Abstract

We show that a system characterized by long-lived coherent population oscillations (CPOs), such as a two-level system that decays via a shelving state, can be used to construct a spatial optical memory. In the presence of a cw control field, a field is generated at the four-wave mixing (FWM) frequency with the same spatial profile as the initial probe. When the control field is switched off, these spatial profiles are encoded in the CPOs of the ground and storage states. When the control field is switched on again, the probe and FWM fields are retrieved simultaneously with the same spatial profiles as the initial probe.

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  1. K. Hammerer, A. S. Sorensen, and E. S. Polzik, arXiv:0807.3358v4[quant-ph] (2009).
  2. P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
    [CrossRef] [PubMed]
  3. M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
    [CrossRef] [PubMed]
  4. R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, Phys. Rev. A 24, 411 (1981).
    [CrossRef]
  5. H. Friedmann, A. D. Wilson-Gordon, and M. Rosenbluh, Phys. Rev. A 33, 1783 (1986).
    [CrossRef] [PubMed]
  6. M. Sargent III, Phys. Rep. 43, 223 (1978).
    [CrossRef]
  7. A. V. Sharypov, A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 81, 013829 (2010).
    [CrossRef]
  8. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, Phys. Rev. A 67, 033807 (2003).
    [CrossRef]
  9. A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Lett. 33, 1605 (2008).
    [CrossRef] [PubMed]
  10. T. H. Maiman, Phys. Rev. Lett. 4, 564 (1960).
    [CrossRef]
  11. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
    [CrossRef] [PubMed]
  12. R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
    [CrossRef]
  13. L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
    [CrossRef]
  14. J. H. Lee, J. J. Song, M. A. F. Scarparo, and M. D. Levenson, Opt. Lett. 5, 196 (1980).
    [CrossRef] [PubMed]
  15. L. Cerdan, R. Weigand, J. M. G. Perez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
    [CrossRef]
  16. V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
    [CrossRef] [PubMed]

2010 (1)

A. V. Sharypov, A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 81, 013829 (2010).
[CrossRef]

2009 (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

2008 (4)

L. Cerdan, R. Weigand, J. M. G. Perez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Lett. 33, 1605 (2008).
[CrossRef] [PubMed]

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef] [PubMed]

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef] [PubMed]

2007 (1)

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

2003 (1)

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, Phys. Rev. A 67, 033807 (2003).
[CrossRef]

2000 (1)

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

1986 (1)

H. Friedmann, A. D. Wilson-Gordon, and M. Rosenbluh, Phys. Rev. A 33, 1783 (1986).
[CrossRef] [PubMed]

1983 (1)

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

1981 (1)

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, Phys. Rev. A 24, 411 (1981).
[CrossRef]

1980 (1)

1978 (1)

M. Sargent III, Phys. Rep. 43, 223 (1978).
[CrossRef]

1960 (1)

T. H. Maiman, Phys. Rev. Lett. 4, 564 (1960).
[CrossRef]

Arimondo, E.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Boyd, R. W.

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, Phys. Rev. A 24, 411 (1981).
[CrossRef]

Boyer, V.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Camacho, R. M.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef] [PubMed]

Cerdan, L.

L. Cerdan, R. Weigand, J. M. G. Perez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Crespo, H.

L. Cerdan, R. Weigand, J. M. G. Perez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Davidson, N.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef] [PubMed]

Eilam, A.

A. V. Sharypov, A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 81, 013829 (2010).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Lett. 33, 1605 (2008).
[CrossRef] [PubMed]

Firstenberg, O.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

Friedmann, H.

A. V. Sharypov, A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 81, 013829 (2010).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Lett. 33, 1605 (2008).
[CrossRef] [PubMed]

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, Phys. Rev. A 67, 033807 (2003).
[CrossRef]

H. Friedmann, A. D. Wilson-Gordon, and M. Rosenbluh, Phys. Rev. A 33, 1783 (1986).
[CrossRef] [PubMed]

Goren, C.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, Phys. Rev. A 67, 033807 (2003).
[CrossRef]

Hammerer, K.

K. Hammerer, A. S. Sorensen, and E. S. Polzik, arXiv:0807.3358v4[quant-ph] (2009).

Harter, D. J.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, Phys. Rev. A 24, 411 (1981).
[CrossRef]

Hillman, L. W.

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

Howell, J. C.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef] [PubMed]

Krasinski, J.

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

Lee, J. H.

Lett, P. D.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Levenson, M. D.

Lukin, M. D.

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

Maiman, T. H.

T. H. Maiman, Phys. Rev. Lett. 4, 564 (1960).
[CrossRef]

McCormick, C. F.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Narum, P.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, Phys. Rev. A 24, 411 (1981).
[CrossRef]

Perez, J. M. G.

L. Cerdan, R. Weigand, J. M. G. Perez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Polzik, E. S.

K. Hammerer, A. S. Sorensen, and E. S. Polzik, arXiv:0807.3358v4[quant-ph] (2009).

Pugatch, R.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef] [PubMed]

Raymer, M. G.

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, Phys. Rev. A 24, 411 (1981).
[CrossRef]

Ron, A.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef] [PubMed]

Rosenbluh, M.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, Phys. Rev. A 67, 033807 (2003).
[CrossRef]

H. Friedmann, A. D. Wilson-Gordon, and M. Rosenbluh, Phys. Rev. A 33, 1783 (1986).
[CrossRef] [PubMed]

Sargent, M.

M. Sargent III, Phys. Rep. 43, 223 (1978).
[CrossRef]

Scarparo, M. A. F.

Sharypov, A. V.

A. V. Sharypov, A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 81, 013829 (2010).
[CrossRef]

Shuker, M.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef] [PubMed]

Song, J. J.

