Abstract

We study the dynamics of entanglement in continuous variable quantum systems. Specifically, we study the phenomena of entanglement sudden death (ESD) in general two-mode-N-photon states undergoing pure dephasing. We show that for these circumstances, ESD never occurs. These states are generalizations of the so-called high NOON states (i.e., a superposition of N photons in the first mode, O in the second, with O photons in the first, N in the second), shown to decrease the Rayleigh limit of λ to λN, which promises great improvement in resolution of interference patterns if states with large N are physically realized [Phys. Rev. Lett. 85, 2733 (2000) ]. However, we show that in dephasing NOON states, the time to reach some critical visibility Vcrit, scales inversely with N2. On the practical level, this shows that as N increases, the visibility degrades much faster, which is likely to be a considerable drawback for any practical application of these states.

© 2009 Optical Society of America

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  1. T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004).
    [CrossRef] [PubMed]
  2. T. Yu and J. H. Eberly, Opt. Commun. 264, 393 (2006).
    [CrossRef]
  3. A. Al-Qasimi and D. F. V. James, Phys. Rev. A 77, 012117 (2008).
    [CrossRef]
  4. J. Li, K. Chalapat, and G. S. Paraoanu, J. Low Temp. Phys. 153, 294 (2008).
    [CrossRef]
  5. T. Yu and J. H. Eberly, “Many-body separability of warm qubits,” arXiv:0707.3215.
  6. C.-H. Chou, T. Yu, and B. L. Hu, Phys. Rev. E 77, 011112 (2008).
    [CrossRef]
  7. J. P. Paz and A. J. Roncaglia, Phys. Rev. Lett. 100, 220401 (2008).
    [CrossRef] [PubMed]
  8. S.-Y. Lin, C.-H. Chou, and B. L. Hu, Phys. Rev. D 78, 125025 (2008).
    [CrossRef]
  9. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
    [CrossRef] [PubMed]
  10. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
    [CrossRef]
  11. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
    [CrossRef] [PubMed]
  12. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
    [CrossRef] [PubMed]
  13. R. Simon, Phys. Rev. Lett. 84, 2726 (2000).
    [CrossRef] [PubMed]
  14. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
    [CrossRef] [PubMed]

2008

A. Al-Qasimi and D. F. V. James, Phys. Rev. A 77, 012117 (2008).
[CrossRef]

J. Li, K. Chalapat, and G. S. Paraoanu, J. Low Temp. Phys. 153, 294 (2008).
[CrossRef]

C.-H. Chou, T. Yu, and B. L. Hu, Phys. Rev. E 77, 011112 (2008).
[CrossRef]

J. P. Paz and A. J. Roncaglia, Phys. Rev. Lett. 100, 220401 (2008).
[CrossRef] [PubMed]

S.-Y. Lin, C.-H. Chou, and B. L. Hu, Phys. Rev. D 78, 125025 (2008).
[CrossRef]

2006

T. Yu and J. H. Eberly, Opt. Commun. 264, 393 (2006).
[CrossRef]

2004

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

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

2000

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

R. Simon, Phys. Rev. Lett. 84, 2726 (2000).
[CrossRef] [PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

1998

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

1996

A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
[CrossRef] [PubMed]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Al-Qasimi, A.

A. Al-Qasimi and D. F. V. James, Phys. Rev. A 77, 012117 (2008).
[CrossRef]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Chalapat, K.

J. Li, K. Chalapat, and G. S. Paraoanu, J. Low Temp. Phys. 153, 294 (2008).
[CrossRef]

Chou, C.-H.

S.-Y. Lin, C.-H. Chou, and B. L. Hu, Phys. Rev. D 78, 125025 (2008).
[CrossRef]

C.-H. Chou, T. Yu, and B. L. Hu, Phys. Rev. E 77, 011112 (2008).
[CrossRef]

Cirac, J. I.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Duan, L.-M.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

Eberly, J. H.

T. Yu and J. H. Eberly, Opt. Commun. 264, 393 (2006).
[CrossRef]

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

T. Yu and J. H. Eberly, “Many-body separability of warm qubits,” arXiv:0707.3215.

Giedke, G.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

Hu, B. L.

C.-H. Chou, T. Yu, and B. L. Hu, Phys. Rev. E 77, 011112 (2008).
[CrossRef]

S.-Y. Lin, C.-H. Chou, and B. L. Hu, Phys. Rev. D 78, 125025 (2008).
[CrossRef]

James, D. F. V.

A. Al-Qasimi and D. F. V. James, Phys. Rev. A 77, 012117 (2008).
[CrossRef]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Li, J.

J. Li, K. Chalapat, and G. S. Paraoanu, J. Low Temp. Phys. 153, 294 (2008).
[CrossRef]

Lin, S.-Y.

S.-Y. Lin, C.-H. Chou, and B. L. Hu, Phys. Rev. D 78, 125025 (2008).
[CrossRef]

Lundeen, J. S.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

Mitchell, M. W.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

Paraoanu, G. S.

