Abstract

The successful formation of stationary light pulses in a cold atomic medium was demonstrated recently. However, unlike in hot media, a detuning between the counterpropagating fields had to be applied. Here we demonstrate that a significant nonuniform phase variation can be induced during a period of stationary light owing to off-resonantly driven transitions. The experimental results are in good agreement with theoretical predictions for media of low optical depth. For media of high optical depth the numerical simulations indicate that such phase variation becomes negligible. Thus stationary light based on this coupling scheme could be used for possible future applications in quantum information processing.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
    [CrossRef]

2009

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

2008

F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M. Fleischhauer, Phys. Rev. A 77, 063823 (2008).
[CrossRef]

Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, Opt. Express 16, 3753 (2008).
[CrossRef] [PubMed]

2006

S. A. Moiseev and B. S. Ham, Phys. Rev. A 73, 033812 (2006).
[CrossRef]

Y.-F. Chen, Y.-M. Kao, W.-H. Lin, and I. A. Yu, Phys. Rev. A 74, 063807 (2006).
[CrossRef]

2005

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

A. André, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

2003

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef] [PubMed]

1997

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

1994

M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).
[CrossRef] [PubMed]

André, A.

A. André, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

Bajcsy, M.

A. André, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef] [PubMed]

Chen, Y.-C.

Chen, Y.-F.

Y.-F. Chen, Y.-M. Kao, W.-H. Lin, and I. A. Yu, Phys. Rev. A 74, 063807 (2006).
[CrossRef]

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Cho, H.-W.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Chou, H.-C.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, Opt. Express 16, 3753 (2008).
[CrossRef] [PubMed]

Dwivedi, P. P.

Fleischhauer, M.

F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M. Fleischhauer, Phys. Rev. A 77, 063823 (2008).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).
[CrossRef] [PubMed]

Ham, B. S.

S. A. Moiseev and B. S. Ham, Phys. Rev. A 73, 033812 (2006).
[CrossRef]

Harris, S. E.

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

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Kao, Y.-M.

Y.-F. Chen, Y.-M. Kao, W.-H. Lin, and I. A. Yu, Phys. Rev. A 74, 063807 (2006).
[CrossRef]

Kuan, P.-C.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Liao, W.-T.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Lin, W.-H.

Y.-F. Chen, Y.-M. Kao, W.-H. Lin, and I. A. Yu, Phys. Rev. A 74, 063807 (2006).
[CrossRef]

Lin, Y.-W.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, Opt. Express 16, 3753 (2008).
[CrossRef] [PubMed]

Liu, Y.-C.

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Lukin, M. D.

A. André, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Moiseev, S. A.

S. A. Moiseev and B. S. Ham, Phys. Rev. A 73, 033812 (2006).
[CrossRef]

Otterbach, J.

F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M. Fleischhauer, Phys. Rev. A 77, 063823 (2008).
[CrossRef]

Peters, T.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Scully, M. O.

M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).
[CrossRef] [PubMed]

Shore, B. W.

F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M. Fleischhauer, Phys. Rev. A 77, 063823 (2008).
[CrossRef]

Tsai, Z.-H.

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Unanyan, R. G.

F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M. Fleischhauer, Phys. Rev. A 77, 063823 (2008).
[CrossRef]

Wang, J.-S.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Wang, S.-H.

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Yu, I. A.

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Y.-W. Lin, H.-C. Chou, P. P. Dwivedi, Y.-C. Chen, and I. A. Yu, Opt. Express 16, 3753 (2008).
[CrossRef] [PubMed]

Y.-F. Chen, Y.-M. Kao, W.-H. Lin, and I. A. Yu, Phys. Rev. A 74, 063807 (2006).
[CrossRef]

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

Zibrov, A. S.

A. André, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef] [PubMed]

Zimmer, F. E.

F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M. Fleischhauer, Phys. Rev. A 77, 063823 (2008).
[CrossRef]

Nature

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. A

Y.-F. Chen, Y.-C. Liu, Z.-H. Tsai, S.-H. Wang, and I. A. Yu, Phys. Rev. A 72, 033812 (2005).
[CrossRef]

S. A. Moiseev and B. S. Ham, Phys. Rev. A 73, 033812 (2006).
[CrossRef]

M. Fleischhauer and M. O. Scully, Phys. Rev. A 49, 1973 (1994).
[CrossRef] [PubMed]

Y.-F. Chen, Y.-M. Kao, W.-H. Lin, and I. A. Yu, Phys. Rev. A 74, 063807 (2006).
[CrossRef]

F. E. Zimmer, J. Otterbach, R. G. Unanyan, B. W. Shore, and M. Fleischhauer, Phys. Rev. A 77, 063823 (2008).
[CrossRef]

Phys. Rev. Lett.

