Abstract

We show analytically and numerically that the application, during the storage time, of an additional weak field connecting the lower levels (LLs) of a Λ system can modify the spin coherence and the amplitude of the retrieved probe without causing distortion. The LL coupling field adds an additional phase-dependent term to the probe propagation equation. The retrieved probe is amplified when the total relative phase Φ=0 or π and decreased when Φ=π2.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. E. Harris, Phys. Today 50(7), 36 (1997).
    [CrossRef]
  2. R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 42.
  3. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
    [CrossRef] [PubMed]
  4. I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
    [CrossRef] [PubMed]
  5. A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Lett. 33, 1605 (2008).
    [CrossRef] [PubMed]
  6. Y. Xiao, I. Novikova, D. F. Phillips, and R. Walsworth, Phys. Rev. Lett. 96, 043601 (2006).
    [CrossRef] [PubMed]
  7. A. V. Gorshkov, A. Andre, M. Fleischhauer, A. S. Sorenson, and M. D. Lukin, Phys. Rev. Lett. 98, 123601 (2007).
    [CrossRef] [PubMed]
  8. M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Phys. Rev. Lett. 100, 223601 (2008).
    [CrossRef] [PubMed]
  9. M. S. Shahriar and P. R. Hemmer, Phys. Rev. Lett. 65, 1865 (1997).
    [CrossRef]
  10. H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. Welch, P. R. Hemmer, and M. O. Scully, arXiv:0903.1457v1[quant-ph].
  11. G. S. Agarwal, T. N. Dey, and S. Menon, Phys. Rev. A 64, 053809 (2001).
    [CrossRef]
  12. F. Renzoni, S. Cartaleva, G. Alzetta, and E. A. Arimondo, Phys. Rev. A 63, 065401 (2001).
    [CrossRef]
  13. A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, Phys. Rev. A 65, 031802 (2002).
    [CrossRef]

2008 (2)

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

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

2007 (2)

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

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

2006 (1)

Y. Xiao, I. Novikova, D. F. Phillips, and R. Walsworth, Phys. Rev. Lett. 96, 043601 (2006).
[CrossRef] [PubMed]

2002 (2)

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 42.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, Phys. Rev. A 65, 031802 (2002).
[CrossRef]

2001 (2)

G. S. Agarwal, T. N. Dey, and S. Menon, Phys. Rev. A 64, 053809 (2001).
[CrossRef]

F. Renzoni, S. Cartaleva, G. Alzetta, and E. A. Arimondo, Phys. Rev. A 63, 065401 (2001).
[CrossRef]

2000 (1)

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

1997 (2)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

M. S. Shahriar and P. R. Hemmer, Phys. Rev. Lett. 65, 1865 (1997).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, T. N. Dey, and S. Menon, Phys. Rev. A 64, 053809 (2001).
[CrossRef]

Alzetta, G.

F. Renzoni, S. Cartaleva, G. Alzetta, and E. A. Arimondo, Phys. Rev. A 63, 065401 (2001).
[CrossRef]

Andre, A.

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

Arimondo, E. A.

F. Renzoni, S. Cartaleva, G. Alzetta, and E. A. Arimondo, Phys. Rev. A 63, 065401 (2001).
[CrossRef]

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 42.

Cartaleva, S.

F. Renzoni, S. Cartaleva, G. Alzetta, and E. A. Arimondo, Phys. Rev. A 63, 065401 (2001).
[CrossRef]

Davidson, N.

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

Dey, T. N.

G. S. Agarwal, T. N. Dey, and S. Menon, Phys. Rev. A 64, 053809 (2001).
[CrossRef]

Eilam, A.

Firstenberg, O.

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

Fleischhauer, M.

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

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

Friedmann, H.

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 42.

Gorshkov, A. V.

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

Hager, J.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Harris, S. E.

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

Hemmer, P. R.

M. S. Shahriar and P. R. Hemmer, Phys. Rev. Lett. 65, 1865 (1997).
[CrossRef]

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. Welch, P. R. Hemmer, and M. O. Scully, arXiv:0903.1457v1[quant-ph].

Li, H.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. Welch, P. R. Hemmer, and M. O. Scully, arXiv:0903.1457v1[quant-ph].

Lukin, M. D.

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

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, Phys. Rev. A 65, 031802 (2002).
[CrossRef]

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

Mair, A.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Menon, S.

G. S. Agarwal, T. N. Dey, and S. Menon, Phys. Rev. A 64, 053809 (2001).
[CrossRef]

Novikova, I.

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

Y. Xiao, I. Novikova, D. F. Phillips, and R. Walsworth, Phys. Rev. Lett. 96, 043601 (2006).
[CrossRef] [PubMed]

Phillips, D. F.

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

Y. Xiao, I. Novikova, D. F. Phillips, and R. Walsworth, Phys. Rev. Lett. 96, 043601 (2006).
[CrossRef] [PubMed]

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Pugatch, R.

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

Renzoni, F.

F. Renzoni, S. Cartaleva, G. Alzetta, and E. A. Arimondo, Phys. Rev. A 63, 065401 (2001).
[CrossRef]

Ron, A.

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

Rostovtsev, Y. V.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. Welch, P. R. Hemmer, and M. O. Scully, arXiv:0903.1457v1[quant-ph].

