Abstract

We propose a photon echo quantum memory scheme using detuned Raman coupling to long-lived ground states. In contrast to previous three-level schemes based on controlled reversible inhomogeneous broadening that use sequences of π pulses, the scheme does not require accurate control of the coupling dynamics to the ground states. We present a proof-of-principle experimental realization of our proposal using rubidium atoms in a warm vapor cell. The Raman resonance line is broadened using a magnetic field that varies linearly along the direction of light propagation. Inverting the magnetic field gradient rephases the atomic dipoles and re-emits the light pulse in the forward direction.

© 2008 Optical Society of America

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  1. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2000).
    [CrossRef]
  2. C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature 409, 490 (2001).
    [CrossRef] [PubMed]
  3. A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A 76, 033804 (2007).
    [CrossRef]
  4. A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
    [CrossRef] [PubMed]
  5. I. Novikova, N. B. Phillips, A. V. Gorshkov, arXiv.org e-Print archive, arXiv:org/abs/0805.1927v1 (2008).
  6. G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope and P. K. Lam, Phys. Rev. A 77, 012323 (2008).
    [CrossRef]
  7. A. Dantan, and M. Pinard, Phys. Rev. A 69, 043810 (2004).
    [CrossRef]
  8. A. E. Kozhekin, K. Molmer, and E. Polzik, Phys. Rev. A 62, 033809 (2000).
    [CrossRef]
  9. J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
    [CrossRef]
  10. N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964).
    [CrossRef]
  11. T. W. Mossberg, Opt. Lett. 7, 77(1982).
    [CrossRef] [PubMed]
  12. S. A. Moiseev and S. Kroll, Phys. Rev. Lett. 87, 173601 (2001).
    [CrossRef] [PubMed]
  13. M. Nilsson and S. Kroll, Opt. Commun. 247, 393 (2005).
    [CrossRef]
  14. B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
    [CrossRef]
  15. N. Sangouard, C. Simon, M. Afzelius and N. Gisin, Phys. Rev. A 75, 032327 (2007).
    [CrossRef]
  16. G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
    [CrossRef] [PubMed]
  17. G. Hétet, J. J. Longdell, M. J. Sellars, P. K. Lam, and B. C. Buchler, arXiv.org e-Print archive, arXiv:0801.3860v1(2008).

2008 (2)

G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope and P. K. Lam, Phys. Rev. A 77, 012323 (2008).
[CrossRef]

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
[CrossRef] [PubMed]

2007 (4)

N. Sangouard, C. Simon, M. Afzelius and N. Gisin, Phys. Rev. A 75, 032327 (2007).
[CrossRef]

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A 76, 033804 (2007).
[CrossRef]

A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
[CrossRef] [PubMed]

2006 (1)

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
[CrossRef]

2005 (1)

M. Nilsson and S. Kroll, Opt. Commun. 247, 393 (2005).
[CrossRef]

2004 (1)

A. Dantan, and M. Pinard, Phys. Rev. A 69, 043810 (2004).
[CrossRef]

2001 (2)

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

S. A. Moiseev and S. Kroll, Phys. Rev. Lett. 87, 173601 (2001).
[CrossRef] [PubMed]

2000 (2)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2000).
[CrossRef]

A. E. Kozhekin, K. Molmer, and E. Polzik, Phys. Rev. A 62, 033809 (2000).
[CrossRef]

1982 (1)

1964 (1)

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964).
[CrossRef]

Abella, I. D.

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964).
[CrossRef]

Afzelius, M.

N. Sangouard, C. Simon, M. Afzelius and N. Gisin, Phys. Rev. A 75, 032327 (2007).
[CrossRef]

Alexander, A. L.

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
[CrossRef] [PubMed]

André, A.

A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A 76, 033804 (2007).
[CrossRef]

A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
[CrossRef] [PubMed]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Buchler, B. C.

G. Hétet, J. J. Longdell, M. J. Sellars, P. K. Lam, and B. C. Buchler, arXiv.org e-Print archive, arXiv:0801.3860v1(2008).

Cirac, J. I.

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
[CrossRef]

Dantan, A.

A. Dantan, and M. Pinard, Phys. Rev. A 69, 043810 (2004).
[CrossRef]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2000).
[CrossRef]

Fleischhauer, M.

A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
[CrossRef] [PubMed]

Gisin, N.

