Abstract

We examine the entanglement between two qubits, supposed to be remotely located and driven by independent quantized optical fields. No interaction is allowed between the qubits, but their degree of entanglement changes as a function of time. We report a collapse and revival of entanglement that is similar to the collapse and revival of single-atom properties in cavity QED.

© 2008 Optical Society of America

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References

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  1. M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, Phys. Rev. A 65, 040101(R) (2002).
    [CrossRef]
  2. L. Zhou and G.-H. Yang, J. Phys. B 39, 5143 (2006).
    [CrossRef]
  3. R. W. Rendell and A. K. Rajagopal, Phys. Rev. A 67, 062110 (2003).
    [CrossRef]
  4. M. Yönaç, T. Yu, and J. H. Eberly, J. Phys. B 39, S621 (2006).
    [CrossRef]
  5. M. Yönaç, T. Yu, and J. H. Eberly, J. Phys. B 40, S45 (2007).
    [CrossRef]
  6. T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004).
    [CrossRef] [PubMed]
  7. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
    [CrossRef]
  8. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
    [CrossRef]
  9. T. Yu and J. H. Eberly, Quantum. Inf. Comput. 7, 459 (2007).
  10. J. H. Eberly, N. B. Narozhny, and J. J. Sanchez Mondragon, Phys. Rev. Lett. 44, 20 (1980).
    [CrossRef]

2007

M. Yönaç, T. Yu, and J. H. Eberly, J. Phys. B 40, S45 (2007).
[CrossRef]

T. Yu and J. H. Eberly, Quantum. Inf. Comput. 7, 459 (2007).

2006

L. Zhou and G.-H. Yang, J. Phys. B 39, 5143 (2006).
[CrossRef]

M. Yönaç, T. Yu, and J. H. Eberly, J. Phys. B 39, S621 (2006).
[CrossRef]

2004

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

2003

R. W. Rendell and A. K. Rajagopal, Phys. Rev. A 67, 062110 (2003).
[CrossRef]

2002

M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, Phys. Rev. A 65, 040101(R) (2002).
[CrossRef]

1998

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

1980

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez Mondragon, Phys. Rev. Lett. 44, 20 (1980).
[CrossRef]

1963

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

J. Phys. B

M. Yönaç, T. Yu, and J. H. Eberly, J. Phys. B 39, S621 (2006).
[CrossRef]

M. Yönaç, T. Yu, and J. H. Eberly, J. Phys. B 40, S45 (2007).
[CrossRef]

L. Zhou and G.-H. Yang, J. Phys. B 39, 5143 (2006).
[CrossRef]

Phys. Rev. A

R. W. Rendell and A. K. Rajagopal, Phys. Rev. A 67, 062110 (2003).
[CrossRef]

M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, Phys. Rev. A 65, 040101(R) (2002).
[CrossRef]

Phys. Rev. Lett.

J. H. Eberly, N. B. Narozhny, and J. J. Sanchez Mondragon, Phys. Rev. Lett. 44, 20 (1980).
[CrossRef]

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

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

Proc. IEEE

E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).
[CrossRef]

Quantum. Inf. Comput.

T. Yu and J. H. Eberly, Quantum. Inf. Comput. 7, 459 (2007).

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Figures (3)

Fig. 1
Fig. 1

Sketch indicating noninteracting qubits in a quantum storage network. The dashed line indicates that two are entangled.

Fig. 2
Fig. 2

Analytical and numerical results for entanglement. As expected, revivals occur, which are predicted reasonably well by the approximate analytical results. Better resolution of the rapid oscillations is provided in Fig. 3.

Fig. 3
Fig. 3

A more detailed plot of the results around t = 20 π g shown in Fig. 2. Analytical results are for the X-type ρ, while the numerical ones are for the original ρ.

Equations (11)

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

H I = i = 1 , 2 g ( a i σ i + + a i σ i ) ,
Ψ ( 0 ) = ( e g + g e ) 2 .
C ( ρ ) = max { 0 , λ 1 λ 2 λ 3 λ 4 } ,
ζ = ρ ( σ y σ y ) ρ * ( σ y σ y ) .
ρ = ( a x x x x b z x x z c x x x x d ) ( a 0 0 0 0 b z 0 0 z c 0 0 0 0 d ) ,
C ( ρ ) = 2 max [ 0 , z a d ] .
z = 1 2 { n , m A n 2 A m 2 C n C n + 1 C m C m + 1 A n A n 1 A m A m + 1 S n C n + 1 C m S m + 1 + A n A n 2 A m A m + 2 S n S n 1 S m + 1 S m + 2 A n A n 1 A m A m + 1 S n C n 1 S m + 1 C m + 2 } ,
a = 1 2 { n , m A n 2 A m 2 C n + 1 2 S m 2 + A n A n + 1 A m A m 1 S n + 1 C n + 1 S m C m + A n 2 A m 2 S n 2 C m + 1 2 + A n A n 1 A m A m + 1 S n C n S m + 1 C m + 1 } ,
d = 1 2 { n , m A n 2 A m 2 S n + 1 2 C m 2 + A n A n + 1 A m A m 1 S n + 1 C n + 1 S m C m + A n 2 A m 2 C n 2 S m + 1 2 + A n A n 1 A m A m + 1 S n C n S m + 1 C m + 1 } .
n ! = 2 π n n n e n ,
z a d 1 4 [ e g 2 t 2 8 n ¯ 2 1 ] + 1 2 [ n A n 2 cos ( 2 g t n ) ] 2 1 2 [ n A n 2 sin ( 2 g t n ) ] 2 .

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