Abstract

A multimode theory describing quantum interference of a sub-threshold optical parametric oscillator (OPO) with a coherent local oscillator (LO) in a homodyne detection scheme is presented. Analytic expressions for the count rates in terms of the correlation time and relative phase difference between the LO and OPO have been derived. The spectrum of squeezing is also derived and the threshold for squeezing obtained in terms of the crystal nonlinearity and LO and OPO beam intensities.

© 2003 Optical Society of America

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References

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Opt. Express

Opt. Lett.

Phys. Rev. A

A. Gatti and L. Lugiato, �??Quantum images and critical fluctuations in the optical parametric oscillator,�?? Phys. Rev. A 52, 1675-1690 (1995).
[CrossRef] [PubMed]

F. De Martini, M. Marrocco , P. Mataloni, L. Crescentini and R. Loudon, �??�??Spontaneous emission in the optical microscopic cavity,�??�?? Phys. Rev. A 43, 2480-2497 (1991).
[CrossRef] [PubMed]

Phys. Rev. B

A. Kiraz, S. Falth, C. Bechner , B. Gayral, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu and A. Imamoglu, �??Photon correlation spectroscopy of a single quantum dot,�?? Phys. Rev. B 65, 161303-161304 (2002).
[CrossRef]

Phys. Rev. Lett.

C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, �??Triggered single photons from a quantum dot,�?? Phys. Rev. Lett. 86, 1502-1505 (2001).
[CrossRef] [PubMed]

L. Fleury, J. Segura, G. Zumofen, B. Hecht and U. P. Wild, �??Nonclassical photon statistics in single-molecule fluorescence at room temperature,�?? Phys. Rev. Lett. 84, 1148-1151 (2000).
[CrossRef] [PubMed]

Y. J. Lu and Z. Y. Ou, �??Observation of nonclassical photon statistics due to quantum interference,�?? Phys. Rev. Lett. 88, 023601-1-023601-4 (2002).

G. Brassard, N. Lutkenhaus, T. Mor, and B. Sanders, �??Limitations on practical quantum cryptography,�?? Phys. Rev. Lett. 85, 1330-1333 (2000).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1.
Fig. 1.

Schematic showing the interference of the field from a LO and OPO. BS is a 50/50 beam splitter and D1 and D2 are photon counters.

Fig. 2.
Fig. 2.

Normalized two-photon count rates ( A ( 2 ) 2 ) against τ n 1 vd based on Eq. (7) showing antibunching effects. (a) q = 2 and Δφ = 0, (b) q = 2 and Δφ = π and (c) q = 1 and Δφ = π.

Equations (19)

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A ( 2 ) = α LO , α pump , 0 E H ( + ) r 2 t 2 E H ( + ) r 1 t 1 α LO , α pump , 0
A ( 2 ) = 1 2 α LO , α pump , 0 E LO ( + ) r 2 t 2 E LO ( + ) r 1 t 1 α LO , α pump , 0
+ ( 1 2 ε p χ e p d 3 k 1 d 3 k 2 d 3 r 3 U k 1 λ 1 * ( r 3 ) U k 2 λ 2 * ( r 3 ) U k 0 λ 0 ( r 3 )
× α LO , α pump 0 E out ( + ) r 2 t 2 E out ( + ) r 1 t 1 α LO , α pump , k 1 , k 2 δ ω k 1 ω k 2 ω k 0 )
E r 1 t 1 = 1 2 [ E out r 1 t 1 + i E LO r 1 t 1 ]
E r 2 t 2 = 1 2 [ i E out r 2 t 2 E LO r 2 t 2 ]
A ( 2 ) ε l 2 e i 2 ϕ l χ S ε P e i ϕ p e τ n 1 vd
S = π 2 Vt 2 o 2 t 1 p ( 1 + r 2 o ) n 1
n 1 = 2 r 2 o 1 + r 2 o
A ( 2 ) 2 1 + q 2 e 2 τ n 1 vd + 2 q e τ n 1 vd cos ( ϕ p 2 ϕ l )
P ( t ) = E ( ) r 1 t E ( + ) r 1 t E ( ) r 2 t E ( + ) r 2 t
δ P ( t ) = P ( t ) P ( t )
Q ( ω ) = dt e iωt δP ( t ) δP ( 0 )
δP ( t ) δP ( 0 ) = β ε l 2 [ 11 ε l 2 4 γ ε p cos ( 2 ϕ l ϕ p ) F ( t ) + 2 Δ n k 0 2 c ( k 0 2 ) 2 sinc ( Δt ) ]
F ( t ) = d ω e iωt 1 + r 2 o exp ( i 2 vdω ) 2
γ = πVχ ( n k 0 2 ) 2 ( t 2 o 2 t 10 ) ( k 0 2 ) 4
V ( 0 ) = 1 + μ δ cos ( 2 ϕ l ϕ p )
μ = 11 ε l 2 2 π n k 0 2 c ( k 0 2 ) 2
δ = 2 V χ ε p n k 0 2 c ( k 0 2 ) 2 t 2 o 2 t 1 o 1 + r 2 o 2

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