Abstract

We investigate the entanglement dynamics of the bipartite system, consisting of two interacting two-level atoms in QED, which are driven additionally by coherent double ultrashort laser pulses characterized by various phase differences. Results show that the relative phase difference can exert significant influence on the entanglement evolution, such as delaying or accelerating entanglement sudden death and recurrence (ESD and ESR). Furthermore, with the increase of detuning, ESD and ESR disappear, irrespective of various phase differences. Our analysis is helpful in manipulating entanglement.

© 2010 Optical Society of America

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References

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  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).
  2. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
    [CrossRef]
  3. T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004).
    [CrossRef] [PubMed]
  4. T. Yu and J. H. Eberly, Phys. Rev. Lett. 97, 140403 (2006).
    [CrossRef] [PubMed]
  5. M. P. Almeida and F. D. Melo, Science 316, 579 (2007).
    [CrossRef] [PubMed]
  6. J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
    [CrossRef] [PubMed]
  7. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic, 2006).
  8. J. S. Zhang and J. B. Xu, Opt. Commun. 282, 3652 (2009).
    [CrossRef]
  9. V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 93, 190502(2004).
    [CrossRef] [PubMed]
  10. E. Paspalakis and P. L. Knight, Phys. Rev. Lett. 81, 293(1998).
    [CrossRef]
  11. V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 96, 050502(2006).
    [CrossRef] [PubMed]
  12. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
    [CrossRef]
  13. Y. Li, J. Zhou, and H. Guo, Phys. Rev. A 79, 012309 (2009).
    [CrossRef]

2010 (1)

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

2009 (3)

J. S. Zhang and J. B. Xu, Opt. Commun. 282, 3652 (2009).
[CrossRef]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
[CrossRef]

Y. Li, J. Zhou, and H. Guo, Phys. Rev. A 79, 012309 (2009).
[CrossRef]

2007 (1)

M. P. Almeida and F. D. Melo, Science 316, 579 (2007).
[CrossRef] [PubMed]

2006 (2)

T. Yu and J. H. Eberly, Phys. Rev. Lett. 97, 140403 (2006).
[CrossRef] [PubMed]

V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 96, 050502(2006).
[CrossRef] [PubMed]

2004 (2)

T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 93, 190502(2004).
[CrossRef] [PubMed]

1998 (2)

E. Paspalakis and P. L. Knight, Phys. Rev. Lett. 81, 293(1998).
[CrossRef]

W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
[CrossRef]

Almeida, M. P.

M. P. Almeida and F. D. Melo, Science 316, 579 (2007).
[CrossRef] [PubMed]

Chen, G.

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).

Diels, J. C.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic, 2006).

Eberly, J. H.

T. Yu and J. H. Eberly, Phys. Rev. Lett. 97, 140403 (2006).
[CrossRef] [PubMed]

T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

Gong, M.

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

Guo, G. C.

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

Guo, H.

Y. Li, J. Zhou, and H. Guo, Phys. Rev. A 79, 012309 (2009).
[CrossRef]

Horodecki, K.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
[CrossRef]

Horodecki, M.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
[CrossRef]

Horodecki, P.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
[CrossRef]

Horodecki, R.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
[CrossRef]

Knight, P. L.

E. Paspalakis and P. L. Knight, Phys. Rev. Lett. 81, 293(1998).
[CrossRef]

Li, C. F.

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

Li, Y.

Y. Li, J. Zhou, and H. Guo, Phys. Rev. A 79, 012309 (2009).
[CrossRef]

Malinovsky, V. S.

V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 96, 050502(2006).
[CrossRef] [PubMed]

V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 93, 190502(2004).
[CrossRef] [PubMed]

Melo, F. D.

M. P. Almeida and F. D. Melo, Science 316, 579 (2007).
[CrossRef] [PubMed]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).

Paspalakis, E.

E. Paspalakis and P. L. Knight, Phys. Rev. Lett. 81, 293(1998).
[CrossRef]

Rudolph, W.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic, 2006).

Shi, C. H.

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

Sola, I. R.

V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 96, 050502(2006).
[CrossRef] [PubMed]

V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 93, 190502(2004).
[CrossRef] [PubMed]

Wootters, W. K.

W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
[CrossRef]

Xu, J. B.

J. S. Zhang and J. B. Xu, Opt. Commun. 282, 3652 (2009).
[CrossRef]

Xu, J. S.

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

Yu, T.

T. Yu and J. H. Eberly, Phys. Rev. Lett. 97, 140403 (2006).
[CrossRef] [PubMed]

T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

Zhang, J. S.

J. S. Zhang and J. B. Xu, Opt. Commun. 282, 3652 (2009).
[CrossRef]

Zhou, J.

Y. Li, J. Zhou, and H. Guo, Phys. Rev. A 79, 012309 (2009).
[CrossRef]

Zou, X. B.

