Abstract

We show that a high degree of steady-state entanglement between two spatially separated and initially uncoupled qubits can be achieved via interaction with a quantized squeezed field in a cavity. The cavity field induces two-photon coherence, which is crucial in creating entanglement between the qubits. Optimum entanglement is obtained when the less dissipative qubit is incoherently pumped while the other dissipates the excitation. Given the current state-of-the-art in cavity quantum electrodynamics and squeezed light sources, our scheme presents an effective way for light-to-matter entanglement transfer.

© 2012 Optical Society of America

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  1. M. A. Nielsen and I. L. Chuang, Quantum Computing and Quantum Information (Cambridge University, 2000).
  2. J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
    [CrossRef]
  3. E. A. Sete and S. Das, Phys. Rev. A 83, 042301 (2011).
    [CrossRef]
  4. D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
    [CrossRef]
  5. J. Clarke and F. K. Wilhelm, Nature 453, 1031 (2008).
    [CrossRef]
  6. A. Rai, S. Das, and G. Agarwal, Opt. Express 18, 6241 (2010).
    [CrossRef]
  7. B. Kraus and J. I. Cirac, Phys. Rev. Lett. 92, 013602 (2004).
    [CrossRef]
  8. C. Cabrillo, J. I. Cirac, P. Garca-Fernández, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
    [CrossRef]
  9. A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
    [CrossRef]
  10. A. Serafini, M. Paternostro, M. S. Kim, and S. Bose, Phys. Rev. A 73, 022312 (2006).
    [CrossRef]
  11. E. del Valle, J. Opt. Soc. Am. B 28, 228 (2011).
    [CrossRef]
  12. J.-B. Xu and S.-B. Li, New J. Phys. 7, 72 (2005).
    [CrossRef]
  13. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
    [CrossRef]
  14. J. I. Cirac, Phys. Rev. A 46, 4354 (1992).
    [CrossRef]
  15. J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
    [CrossRef]
  16. N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, Phys. Rev. Lett. 75, 3426 (1995).
    [CrossRef]

2011 (2)

E. A. Sete and S. Das, Phys. Rev. A 83, 042301 (2011).
[CrossRef]

E. del Valle, J. Opt. Soc. Am. B 28, 228 (2011).
[CrossRef]

2010 (1)

2008 (1)

J. Clarke and F. K. Wilhelm, Nature 453, 1031 (2008).
[CrossRef]

2006 (1)

A. Serafini, M. Paternostro, M. S. Kim, and S. Bose, Phys. Rev. A 73, 022312 (2006).
[CrossRef]

2005 (1)

J.-B. Xu and S.-B. Li, New J. Phys. 7, 72 (2005).
[CrossRef]

2004 (1)

B. Kraus and J. I. Cirac, Phys. Rev. Lett. 92, 013602 (2004).
[CrossRef]

2003 (1)

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

2001 (1)

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

1999 (2)

C. Cabrillo, J. I. Cirac, P. Garca-Fernández, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

1998 (2)

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

D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
[CrossRef]

1995 (1)

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

1992 (1)

J. I. Cirac, Phys. Rev. A 46, 4354 (1992).
[CrossRef]

Agarwal, G.

Awschalom, D. D.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Boozer, A. D.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

Bose, S.

A. Serafini, M. Paternostro, M. S. Kim, and S. Bose, Phys. Rev. A 73, 022312 (2006).
[CrossRef]

Brune, M.

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

Buck, J. R.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

Burkard, G.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Cabrillo, C.

C. Cabrillo, J. I. Cirac, P. Garca-Fernández, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computing and Quantum Information (Cambridge University, 2000).

Cirac, J. I.

B. Kraus and J. I. Cirac, Phys. Rev. Lett. 92, 013602 (2004).
[CrossRef]

C. Cabrillo, J. I. Cirac, P. Garca-Fernández, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

J. I. Cirac, Phys. Rev. A 46, 4354 (1992).
[CrossRef]

Clarke, J.

J. Clarke and F. K. Wilhelm, Nature 453, 1031 (2008).
[CrossRef]

Das, S.

E. A. Sete and S. Das, Phys. Rev. A 83, 042301 (2011).
[CrossRef]

A. Rai, S. Das, and G. Agarwal, Opt. Express 18, 6241 (2010).
[CrossRef]

del Valle, E.

DiVincenzo, D. P.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
[CrossRef]

Edamatsu, K.

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

Garca-Fernández, P.

C. Cabrillo, J. I. Cirac, P. Garca-Fernández, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

Haroche, S.

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

Imamoglu, A.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Kim, M. S.

A. Serafini, M. Paternostro, M. S. Kim, and S. Bose, Phys. Rev. A 73, 022312 (2006).
[CrossRef]

Kimble, H. J.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

Kraus, B.

B. Kraus and J. I. Cirac, Phys. Rev. Lett. 92, 013602 (2004).
[CrossRef]

Kuzmich, A.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

Li, S.-B.

