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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  1. G. Brassard, N. Lutkenhaus, T. Mor, and B. Sanders, “Limitations on practical quantum cryptography,” Phys. Rev. Lett. 85, 1330–1333 (2000).
    [CrossRef] [PubMed]
  2. 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]
  3. 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]
  4. R. Brouri, A. Beveratos, J. Poizat, and P. Grangier, “Photon antibunching in the fluorescence of individual color centers in diamond,” Opt. Lett. 25, 1294–1296 (2000).
    [CrossRef]
  5. 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]
  6. 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).
  7. R. Andrews, E. R. Pike, and Sarben Sarkar, “Photon correlations of a sub-threshold optical parametric oscillator,” Opt. Express 10, 461–468 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-11-461.
    [CrossRef] [PubMed]
  8. A. Gatti and L. Lugiato, “Quantum images and critical fluctuations in the optical parametric oscillator,” Phys. Rev. A 52, 1675–1690 (1995).
    [CrossRef] [PubMed]
  9. 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]

2002 (3)

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]

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).

R. Andrews, E. R. Pike, and Sarben Sarkar, “Photon correlations of a sub-threshold optical parametric oscillator,” Opt. Express 10, 461–468 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-11-461.
[CrossRef] [PubMed]

2001 (1)

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]

2000 (3)

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]

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

R. Brouri, A. Beveratos, J. Poizat, and P. Grangier, “Photon antibunching in the fluorescence of individual color centers in diamond,” Opt. Lett. 25, 1294–1296 (2000).
[CrossRef]

1995 (1)

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

1991 (1)

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]

Andrews, R.

Bechner, C.

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]

Beveratos, A.

Brassard, G.

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

Brouri, R.

Crescentini, L.

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]

Dale, Y.

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]

De Martini, F.

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]

Falth, S.

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]

Fleury, L.

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]

Gatti, 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]

Gayral, 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]

Grangier, P.

Hecht, B.

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]

Hu, E.

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]

Imamoglu, A.

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]

Kiraz, A.

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]

Loudon, R.

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]

Lu, Y. J.

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).

Lugiato, L.

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

Lutkenhaus, N.

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

Marrocco, M.

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]

Mataloni, P.

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]

Mor, T.

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

Ou, Z. Y.

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).

Pelton, M.

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]

Petroff, P. M.

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]

Pike, E. R.

Poizat, J.

Sanders, B.

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

Santori, C.

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]

Sarkar, Sarben

Schoenfeld, W. V.

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]

Segura, J.

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]

Solomon, G.

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]

Wild, U. P.

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]

Yamamoto, Y.

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]

Zhang, Lidong

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]

Zumofen, G.

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]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

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 (1)

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. (4)

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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