A. André, M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Phys. Rev. Lett. 94, 063902 (2005).
[CrossRef] [PubMed]

Y.-W. Lin, W.-T. Liao, T. Peters, H.-C. Chou, J.-S. Wang, H.-W. Cho, P.-C. Kuan, and I. A. Yu, Phys. Rev. Lett. 102, 213601 (2009).
[CrossRef] [PubMed]

Phys. Today

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

Rev. Mod. Phys.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Λ-type coupling scheme for EIT. (b) Possible double-Λ scheme for the formation of SLPs.

Fig. 2
Fig. 2

Numerical simulation based on Eqs. (1, 2, 3, 4) of the PV across the temporal e 1 full width 2 τ of a probe pulse for a SLP duration of τ SLP = 2 μ s ( 75 Γ 1 ) . (a) Asymmetric detuning Δ + = ± ( 4 6 ) Γ , Δ = 0 (solid curves) and Δ + = 0 , Δ = ± ( 4 6 ) Γ (dashed curves) for α = 40 ( Ω c = 0.7 Γ ) . The detuning is positive for black and negative for red (gray in print) curves. (b) Same as (a), except for α = 100 ( Ω c = 1.1 Γ ) . (c) Symmetric detuning Δ ± = ± ( 4 6 ) Γ [blue (dark gray in print)] and Δ ± = ( 4 6 ) Γ [magenta (gray in print)] for α = 40 (solid curves) and α = 100 (dashed-dotted curves). A Gaussian-shaped pulse of e 1 full width of 800 ns ( 30 Γ 1 ) is initially sent into the medium. The group velocity of the slow probe pulse is kept constant in all plots.

Fig. 3
Fig. 3

(a) Pulse sequence of the SLP PV measurements. Experimental (symbols) and numerical data (curves) of the input probe pulses (magenta squares) and transmission in the forward (red circles) and backward direction (blue triangles whose values are all nearly zero). The timing of the coupling fields in the forward (black diamonds) and backward direction (gray triangles) is shown by solid lines. The detuning of the coupling fields was either kept constant or changed within the two storage periods 500 ns before and after the SLP period. (b) Beat note of the transmitted probe pulse in the forward direction (red line between 6.5 and 9 μ s ) and the reference pulse (magenta line between 9 and 10.5 μ s ). This reference pulse was obtained by splitting off part of the probe pulses before entering the medium.

Fig. 4
Fig. 4

Measured phase φ across the e 1 full width 2 τ of (a) slow-light pulses after propagation through a medium for different two-photon detunings δ and (b)–(d) retrieved pulses after an SLP period of τ SLP = 2.00 ( 5 ) μ s for different detunings Δ ± . t = 0 corresponds to the center of the detected pulses. (a) δ = 0 (red diamonds), 25 kHz (blue circles), 162 kHz (black squares), 112 kHz (magenta triangles). The solid curves correspond to the best linear fit. (b) Δ + = 0 , Δ = + ( 7 6 ) Γ . (c) Δ + = 0 , Δ = ( 7 6 ) Γ . Measured (circles) and numerical data (curves) as obtained for a pulse timing, as shown in Fig. 3a. The detunings Δ ± were constant during the whole sequence. (d) Symmetric detuning of Δ ± = ( 4 6 ) Γ . The detunings Δ ± were applied symmetrically only within τ SLP ± 500 ns . The error bars represent the error obtained from the best fit for each interval. In all plots α = 40 ( 2 ) , γ ( 0 ) = 0.0005 ( 2 ) Γ , and γ ( 2 ) = 0.016 ( 1 ) Γ . The error bar indicator in the lower right corner of (d) represents the error in the t in all plots.

Equations (5)

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t ρ 31 ( ± 1 ) = i 2 Ω p ± + i 2 ( Ω c ± ρ 21 ( 0 ) + Ω c ρ 21 ( ± 2 ) ) ( Γ 2 i Δ ± ) ρ 31 ( ± 1 ) ,
t ρ 21 ( ± 2 ) = i 2 ( Ω c ) * ρ 31 ( ± 1 ) [ γ ( 2 ) i ( Δ ± Δ ) ] ρ 21 ( ± 2 ) ,
t ρ 21 ( 0 ) = i 2 [ ( Ω c + ) * ρ 31 ( + 1 ) + ( Ω c ) * ρ 31 ( 1 ) ] γ ( 0 ) ρ 21 ( 0 ) ,
1 c t Ω p ± ± z Ω p ± = i α Γ 2 L ρ 31 ( ± 1 ) .
I d ( t ) = I 0 ( t ) + I 1 ( t ) [ cos ( 2 π f AOM t + φ ( t ) ) ] ,

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