Mossberg, “Storage and phase conjugation of light pulses using stimulated photon echoes,” Opt. Lett. 8, 623–625 (1983).
    [CrossRef]
  8. M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
    [CrossRef]
  9. B. S. Ham and J. Hahn, “Phase locked photon echoes for near perfect retrieval efficiency and extended storage time,” arXiv:0911.3869.
  10. B. S. Ham, “Control of photon storage time using phase locking,” Opt. Express 18, 1704–1713 (2010).
    [CrossRef]
  11. M. Mitsunaga and N. Uesugi, “248 bit optical storage in Eu3+:YAlO3 by accumulated photon echoes,” Opt. Lett. 15, 195–197 (1990).
    [CrossRef]
  12. 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, 773–777 (2008).
    [CrossRef]
  13. S. A. Moiseev and S. Kroll, “Complete reconstruction of the quantum state of a single-photon wave packet absorbed by a Doppler-broadened transition,” Phys. Rev. Lett. 87, 173601(2001).
    [CrossRef]
  14. B. S. Ham, “A contradictory phenomenon of deshelving pulses in a dilute medium used for lengthened photon storage time,” Opt. Express 18, 17749–17755 (2010).
    [CrossRef]
  15. E. Fraval, M. J. Sellars, and J. J. Longdell, “Method of extending hyperfine coherence times in Pr3+:Y2SiO5,” Phys. Rev. Lett. 92, 077601 (2004).
    [CrossRef]
  16. B. S. Ham, “Atom phase controlled noise-free photon echo,” arXiv:1101.5480.

2010 (3)

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

B. S. Ham, “Control of photon storage time using phase locking,” Opt. Express 18, 1704–1713 (2010).
[CrossRef]

B. S. Ham, “A contradictory phenomenon of deshelving pulses in a dilute medium used for lengthened photon storage time,” Opt. Express 18, 17749–17755 (2010).
[CrossRef]

2009 (2)

M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
[CrossRef]

B. S. Ham and J. Hahn, “Atomic coherence swing in a double L-type system using ultraslow light,” Opt. Lett. 34, 776–778(2009).
[CrossRef]

2008 (1)

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, 773–777 (2008).
[CrossRef]

2007 (1)

V. Boyer, D. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

2004 (1)

E. Fraval, M. J. Sellars, and J. J. Longdell, “Method of extending hyperfine coherence times in Pr3+:Y2SiO5,” Phys. Rev. Lett. 92, 077601 (2004).
[CrossRef]

2001 (1)

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

1999 (1)

B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient phase conjugation via two-photon coherence in an optically dense crystal,” Phys. Rev. A 59, R2583–R2586 (1999).
[CrossRef]

1990 (1)

1983 (1)

1982 (1)

1964 (1)

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

Afzelius, M.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[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, 773–777 (2008).
[CrossRef]

Amari, A.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

Arimondo, E.

V. Boyer, D. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

Babbitt, W. R.

Boyer, V.

V. Boyer, D. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

Buchler, B. C.

M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
[CrossRef]

Carlson, N. W.

de Riedmatten, H.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[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, 773–777 (2008).
[CrossRef]

Fraval, E.

E. Fraval, M. J. Sellars, and J. J. Longdell, “Method of extending hyperfine coherence times in Pr3+:Y2SiO5,” Phys. Rev. Lett. 92, 077601 (2004).
[CrossRef]

Gisin, N.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[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, 773–777 (2008).
[CrossRef]

Hahn, J.

B. S. Ham and J. Hahn, “Atomic coherence swing in a double L-type system using ultraslow light,” Opt. Lett. 34, 776–778(2009).
[CrossRef]

B. S. Ham and J. Hahn, “Phase locked photon echoes for near perfect retrieval efficiency and extended storage time,” arXiv:0911.3869.

Ham, B. S.

B. S. Ham, “Control of photon storage time using phase locking,” Opt. Express 18, 1704–1713 (2010).
[CrossRef]

B. S. Ham, “A contradictory phenomenon of deshelving pulses in a dilute medium used for lengthened photon storage time,” Opt. Express 18, 17749–17755 (2010).
[CrossRef]

B. S. Ham and J. Hahn, “Atomic coherence swing in a double L-type system using ultraslow light,” Opt. Lett. 34, 776–778(2009).
[CrossRef]

B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient phase conjugation via two-photon coherence in an optically dense crystal,” Phys. Rev. A 59, R2583–R2586 (1999).
[CrossRef]

B. S. Ham, “Atom phase controlled noise-free photon echo,” arXiv:1101.5480.

B. S. Ham and J. Hahn, “Phase locked photon echoes for near perfect retrieval efficiency and extended storage time,” arXiv:0911.3869.

Hartmann, S. R.

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

Hemmer, P. R.

B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient phase conjugation via two-photon coherence in an optically dense crystal,” Phys. Rev. A 59, R2583–R2586 (1999).
[CrossRef]

Hetet, G.

M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
[CrossRef]

Hosseini, M.

M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
[CrossRef]

Kroll, S.

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

Kröll, S.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

Kurnit, N. A.

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

Lam, P. K.

M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
[CrossRef]

Lauritzen, B.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

Lett, P. D.

V. Boyer, D. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

Longdell, J. J.

M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
[CrossRef]

E. Fraval, M. J. Sellars, and J. J. Longdell, “Method of extending hyperfine coherence times in Pr3+:Y2SiO5,” Phys. Rev. Lett. 92, 077601 (2004).
[CrossRef]

McCormick, D. F.