J. Li, K. Chalapat, and G. S. Paraoanu, J. Low Temp. Phys. 153, 294 (2008).
[CrossRef]

Paz, J. P.

J. P. Paz and A. J. Roncaglia, Phys. Rev. Lett. 100, 220401 (2008).
[CrossRef] [PubMed]

Peres, A.

A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
[CrossRef] [PubMed]

Roncaglia, A. J.

J. P. Paz and A. J. Roncaglia, Phys. Rev. Lett. 100, 220401 (2008).
[CrossRef] [PubMed]

Simon, R.

R. Simon, Phys. Rev. Lett. 84, 2726 (2000).
[CrossRef] [PubMed]

Steinberg, A. M.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Wootters, W. K.

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

Yu, T.

C.-H. Chou, T. Yu, and B. L. Hu, Phys. Rev. E 77, 011112 (2008).
[CrossRef]

T. Yu and J. H. Eberly, Opt. Commun. 264, 393 (2006).
[CrossRef]

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

T. Yu and J. H. Eberly, “Many-body separability of warm qubits,” arXiv:0707.3215.

Zoller, P.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

J. Low Temp. Phys.

J. Li, K. Chalapat, and G. S. Paraoanu, J. Low Temp. Phys. 153, 294 (2008).
[CrossRef]

Nature

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Nature 429, 161 (2004).
[CrossRef] [PubMed]

Opt. Commun.

T. Yu and J. H. Eberly, Opt. Commun. 264, 393 (2006).
[CrossRef]

Phys. Rev. A

A. Al-Qasimi and D. F. V. James, Phys. Rev. A 77, 012117 (2008).
[CrossRef]

Phys. Rev. D

S.-Y. Lin, C.-H. Chou, and B. L. Hu, Phys. Rev. D 78, 125025 (2008).
[CrossRef]

Phys. Rev. E

C.-H. Chou, T. Yu, and B. L. Hu, Phys. Rev. E 77, 011112 (2008).
[CrossRef]

Phys. Rev. Lett.

J. P. Paz and A. J. Roncaglia, Phys. Rev. Lett. 100, 220401 (2008).
[CrossRef] [PubMed]

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

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

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

A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
[CrossRef] [PubMed]

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

R. Simon, Phys. Rev. Lett. 84, 2726 (2000).
[CrossRef] [PubMed]

Other

T. Yu and J. H. Eberly, “Many-body separability of warm qubits,” arXiv:0707.3215.

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Figures (1)

Fig. 1
Fig. 1

Interface pattern formation adapted from Fig. 1 of [1]. Two photon beams pass through a beam splitter and get reflected off the upper and lower mirrors to form an interference pattern on the screen. The upper beam passes through a phase shifter before reaching the screen. The phase aquired depends on the number of photons N that pass through the upper path, and it equals e i N ϕ .

Equations (15)

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ρ ̂ ( t ) = k = 0 N ρ k k ( t ) N k , k N k , k + k , m = 0 , k m N ρ k m ( t ) N k , k N m , m .
ρ ̂ ( t ) t = 2 ( Γ 1 { [ n 1 ̂ , ρ ̂ ( t ) n 1 ̂ ] + [ n 1 ̂ ρ ̂ ( t ) , n 1 ̂ ] } + Γ 2 { [ n 2 ̂ , ρ ̂ ( t ) n 2 ̂ ] + [ n 2 ̂ ρ ̂ ( t ) , n 2 ̂ ] } ) ,
ρ ̂ ( t ) = k = 0 N ρ k k ( 0 ) N k , k N k , k + k , m = 0 , k m N ρ k m ( 0 ) e ( 1 2 ) ( k m ) 2 ( Γ 1 + Γ 2 ) t N k , k N m , m .
ρ ̂ = i c i ρ ̂ i ρ ̂ i .
σ ̂ = i c i ( ρ ̂ i ) T ρ ̂ i .
σ ̂ = k = 0 N ρ k k ( 0 ) N k , k N k , k + k , m = 0 , k m N ρ k m ( 0 ) e ( 1 2 ) ( k m ) 2 ( Γ 1 + Γ 2 ) t N k , m N m , k .
ρ k m ( 0 ) e ( 1 2 ) ( k m ) 2 ( Γ 1 + Γ 2 ) t { e i θ N k , m N m , k + e i θ N m , k N k , m } ,
ψ = 1 2 { e i θ N k , m N m , k } ,
ρ k m ( 0 ) e ( 1 2 ) ( k m ) 2 ( Γ 1 + Γ 2 ) t .
ψ = 1 2 { N 0 + 0 N } ,
ψ = a 30 + b 21 + c 12 + d 03 ,
ψ = 1 2 { N 0 + e i N ϕ 0 N } .
ρ ( t ) ̂ = 1 2 ( N 0 N 0 + e N 2 Γ t e i N ϕ 0 N N 0 + e N 2 Γ t e i N ϕ N 0 0 N + 0 N 0 N ) ,
V = δ ̂ max δ ̂ min δ ̂ max + δ ̂ min = e N 2 Γ t .
t crit = 1 Γ N 2 ln ( 1 V crit ) .

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