Abstract

The losses of the transmission, absorption, and scattering of optical mirrors govern the extraction efficiency of a nonclassical state that is generated inside a cavity. By measuring the reflectivities and transmittances and the matching factors from both sides of a super-mirror-made microcavity at various mode-matching efficiencies, the transmission losses and the unwanted losses, including the absorption and scatter losses, of the left and right cavity mirrors were both determined at the parts-per-million level.

© 2006 Optical Society of America

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References

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  1. J. Ye and T. W. Lynn, "Applications of optical cavities in modern atomic, molecular, and optical physics," in Advances in Atomic Molecular and Optical Physics, B.Bederson and H.Walther, eds. (Academic, 2003), p. 1.
  2. A. Sappey, E. Hill, T. Settersten, and M. Linne, "Fixed-frequency cavity ringdown diagnostic for atmospheric particulate matter," Opt. Lett. 23, 954-956 (1998).
    [CrossRef]
  3. P. Fritschel, G. González, B. Lantz, P. Saha, and M. Zucker, "High power interferometric phase measurement limited by quantum noise and application to detection of gravitational waves," Phys. Rev. Lett. 80, 3181-3184 (1998).
    [CrossRef]
  4. R. J. Jones, J.-C. Diels, J. Jasapara, and W. Rudolph, "Stabilization of the frequency, phase, and repetition rate of an ultra-short pulse train to a Fabry-Perot reference cavity," Opt. Commun. 175, 409-418 (2000).
    [CrossRef]
  5. P. Grangier, G. Reymond, and N. Schlosser, "Implementations of quantum computing using cavity quantum electrodynamics schemes," Fortschr. Phys. 48, 859-874 (2000).
    [CrossRef]
  6. H. J. Kimble, "Strong interaction of single atoms and photons in cavity QED," Phys. Scr. , T76, 127-137 (1998).
    [CrossRef]
  7. G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, "Measurement of ultralow losses in an optical interferometer," Opt. Lett. 17, 363-365 (1992).
    [CrossRef] [PubMed]
  8. M. Khanbekyan, L. Knöll, A. A. Semenov, W. Vogel, and D.-G. Welsch, "Quantum-state extraction from high-Q cavities," Phys. Rev. A 69, 043807 (2004).
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    [CrossRef] [PubMed]
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  11. K. An, B. A. Sones, C. Fang-Yen, R. R. Dasari, and M. S. Feld, "Optical bistability induced by mirror absorption: measurement of absorption coefficients at the sub-ppm level," Opt. Lett. 22, 1433-1435 (1997).
    [CrossRef]
  12. N. Uehara, A. Ueda, K. Ueda, H. Sekiguchi, T. Mitake, K. Nakamura, N. Kitajima, and I. Kataoka, "Ultralow-loss mirror of the parts-in-106 level at 1064 nm," Opt. Lett. 20, 530-532 (1995).
    [CrossRef] [PubMed]
  13. H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley, 2004), p. 124.
    [CrossRef]
  14. Y. Honda, "Review talk of laser wire in cavity," presented at the International Linear Collider European Regional Meeting and ILC-BDIR, London, U.K., 20-23 June 2005.
  15. We get this error range by taking a maximum value that can cover both error ranges of the two transmitted ratios.

2000 (2)

R. J. Jones, J.-C. Diels, J. Jasapara, and W. Rudolph, "Stabilization of the frequency, phase, and repetition rate of an ultra-short pulse train to a Fabry-Perot reference cavity," Opt. Commun. 175, 409-418 (2000).
[CrossRef]

P. Grangier, G. Reymond, and N. Schlosser, "Implementations of quantum computing using cavity quantum electrodynamics schemes," Fortschr. Phys. 48, 859-874 (2000).
[CrossRef]

1998 (3)

H. J. Kimble, "Strong interaction of single atoms and photons in cavity QED," Phys. Scr. , T76, 127-137 (1998).
[CrossRef]

A. Sappey, E. Hill, T. Settersten, and M. Linne, "Fixed-frequency cavity ringdown diagnostic for atmospheric particulate matter," Opt. Lett. 23, 954-956 (1998).
[CrossRef]

P. Fritschel, G. González, B. Lantz, P. Saha, and M. Zucker, "High power interferometric phase measurement limited by quantum noise and application to detection of gravitational waves," Phys. Rev. Lett. 80, 3181-3184 (1998).
[CrossRef]

1997 (1)

1995 (1)

1992 (1)

1984 (1)

An, K.

