Abstract

The frequency conversion of cw continuous variable quantum states via second-order nonlinear optical processes is theoretically analyzed. It is shown that wideband frequency conversion of cw continuous variable quantum states is feasible by sum-frequency generation. For difference-frequency generation, besides as an optimal-phase-conjugation frequency-conversion process, any one quadrature of the quantum state can be frequency converted through it. Particularly, we analyze the influence of pump field fluctuations on the fidelity of the frequency-conversion process for a coherent state input.

© 2008 Optical Society of America

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References

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    [CrossRef]
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2007 (1)

2006 (2)

2005 (2)

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, "A photonic quantum information interface," Nature 437, 116-120 (2005).
[CrossRef] [PubMed]

S. L. Braunstein and P. V. Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

2004 (1)

2001 (2)

1998 (2)

1992 (1)

J. M. Huang and P. Kumar, "Observation of quantum frequency conversion," Phys. Rev. Lett. 68, 2153-2156 (1992).
[CrossRef] [PubMed]

1989 (1)

S. Reynaud and A. Heidmann, "A semiclassical linear input output transformation for quantum fluctuations," Opt. Commun. 71, 209-214 (1989).
[CrossRef]

1982 (1)

C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D 26, 1817-1839 (1982).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, "Resonant optical second harmonic generation and mixing," IEEE J. Quantum Electron. QE-2, 109-124 (1966).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, "Resonant optical second harmonic generation and mixing," IEEE J. Quantum Electron. QE-2, 109-124 (1966).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (1)

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, "A photonic quantum information interface," Nature 437, 116-120 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. Reynaud and A. Heidmann, "A semiclassical linear input output transformation for quantum fluctuations," Opt. Commun. 71, 209-214 (1989).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

N. J. Cerf and S. Iblisdir, "Phase conjugation of continuous quantum variables," Phys. Rev. A 64, 032307 (2001).
[CrossRef]

A. H. Tan, X. J. Jia, and C. D. Xie, "Frequency conversion of an entangled state," Phys. Rev. A 73, 033817 (2006).
[CrossRef]

Phys. Rev. D (1)

C. M. Caves, "Quantum limits on noise in linear amplifiers," Phys. Rev. D 26, 1817-1839 (1982).
[CrossRef]

Phys. Rev. Lett. (1)

J. M. Huang and P. Kumar, "Observation of quantum frequency conversion," Phys. Rev. Lett. 68, 2153-2156 (1992).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

S. L. Braunstein and P. V. Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

Science (1)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Other (2)

R. L. Byer, "Optical parametric oscillator," in Treatise in Quantum Electronics, H.Rabin and C.L.Tang, eds. (Academic, 1975), pp. 587-702.

P. Grangier and F. Grosshans, "Quantum teleportation criteria for continuous variables," e-print quant-ph/0009079.

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Figures (4)

Fig. 1
Fig. 1

Broadband QFC of cw CV quantum states based on SFG (DFG).

Fig. 2
Fig. 2

The fidelity of the QFC versus the phase quadrature noise of the input pump field ( N P in = 10 log N Y α 2 in ) for ω 2 γ = 0 , 2 , 10 . The total cavity loss is 2 γ τ = 0.05 and A 1 in 2 A 2 2 = 0.001 .

Fig. 3
Fig. 3

Fidelity of the QFC versus the normalized frequency ω 2 γ for different phase quadrature noise of the input pump field. The other parameters are the same as in Fig. 2.

Fig. 4
Fig. 4

The fidelity ( F ) of the QFC versus the phase and amplitude quadratures noise of the input pump field ( N P in X = 10 log N X α 0 in , N P in Y = 10 log N Y α 0 in ) for ω 2 γ = 0 . The other param eters are the same as in Fig. 2.

Equations (42)