J.-B. Xu and S.-B. Li, New J. Phys. 7, 72 (2005).
[CrossRef]

Loss, D.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
[CrossRef]

McKeever, J.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

Ngerl, H.-C.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computing and Quantum Information (Cambridge University, 2000).

Paternostro, M.

A. Serafini, M. Paternostro, M. S. Kim, and S. Bose, Phys. Rev. A 73, 022312 (2006).
[CrossRef]

Ph. Georgiades, N.

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

Polzik, E. S.

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

Rai, A.

Raimond, J. M.

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

Serafini, A.

A. Serafini, M. Paternostro, M. S. Kim, and S. Bose, Phys. Rev. A 73, 022312 (2006).
[CrossRef]

Sete, E. A.

E. A. Sete and S. Das, Phys. Rev. A 83, 042301 (2011).
[CrossRef]

Sherwin, M.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Small, A.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Stamper-Kurn, D. M.

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

Wilhelm, F. K.

J. Clarke and F. K. Wilhelm, Nature 453, 1031 (2008).
[CrossRef]

Wootters, W. K.

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

Xu, J.-B.

J.-B. Xu and S.-B. Li, New J. Phys. 7, 72 (2005).
[CrossRef]

Zoller, P.

C. Cabrillo, J. I. Cirac, P. Garca-Fernández, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

J. Clarke and F. K. Wilhelm, Nature 453, 1031 (2008).
[CrossRef]

New J. Phys. (1)

J.-B. Xu and S.-B. Li, New J. Phys. 7, 72 (2005).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (5)

A. Serafini, M. Paternostro, M. S. Kim, and S. Bose, Phys. Rev. A 73, 022312 (2006).
[CrossRef]

J. I. Cirac, Phys. Rev. A 46, 4354 (1992).
[CrossRef]

C. Cabrillo, J. I. Cirac, P. Garca-Fernández, and P. Zoller, Phys. Rev. A 59, 1025 (1999).
[CrossRef]

E. A. Sete and S. Das, Phys. Rev. A 83, 042301 (2011).
[CrossRef]

D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
[CrossRef]

Phys. Rev. Lett. (5)

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

B. Kraus and J. I. Cirac, Phys. Rev. Lett. 92, 013602 (2004).
[CrossRef]

J. McKeever, J. R. Buck, A. D. Boozer, A. Kuzmich, H.-C. Ngerl, D. M. Stamper-Kurn, and H. J. Kimble, Phys. Rev. Lett. 90, 133602 (2003).
[CrossRef]

N. Ph. Georgiades, E. S. Polzik, K. Edamatsu, and H. J. Kimble, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef]

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

Rev. Mod. Phys. (1)

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

Other (1)

M. A. Nielsen and I. L. Chuang, Quantum Computing and Quantum Information (Cambridge University, 2000).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of the interaction of two qubits with squeezed light in a cavity. When the pump laser of amplitude ε and frequency ν drives the nonlinear crystal of susceptibility χ(2) correlated signal-idler photon pairs of frequency ν1, ν2 (ν=ν1+ν2) are generated. The two-photon correlation is then transferred to the two-qubit system mediated by the cavity (b) Collective state energy-level diagram for the two-qubit system including incoherent pumping rates (w1 and w2).

Fig. 2.
Fig. 2.

(a) Time dependent concurrence [Eq. (4)] for (a) various values of ε at resonance and for γ/γ0=0.05 [κ=80MHz, g=35MHz, γ=1.5MHz] (b) as a function of detuning Δ/γ0 for γ/γ0=0.05 and ε/κ=0.92 (c) Steady-state concurrence as a function of w/γ0 at resonance for γ/γ0=0.02 and various values of ε.

Fig. 3.
Fig. 3.

(a) Concurrence (C) versus ε/κ and Δ/γ01 for γ1/γ01=0.01, γ2/γ02=0.05, γ02=1.08γ01 and w1=3.5γ01, w2=0. (b) C versus linear entropy for randomly generated points using realistic parameters for the present system (red dashed curve) and for maximally entangled mixed state (solid blue curve). (c) C versus Δ/γ01 for ε/κ=0.99 and the same parameters as in (a) but for w2=0,0.5,1.5,2.5,3.5γ01 from top to bottom.

Equations (5)

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H^I=j=1,kj2Δjσ^jσ^j+gj(cσ^ja^j+sσ^ja^k+H.c.),
χ.=i[HI,χ]+Lσ1χ+Lσ2χ+La1χ+La2χ,
ρ.=ij=12Δj[σjσj,ρ]j=12Γj2([σj,σjρ]+[ρσj,σj])ε2κγ1cγ2c{[σ1,ρσ2]+[σ2,ρσ1]+H.c.},
C=μeΓt2{[2Δ2μ2(1+cos2αt)]sin2αtα4}12.
C=4w1Λ[υ2+4Δ2[(υ2+4Δ2)(w1+Γ1)8υΛ2)]2]12,

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