N. Sangouard, C. Simon, M. Afzelius and N. Gisin, Phys. Rev. A 75, 032327 (2007).
[CrossRef]

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
[CrossRef]

Gorshkov, A. V.

A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A 76, 033804 (2007).
[CrossRef]

A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
[CrossRef] [PubMed]

I. Novikova, N. B. Phillips, A. V. Gorshkov, arXiv.org e-Print archive, arXiv:org/abs/0805.1927v1 (2008).

Hartmann, S. R.

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964).
[CrossRef]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Hétet, G.

G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope and P. K. Lam, Phys. Rev. A 77, 012323 (2008).
[CrossRef]

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
[CrossRef] [PubMed]

G. Hétet, J. J. Longdell, M. J. Sellars, P. K. Lam, and B. C. Buchler, arXiv.org e-Print archive, arXiv:0801.3860v1(2008).

Hope, J. J.

G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope and P. K. Lam, Phys. Rev. A 77, 012323 (2008).
[CrossRef]

Jaksch, D.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

Johnsson, M. T.

G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope and P. K. Lam, Phys. Rev. A 77, 012323 (2008).
[CrossRef]

Kozhekin, A. E.

A. E. Kozhekin, K. Molmer, and E. Polzik, Phys. Rev. A 62, 033809 (2000).
[CrossRef]

Kraus, B.

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
[CrossRef]

Kroll, S.

M. Nilsson and S. Kroll, Opt. Commun. 247, 393 (2005).
[CrossRef]

S. A. Moiseev and S. Kroll, Phys. Rev. Lett. 87, 173601 (2001).
[CrossRef] [PubMed]

Kröll, S.

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
[CrossRef]

Kurnit, N. A.

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964).
[CrossRef]

Lam, P. K.

G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope and P. K. Lam, Phys. Rev. A 77, 012323 (2008).
[CrossRef]

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
[CrossRef] [PubMed]

G. Hétet, J. J. Longdell, M. J. Sellars, P. K. Lam, and B. C. Buchler, arXiv.org e-Print archive, arXiv:0801.3860v1(2008).

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Longdell, J. J.

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
[CrossRef] [PubMed]

G. Hétet, J. J. Longdell, M. J. Sellars, P. K. Lam, and B. C. Buchler, arXiv.org e-Print archive, arXiv:0801.3860v1(2008).

Lukin, M. D.

A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A 76, 033804 (2007).
[CrossRef]

A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
[CrossRef] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2000).
[CrossRef]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2000).
[CrossRef]

Moiseev, S. A.

S. A. Moiseev and S. Kroll, Phys. Rev. Lett. 87, 173601 (2001).
[CrossRef] [PubMed]

Molmer, K.

A. E. Kozhekin, K. Molmer, and E. Polzik, Phys. Rev. A 62, 033809 (2000).
[CrossRef]

Mossberg, T. W.

Nilsson, M.

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
[CrossRef]

M. Nilsson and S. Kroll, Opt. Commun. 247, 393 (2005).
[CrossRef]

Novikova, I.

I. Novikova, N. B. Phillips, A. V. Gorshkov, arXiv.org e-Print archive, arXiv:org/abs/0805.1927v1 (2008).

Nunn, J.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

Peng, A.

G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope and P. K. Lam, Phys. Rev. A 77, 012323 (2008).
[CrossRef]

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2000).
[CrossRef]

Phillips, N. B.

I. Novikova, N. B. Phillips, A. V. Gorshkov, arXiv.org e-Print archive, arXiv:org/abs/0805.1927v1 (2008).

Pinard, M.

A. Dantan, and M. Pinard, Phys. Rev. A 69, 043810 (2004).
[CrossRef]

Polzik, E.

A. E. Kozhekin, K. Molmer, and E. Polzik, Phys. Rev. A 62, 033809 (2000).
[CrossRef]

Raymer, M. G.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

Sangouard, N.

N. Sangouard, C. Simon, M. Afzelius and N. Gisin, Phys. Rev. A 75, 032327 (2007).
[CrossRef]

Sellars, M. J.

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
[CrossRef] [PubMed]

G. Hétet, J. J. Longdell, M. J. Sellars, P. K. Lam, and B. C. Buchler, arXiv.org e-Print archive, arXiv:0801.3860v1(2008).

Simon, C.

N. Sangouard, C. Simon, M. Afzelius and N. Gisin, Phys. Rev. A 75, 032327 (2007).
[CrossRef]

Sørensen, A. S.