Sorensen, A. S.

K. Hammerer, A. S. Sorensen, and E. S. Polzik, arXiv:0807.3358v4[quant-ph] (2009).

Stroud, C. R.

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

Vudyasetu, P. K.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef] [PubMed]

Weigand, R.

L. Cerdan, R. Weigand, J. M. G. Perez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Wilson-Gordon, A. D.

A. V. Sharypov, A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 81, 013829 (2010).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Lett. 33, 1605 (2008).
[CrossRef] [PubMed]

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, Phys. Rev. A 67, 033807 (2003).
[CrossRef]

H. Friedmann, A. D. Wilson-Gordon, and M. Rosenbluh, Phys. Rev. A 33, 1783 (1986).
[CrossRef] [PubMed]

Am. J. Phys. (1)

L. Cerdan, R. Weigand, J. M. G. Perez, and H. Crespo, Am. J. Phys. 76, 826 (2008).
[CrossRef]

Nat. Photonics (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, Nat. Photonics 3, 103 (2009).
[CrossRef]

Opt. Commun. (1)

L. W. Hillman, R. W. Boyd, J. Krasinski, and C. R. Stroud, Opt. Commun. 45, 416 (1983).
[CrossRef]

Opt. Lett. (2)

Phys. Rep. (1)

M. Sargent III, Phys. Rep. 43, 223 (1978).
[CrossRef]

Phys. Rev. A (4)

A. V. Sharypov, A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 81, 013829 (2010).
[CrossRef]

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, Phys. Rev. A 67, 033807 (2003).
[CrossRef]

R. W. Boyd, M. G. Raymer, P. Narum, and D. J. Harter, Phys. Rev. A 24, 411 (1981).
[CrossRef]

H. Friedmann, A. D. Wilson-Gordon, and M. Rosenbluh, Phys. Rev. A 33, 1783 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, Phys. Rev. Lett. 100, 123903 (2008).
[CrossRef] [PubMed]

M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
[CrossRef] [PubMed]

T. H. Maiman, Phys. Rev. Lett. 4, 564 (1960).
[CrossRef]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Other (1)

K. Hammerer, A. S. Sorensen, and E. S. Polzik, arXiv:0807.3358v4[quant-ph] (2009).

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Figures (4)

Fig. 1
Fig. 1

TLS with shelving state.

Fig. 2
Fig. 2

Time-dependence of CPOs Re [ ρ 11 , 33 ( δ ) ( t ) ] , calculated for a Gaussian probe and a cw control field, for several values of Γ 31 . V c = 0.1 Γ 21 , V p = 10 3 Γ 21 , Γ 2 = 100 Γ 21 , Γ 31 = 10 4 Γ 21 (dotted-dashed lines), Γ 31 = 10 2 Γ 21 (dashed lines), Γ 31 = 10 1 Γ 21 (dotted lines), and Γ 31 = Γ 21 (solid lines).

Fig. 3
Fig. 3

Time-dependence of probe and FWM absorption, calculated for a Gaussian probe and a control field that is switched off and on at the times indicated by the arrows. The black lines indicate Im [ ρ 21 ( δ ) ( t ) ] , and the gray lines indicate Im [ ρ 12 ( δ ) ( t ) ] . V c = 0.1 Γ 21 , V p = 10 3 Γ 21 , Γ 23 = 100 Γ 21 , Γ 31 = 10 4 Γ 21 , and δ = 0 .

Fig. 4
Fig. 4

Spatial memory. (a) Initial Gaussian transverse intensity profile of the probe, (b) time-dependence of the control field, (c) time-dependence of the transverse profile of the ground-state CPO, and (d) time-dependence of the transverse profile of the FWM transverse intensity profile. Other parameters are the same as in Fig. 3.

Equations (8)

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ρ ̇ 11 ( 0 ) = i ( V c ρ 21 ( 0 ) V c ρ 12 ( 0 ) ) + Γ 21 ρ 22 ( 0 ) + Γ 31 ρ 33 ( 0 ) ,
ρ ̇ 22 ( 0 ) = i ( V c ρ 12 ( 0 ) V c ρ 21 ( 0 ) ) ( Γ 21 + Γ 23 ) ρ 22 ( 0 ) ,
ρ ̇ 21 ( 0 ) = i V c ( ρ 11 ( 0 ) ρ 22 ( 0 ) ) ( i Δ + γ ) ρ 21 ( 0 ) ,
ρ ̇ 11 ( δ ) = i δ ρ 11 ( δ ) + Γ 21 ρ 22 ( δ ) + Γ 31 ρ 33 ( δ ) + i V c ρ 21 ( δ ) i V c ρ 12 ( δ ) i V p ρ 12 ( 0 ) ,
ρ ̇ 22 ( δ ) = i δ ρ 22 ( δ ) ( Γ 21 + Γ 23 ) ρ 22 ( δ ) i V c ρ 21 ( δ ) + i V c ρ 12 ( δ ) + i V p ρ 12 ( 0 ) ,
ρ ̇ 21 ( δ ) = [ i ( δ Δ ) γ ] ρ 21 ( δ ) + i V c ( ρ 11 ( δ ) ρ 22 ( δ ) ) + i V p ( ρ 11 ( 0 ) ρ 22 ( 0 ) ) ,
ρ ̇ 12 ( δ ) = [ i ( δ + Δ ) γ ] ρ 12 ( δ ) i V c ( ρ 11 ( δ ) ρ 22 ( δ ) ) ,
ρ 21 ( δ ) = i V p / γ 1 + κ [ 1 κ Γ 31 / γ ( 1 + κ ) Γ 31 / γ i δ / γ ] ,

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