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. S. Zhang and J. B. Xu, Opt. Commun. 282, 3652 (2009).
[CrossRef]

Phys. Rev. A (1)

Y. Li, J. Zhou, and H. Guo, Phys. Rev. A 79, 012309 (2009).
[CrossRef]

Phys. Rev. Lett. (7)

J. S. Xu, C. F. Li, M. Gong, X. B. Zou, C. H. Shi, G. Chen, and G. C. Guo, Phys. Rev. Lett. 104, 100502 (2010).
[CrossRef] [PubMed]

V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 93, 190502(2004).
[CrossRef] [PubMed]

E. Paspalakis and P. L. Knight, Phys. Rev. Lett. 81, 293(1998).
[CrossRef]

V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. 96, 050502(2006).
[CrossRef] [PubMed]

W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
[CrossRef]

T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

T. Yu and J. H. Eberly, Phys. Rev. Lett. 97, 140403 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
[CrossRef]

Science (1)

M. P. Almeida and F. D. Melo, Science 316, 579 (2007).
[CrossRef] [PubMed]

Other (2)

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2000).

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic, 2006).

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Figures (5)

Fig. 1
Fig. 1

Bipartite system consisting of two interacting two-level atoms marked by A and B in QED, which are driven by coherent double ULPs. τ, the origin of the relative phase difference, represents the time delay between the two pulses, and Δ A , B means the detuning between optical angular frequency ω and atomic transition frequency ω A , B . The dashed arrows describe the interaction and photon exchange between these two atoms. For the purpose of calculating convenience, we assume that the input ULPs are both approximately rectangular.

Fig. 2
Fig. 2

Time evolutions of concurrence for atom–atom entanglement with the MIES of | φ = ( | 3 + | 2 ) / 2 and detuning Δ A , B = 0.1 fs 1 under various phase differences ( ω τ ) : (a) 0.00 and 0.25 π , (b) 0.50 π and 0.75 π , (c) 1.00 π and 1.25 π , and (d) 1.50 π and 1.75 π . The former is marked by the solid curve and the latter by the dashed curve.

Fig. 3
Fig. 3

Same as Fig. 2, except the MIES is | ψ = ( | 4 + | 1 ) / 2 .

Fig. 4
Fig. 4

Same as Fig. 2, except the detuning is Δ A , B = 0.3 fs 1 .

Fig. 5
Fig. 5

Same as Fig. 3, except the detuning is Δ A , B = 0.3 fs 1 .

Equations (12)

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

E ( t ) = 1 2 [ E ˜ 1 ( t ) e i ω t + E ˜ 2 ( t τ ) e i ω ( t τ ) + c.c . ] ,
H = H 0 + H I + H dd ,
H 0 = [ ( ω 1 A + ω 1 B ) | 4 4 | + ( ω 1 A + ω 0 B ) | 3 3 | + ( ω 0 A + ω 1 B ) | 2 2 | + ( ω 0 A + ω 0 B ) | 1 1 | ] ,
H I = μ E ( t ) ( | 4 3 | + | 4 2 | + | 3 1 | + | 2 1 | ) + c.c. ,
H dd = g ( | 3 2 | ) + c.c . ,
i | ψ ˙ ( t ) = H | ψ ( t ) ,
ψ ( t ) = j = 1 4 c ˜ j ( t ) | j ,
c ˜ 4 ( t ) = j = 1 4 { [ K j 3 + a K j 2 ( e 2 + f 2 + 2 b d ) K i a f 2 a e 2 2 b d f ] c ˜ 4 ( 0 ) + b [ K j 2 + ( a + e + f ) K j + a ( e + f ) ] c ˜ 3 ( 0 ) + b [ K j 2 + ( a e + f ) K j a ( e f ) ] c ˜ 2 ( 0 ) + 2 b 2 ( K j + f ) c ˜ 1 ( 0 ) } F 1 e K j t ,
c ˜ 3 ( t ) = j = 1 4 { d [ K j 2 + ( a + e + f ) K j + a ( e + f ) ] c ˜ 4 ( 0 ) + [ K j 3 + e K j 2 ( a 2 + 2 b d ) K j a 2 e ] c ˜ 3 ( 0 ) + ( f K j 2 + 2 b d K j a 2 f ) c ˜ 2 ( 0 ) + b [ K j 2 ( a e f ) K j a ( e + f ) ] c ˜ 1 ( 0 ) } F 1 e K j t ,
c ˜ 2 ( t ) = j = 1 4 { d [ K j 2 + ( a e + f ) K j a ( e f ) ] c ˜ 4 ( 0 ) + ( f K j 2 + 2 b d K j a 2 f ) c ˜ 3 ( 0 ) + [ K j 3 e K j 2 ( a 2 + 2 b d ) K j + a 2 e ] c ˜ 2 ( 0 ) + b [ K j 2 ( a + e f ) K j + a ( e f ) ] c ˜ 1 ( 0 ) } F 1 e K j t ,
c ˜ 1 ( t ) = j = 1 4 { 2 d 2 ( K j + f ) c ˜ 4 ( 0 ) + d [ K j 2 ( a e f ) K j a ( e + f ) ] c ˜ 3 ( 0 ) + d [ K j 2 ( a + e f ) K j + a ( e f ) ] c ˜ 2 ( 0 ) + [ K j 3 a K j 2 ( e 2 + f 2 + 2 b d ) K j + a f 2 + a e 2 2 b d f ] c ˜ 1 ( 0 ) } F 1 e K j t ,
C φ ( t ) = 2 max ( 0 , | c ˜ 2 ( t ) c ˜ 3 ( t ) | | c ˜ 1 ( t ) c ˜ 4 ( t ) | ) , C ψ ( t ) = 2 max ( 0 , | c ˜ 1 ( t ) c ˜ 4 ( t ) | | c ˜ 2 ( t ) c ˜ 3 ( t ) | ) ,

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