A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
[CrossRef] [PubMed]

A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A 76, 033804 (2007).
[CrossRef]

Surmacz, K.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

Tittel, W.

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
[CrossRef]

Waldermann, F. C.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

Walmsley, I. A.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2000).
[CrossRef]

Wang, Z.

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

Nature (1)

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, Nature 409, 490 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Nilsson and S. Kroll, Opt. Commun. 247, 393 (2005).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (7)

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll and J. I. Cirac, Phys. Rev. A 73, 020302(R) (2006).
[CrossRef]

N. Sangouard, C. Simon, M. Afzelius and N. Gisin, Phys. Rev. A 75, 032327 (2007).
[CrossRef]

A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A 76, 033804 (2007).
[CrossRef]

G. Hétet, A. Peng, M. T. Johnsson, J. J. Hope and P. K. Lam, Phys. Rev. A 77, 012323 (2008).
[CrossRef]

A. Dantan, and M. Pinard, Phys. Rev. A 69, 043810 (2004).
[CrossRef]

A. E. Kozhekin, K. Molmer, and E. Polzik, Phys. Rev. A 62, 033809 (2000).
[CrossRef]

J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A 75, 011401 (2007).
[CrossRef]

Phys. Rev. Lett. (5)

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Phys. Rev. Lett. 13, 567 (1964).
[CrossRef]

A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
[CrossRef] [PubMed]

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Phys. Rev. Lett. 100, 023601 (2008).
[CrossRef] [PubMed]

S. A. Moiseev and S. Kroll, Phys. Rev. Lett. 87, 173601 (2001).
[CrossRef] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2000).
[CrossRef]

Other (2)

G. Hétet, J. J. Longdell, M. J. Sellars, P. K. Lam, and B. C. Buchler, arXiv.org e-Print archive, arXiv:0801.3860v1(2008).

I. Novikova, N. B. Phillips, A. V. Gorshkov, arXiv.org e-Print archive, arXiv:org/abs/0805.1927v1 (2008).

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Figures (3)

Fig. 1
Fig. 1

(a)Λ-level scheme used for GEM. (b) Details of the magnetic coil configuration around the Rb cell. (c) Diagram of the optical layout: AO, acousto-optic modulator; QW, quarter-wave plate; BS, beam splitter; LO, local oscillator beam used for heterodyne detection.

Fig. 2
Fig. 2

(a) (i) Probe transmission without control beam. (ii) Raman absorption without a magnetic field gradient. (iii) Absorption line broadened by the magnetic field gradient. (iv) Background level with probe light absent. The parameters were Δ = 600 MHz ; control and probe beam powers of 40 mW and 1 μ W , respectively; and a cell temperature of 60 ° C . (b) The FID shown in (i) has an amplitude decay time of about 2.5 μ s . With a magnetic field gradient the FID decay (ii) is much faster.

Fig. 3
Fig. 3

(a) The input pulse measured without Raman absorption is shown in (i). Incoherent absorption in the gas cell was 50% for this trace. The absorption is further enhanced by the Raman beam, as shown by the left-hand side of (ii). After switching the B field, an echo is generated as seen on the right-hand side of (ii). Numerical modeling (iii) shows good agreement with the experiment. (The parameters were γ 0 = 500 kHz , η = 0.2 G cm , and a B-field switching time of 1 μ s .) (b) As the magnetic field flipping is delayed in steps of 400 ns from (i) to (iv), the pulse emerges later in steps of 800 ns .

Equations (6)

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

H ̂ = ( Δ σ ̂ 33 + δ ( z , t ) σ ̂ 22 g E ̂ σ ̂ 13 Ω c * σ ̂ 23 + h.c. ) ,
σ ̂ ̇ 13 = ( γ + γ 0 2 + i Δ ) σ ̂ 13 + i g E ̂ + i Ω c σ ̂ 12 + F ̂ 13 ,
σ ̂ ̇ 12 = ( γ 0 + i η ( t ) z ) σ ̂ 12 + i Ω c * σ ̂ 13 + F ̂ 12 ,
z E ̂ = i g N σ ̂ 13 ,
σ ̂ ̇ 12 = [ γ 0 + i η ( t ) z ] σ ̂ 12 + i g E ̂ ,
z E ̂ = i g N σ ̂ 12 ,

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