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d α 2 ( t ) d t = γ α 2 ( t ) + i g τ 0 L α 0 ( z , t ) α 1 * ( z , t ) d z + 2 γ 2 τ α 2 in + 2 μ 2 τ b 2 ,
α 1 ( z , t ) z = i g α 0 ( z , t ) α 2 * ( t ) ,
α 0 ( z , t ) z = i g α 1 ( z , t ) α 2 ( t ) ,
α 1 ( z , t ) = α 1 in cos ( g α 2 ( t ) z ) + i α 0 in α 2 ( t ) α 2 ( t ) sin ( g α 2 ( t ) z ) ,
α 0 ( z , t ) = i α 1 in α 2 ( t ) α 2 ( t ) sin ( g α 2 ( t ) z ) + α 0 in cos ( g α 2 ( t ) z ) ,
α 0 ( L , t ) = exp ( i ϕ ) α 1 in ,
F = α ρ out α = 2 [ ( 2 + N X ) ( 2 + N Y ) ] 1 2 ,
N X = N X out N X in , N Y = N Y out N Y in ,
d α 2 ( t ) d t = γ α 2 ( t ) + 2 γ 2 τ α 2 in + 2 μ 2 τ b 2 .
α 2 ( ω ) = 2 γ 2 τ α 2 in ( ω ) + 2 μ 2 τ b 2 ( ω ) i ω + γ .
δ α 0 ( L , t ) = exp ( i θ ) ( i δ α 1 in δ θ A 1 in ) ,
δ X α 0 ( ω ) = δ X α 1 in ( ω ) ,
δ Y α 0 ( ω ) = δ Y α 1 in ( ω ) + 2 δ θ ( ω ) A 1 in .
N X α 0 ( ω ) = δ X α 0 ( ω ) δ X α 0 * ( ω ) = N X α 1 in ( ω ) ,
N Y α 0 ( ω ) = δ Y α 0 ( ω ) δ Y α 0 * ( ω ) = N Y α 1 in ( ω ) + 4 A 1 in 2 δ θ ( ω ) δ θ * ( ω ) .
δ θ ( ω ) δ θ * ( ω ) = 1 4 A 2 2 δ Y α 2 ( ω ) δ Y α 2 * ( ω ) .
δ Y α 2 ( ω ) δ Y α 2 * ( ω ) = ( 2 γ 2 τ ) N Y α 2 in ( ω ) + 2 μ 2 τ ω 2 + γ 2 ,
N X = 0 ,
N Y = ( A 1 in 2 A 2 2 ) ( 2 γ 2 τ ) N Y α 2 in ( ω ) + 2 μ 2 τ ω 2 + γ 2 .
F = 2 [ 2 ( 2 + ( A 1 in 2 A 2 2 ) ( 2 γ 2 τ ) N Y α 2 in ( ω ) + 2 μ 2 τ ω 2 + γ 2 ) ] 1 2 .
d α 0 ( t ) d t = γ α 0 ( t ) + i g τ 0 L α 1 ( z , t ) α 2 ( z , t ) d z + 2 γ 0 τ α 0 in + 2 μ 0 τ b 0 ,
α 1 ( z , t ) z = i g α 0 ( t ) α 2 * ( z , t ) ,
α 2 ( z , t ) z = i g α 0 ( t ) α 1 * ( z , t ) ,
α 1 ( z , t ) = α 1 in cosh ( g α 0 ( t ) z ) + i α 2 in * α 0 ( t ) α 0 ( t ) sinh ( g α 0 ( t ) z ) ,
α 2 ( z , t ) = i α 1 in * α 0 ( t ) α 0 ( t ) sinh ( g α 0 ( t ) z ) + α 2 in cosh ( g α 0 ( t ) z ) ,
α 2 ( L , t ) = exp ( i ϕ ) α 1 in * + 2 α 2 in ,
F = α * ρ out α * = 1 2 ,
N Y α 0 ( ω ) = ( 2 γ 0 τ ) N Y α 0 in ( ω ) + 2 μ 0 τ ω 2 + γ 2 ,
N X α 0 ( ω ) = ( 2 γ 0 τ ) N X α 0 in ( ω ) + 2 μ 0 τ ω 2 + γ 2 ,
δ α 2 ( L , t ) = i exp ( θ ) ( δ α 1 in * + 2 ln ( 1 + 2 ) δ α 0 ( t ) A 0 A 1 in * + i δ θ A 1 in * ) + 2 α 2 in ,
N X α 2 ( ω ) = N X α 1 in ( ω ) + C 2 A 1 in 2 A 0 2 N X α 0 ( ω ) + 2 N X α 2 in ( ω ) ,
N Y α 2 ( ω ) = N Y α 1 in ( ω ) + A 1 in 2 A 0 2 N Y α 0 ( ω ) + 2 N Y α 2 in ( ω ) ,
F = α * ρ out α * = 2 [ ( 2 + N X ) ( 2 + N Y ) ] 1 2 ,
N X = C 2 A 1 in 2 A 0 2 ( 2 γ 0 τ ) N X α 0 in ( ω ) + 2 μ 0 τ ω 2 + γ 2 + 2 ,
N Y = A 1 in 2 A 0 2 ( 2 γ 0 τ ) N Y α 0 in ( ω ) + 2 μ 0 τ ω 2 + γ 2 + 2 .
α 1 ( L , t ) = 2 α 1 in + α 2 in * ,
α 2 ( L , t ) = α 1 in * + 2 α 2 in .
X α 1 ( φ ) = 2 X α 1 in ( φ ) + X α 2 in ( φ ) ,
X α 2 ( φ ) = X α 1 in ( φ ) + 2 X α 2 in ( φ ) .
X α 2 ( φ ) = X α 1 in ( φ ) + 2 X α 1 ( φ ) .
X α 2 ( φ ) M = X α 1 in ( φ ) + 2 X α 1 ( φ ) + g i ,
X α 2 ( φ ) M = X α 1 in ( π φ ) .

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