Sautenkov, V. A.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. Welch, P. R. Hemmer, and M. O. Scully, arXiv:0903.1457v1[quant-ph].

Scully, M. O.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. Welch, P. R. Hemmer, and M. O. Scully, arXiv:0903.1457v1[quant-ph].

Shahriar, M. S.

M. S. Shahriar and P. R. Hemmer, Phys. Rev. Lett. 65, 1865 (1997).
[CrossRef]

Shuker, M.

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

Sorenson, A. S.

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

Walsworth, R.

Y. Xiao, I. Novikova, D. F. Phillips, and R. Walsworth, Phys. Rev. Lett. 96, 043601 (2006).
[CrossRef] [PubMed]

Walsworth, R. L.

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Welch, G.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. Welch, P. R. Hemmer, and M. O. Scully, arXiv:0903.1457v1[quant-ph].

Wilson-Gordon, A. D.

Xiao, Y.

Y. Xiao, I. Novikova, D. F. Phillips, and R. Walsworth, Phys. Rev. Lett. 96, 043601 (2006).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (3)

G. S. Agarwal, T. N. Dey, and S. Menon, Phys. Rev. A 64, 053809 (2001).
[CrossRef]

F. Renzoni, S. Cartaleva, G. Alzetta, and E. A. Arimondo, Phys. Rev. A 63, 065401 (2001).
[CrossRef]

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, Phys. Rev. A 65, 031802 (2002).
[CrossRef]

Phys. Rev. Lett. (6)

Y. Xiao, I. Novikova, D. F. Phillips, and R. Walsworth, Phys. Rev. Lett. 96, 043601 (2006).
[CrossRef] [PubMed]

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

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

M. S. Shahriar and P. R. Hemmer, Phys. Rev. Lett. 65, 1865 (1997).
[CrossRef]

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

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

Other (2)

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 42.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. Welch, P. R. Hemmer, and M. O. Scully, arXiv:0903.1457v1[quant-ph].

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 (4)

Fig. 1
Fig. 1

(a) Three-level Λ scheme for an atom interacting with resonant control and probe fields with Rabi frequencies V c and V p , (b) Λ system with additional LL coupling field with Rabi frequency V L L , (c) temporal shape of V c (solid curve) and V L L × 10 6 (dashed curve) where V c = V c ( 0 ) [ 1 0.5 tanh ( Γ t Γ τ 1 ) + 0.5 tanh ( Γ t Γ τ 4 ) ] and V L L = V L L ( 0 ) [ 0.5 tanh ( Γ t Γ τ 2 ) 0.5 tanh ( Γ t Γ τ 3 ) ] with τ 1 < τ 2 < τ 3 < τ 4 . The incident probe pulse is given by V p = V p ( 0 ) exp [ ( Γ t Γ τ ) 2 ] . Γ is the longitudinal decay rate of the upper state to one of the lower states, and t is the retarded time.

Fig. 2
Fig. 2

Intensity of retrieved probe as a function of propagation distance, calculated from analytical model, in the absence or presence of the LL coupling field. We plot the intensity of the retrieved probe in region III, normalized by the initial probe intensity, as a function of Γ ( z c t III ) , where t III is some time in region III after the pulse has been completely retrieved. V c ( 0 ) = 100 Γ , V p ( 0 ) = Γ exp [ ( z Γ ) 2 ] , τ 1 = 15 Γ , τ 2 = 40 Γ , τ 3 = 60 Γ , and τ 4 = 80 Γ . V L L ( 0 ) = 0 (solid curve), V L L ( 0 ) = 0.2 Γ , Φ = 0 , π (dotted-dashed curve), V L L ( 0 ) = 0.2 Γ , and Φ = π 2 (dashed curve).

Fig. 3
Fig. 3

Normalized maximum probe intensity as a function of V L L ( 0 ) , calculated from the full Maxwell–Bloch equations, for the case where V L L ( 0 ) V p ( 0 ) and Φ = 0 , π , for the parameters V c ( 0 ) = 10 Γ , V p ( 0 ) = 0.1 Γ , τ 1 = 7 Γ , τ 2 = 12 Γ , τ 3 = 18 Γ , τ 4 = 25 Γ , τ = 8 Γ , and γ 21 Γ = 10 3 .

Fig. 4
Fig. 4

Propagation of the probe pulse in the medium, calculated from the full Maxwell–Bloch equations, under the control field sequence shown in Fig. 1c when V L L ( 0 ) = 9 × 10 4 Γ ; the other parameters are the same as in Fig. 3.

Equations (5)

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

ρ ̇ 21 = i [ V c ρ 23 + V L L ] ,
ρ ̇ 32 = i [ V p + V c ρ 12 ] Γ ρ 32 .
ρ 32 = i ( V ̇ c V c 2 ) ρ 12 + i ( V ̇ p V c 2 ) .
ρ 21 ( t ) = ρ 21 ( 0 ) ( t ) + ρ 21 ( 1 ) ( t ) = ρ 21 ( 0 ) ( t ) i t 1 t V L L d t .
z V p = ( α 0 V c 2 + 1 c ) V ̇ p + α 0 V ̇ c V c 2 V ̇ c V p i α 0 V ̇ c V c 2 exp ( i Φ ) 0 t V L L d t ,

Metrics