V. Boyer, D. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

Minar, J.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

Mitsunaga, M.

Moiseev, S. A.

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

Mossberg, T. W.

Sangouard, N.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

Sellars, M. J.

E. Fraval, M. J. Sellars, and J. J. Longdell, “Method of extending hyperfine coherence times in Pr3+:Y2SiO5,” Phys. Rev. Lett. 92, 077601 (2004).
[CrossRef]

Shahriar, M. S.

B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient phase conjugation via two-photon coherence in an optically dense crystal,” Phys. Rev. A 59, R2583–R2586 (1999).
[CrossRef]

Simon, C.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[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, 773–777 (2008).
[CrossRef]

Sparkes, B. M.

M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (2009).
[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, 773–777 (2008).
[CrossRef]

Uesugi, N.

Usmani, I.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

Walther, A.

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

Nature (2)

M. Hosseini, B. M. Sparkes, G. Hetet, J. J. Longdell, P. K. Lam, and B. C. Buchler, “Coherent optical pulse sequencer for quantum applications,” Nature 461, 241–245 (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, 773–777 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient phase conjugation via two-photon coherence in an optically dense crystal,” Phys. Rev. A 59, R2583–R2586 (1999).
[CrossRef]

Phys. Rev. Lett. (5)

E. Fraval, M. J. Sellars, and J. J. Longdell, “Method of extending hyperfine coherence times in Pr3+:Y2SiO5,” Phys. Rev. Lett. 92, 077601 (2004).
[CrossRef]

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

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

V. Boyer, D. F. McCormick, E. Arimondo, and P. D. Lett, “Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor,” Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef]

M. Afzelius, I. Usmani, A. Amari, B. Lauritzen, A. Walther, C. Simon, N. Sangouard, J. Minar, H. de Riedmatten, N. Gisin, and S. Kröll, “Demonstration of atomic frequency comb memory for light with spin-wave storage,” Phys. Rev. Lett. 104, 040503(2010).
[CrossRef]

Other (2)

B. S. Ham and J. Hahn, “Phase locked photon echoes for near perfect retrieval efficiency and extended storage time,” arXiv:0911.3869.

B. S. Ham, “Atom phase controlled noise-free photon echo,” arXiv:1101.5480.

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Figures (3)

Fig. 1
Fig. 1

(a) Energy level diagram and (b) pulse sequence.

Fig. 2
Fig. 2

(a) AFC echo pulse sequence. Each pulse turns on at 5, 15, 35, 45, 65, 75, 95, 105, 125, 135, and 175 μs . Each pulse duration is 100 ns . (b), (c) Absorption versus time for (a). For the red curve in (c), the INPUT pulse in (a) is reduced to one fifth. The dotted circle indicates the AFC echo. (d) Population ρ 11 versus atom detuning. t = 16 (red), 46 (green), 76 (magenta), 106 (cyan), and 136 μs (black). (top to bottom) Dotted curve represents initial spectral distribution at t = 0 . (e) Conventional three-pulse (stimulated) photon echo (see mark “2”). Mark “1” is for a reference as a two-pulse photon echo. (f) Population ρ 11 versus atom detuning. Blue, t = 16 μs ; red, t = 136 μs . For all, Γ 31 = Γ 32 = 20 kHz (population decay rate), γ 31 = γ 32 = 30 kH (phase decay rate), Γ 21 = γ 21 = 0 . Inhomogeneously broadened atoms are Gaussian distributed: FWHM = 680 kHz . Initial population is ρ 11 = 1 , ρ 22 = ρ 33 = 0 .

Fig. 3
Fig. 3

(a), (b) AFC echo pulse sequence with control pulses B1 and B2 for Δ T < τ and Δ T < τ , respectively. Pulse area of B1 and B2 satisfies π and 3 π . (c) For identical control pulses B1 and B2, as shown in [8], whose pulse area is π, resulting in no AFC echo: Δ T < τ . (d)–(f) Numerical simulations of (a)–(c), respectively. Each pulse is turned on at 5, 10, 30, 35, 55, 60, 120, 120.1, and 160 μs . Each pulse duration is 100 ns . τ = 5 μs , δ = 3 μs . (g), (h) Phase-locked echo corresponding to (a) and (d). Each pulse is turned on at 5, 15, and 175 μs for the blue line (three-pulse echo) with identical pulse durations of 100 ns to satisfy π / 2 pulse area. For the red curve (phase-locked echo), each pulse turns on at 5, 15, 15.1, and 175 μs , with pulse areas π / 2 , π, π, and 3 π , respectively. The last two pulses are optical-locking pulses, B1 and B2. Two different cases of B1 delay from the rephasing pulse at t = 15 μs are overlapped. The delay difference is Δ T = 5 μs , which is shorter than the two-pulse delay τ = 10 μs . (i) Individual atom phase evolution of (g) as a function of time: δ = 40 kHz . Green curve is for ρ 33 . For all, Γ 31 = Γ 32 = 20 kHz (population decay rate), γ 31 = γ 32 = 30 kH (phase decay rate), Γ 21 = γ 21 = 0 . Inhomogeneously broadened atoms are Gaussian distributed: FWHM = 680 kHz . Initial population is ρ 11 = 1 , ρ 22 = ρ 33 = 0 .

Equations (1)

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i ρ ˙ = [ H , ρ ] + decay terms ,

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