Anderson, D. Z.

Bachor, H. A.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley, 2004), p. 124.
[CrossRef]

Dasari, R. R.

Diels, J.-C.

R. J. Jones, J.-C. Diels, J. Jasapara, and W. Rudolph, "Stabilization of the frequency, phase, and repetition rate of an ultra-short pulse train to a Fabry-Perot reference cavity," Opt. Commun. 175, 409-418 (2000).
[CrossRef]

Fang-Yen, C.

Feld, M. S.

Frisch, J. C.

Fritschel, P.

P. Fritschel, G. González, B. Lantz, P. Saha, and M. Zucker, "High power interferometric phase measurement limited by quantum noise and application to detection of gravitational waves," Phys. Rev. Lett. 80, 3181-3184 (1998).
[CrossRef]

González, G.

P. Fritschel, G. González, B. Lantz, P. Saha, and M. Zucker, "High power interferometric phase measurement limited by quantum noise and application to detection of gravitational waves," Phys. Rev. Lett. 80, 3181-3184 (1998).
[CrossRef]

Grangier, P.

P. Grangier, G. Reymond, and N. Schlosser, "Implementations of quantum computing using cavity quantum electrodynamics schemes," Fortschr. Phys. 48, 859-874 (2000).
[CrossRef]

Hill, E.

Honda, Y.

Y. Honda, "Review talk of laser wire in cavity," presented at the International Linear Collider European Regional Meeting and ILC-BDIR, London, U.K., 20-23 June 2005.

Hood, C. J.

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors loss, phase shifts, and mode structure in an optical cavity," Phys. Rev. A 64, 033804 (2001).

Jasapara, J.

R. J. Jones, J.-C. Diels, J. Jasapara, and W. Rudolph, "Stabilization of the frequency, phase, and repetition rate of an ultra-short pulse train to a Fabry-Perot reference cavity," Opt. Commun. 175, 409-418 (2000).
[CrossRef]

Jones, R. J.

R. J. Jones, J.-C. Diels, J. Jasapara, and W. Rudolph, "Stabilization of the frequency, phase, and repetition rate of an ultra-short pulse train to a Fabry-Perot reference cavity," Opt. Commun. 175, 409-418 (2000).
[CrossRef]

Kataoka, I.

Khanbekyan, M.

M. Khanbekyan, L. Knöll, A. A. Semenov, W. Vogel, and D.-G. Welsch, "Quantum-state extraction from high-Q cavities," Phys. Rev. A 69, 043807 (2004).

Kimble, H. J.

H. J. Kimble, "Strong interaction of single atoms and photons in cavity QED," Phys. Scr. , T76, 127-137 (1998).
[CrossRef]

G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, "Measurement of ultralow losses in an optical interferometer," Opt. Lett. 17, 363-365 (1992).
[CrossRef] [PubMed]

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors loss, phase shifts, and mode structure in an optical cavity," Phys. Rev. A 64, 033804 (2001).

Kitajima, N.

Knöll, L.

M. Khanbekyan, L. Knöll, A. A. Semenov, W. Vogel, and D.-G. Welsch, "Quantum-state extraction from high-Q cavities," Phys. Rev. A 69, 043807 (2004).

Lalezari, R.

Lantz, B.

P. Fritschel, G. González, B. Lantz, P. Saha, and M. Zucker, "High power interferometric phase measurement limited by quantum noise and application to detection of gravitational waves," Phys. Rev. Lett. 80, 3181-3184 (1998).
[CrossRef]

Linne, M.

Lynn, T. W.

J. Ye and T. W. Lynn, "Applications of optical cavities in modern atomic, molecular, and optical physics," in Advances in Atomic Molecular and Optical Physics, B.Bederson and H.Walther, eds. (Academic, 2003), p. 1.

Masser, C. S.

Mitake, T.

Nakamura, K.

Ralph, T. C.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley, 2004), p. 124.
[CrossRef]

Rempe, G.

Reymond, G.

P. Grangier, G. Reymond, and N. Schlosser, "Implementations of quantum computing using cavity quantum electrodynamics schemes," Fortschr. Phys. 48, 859-874 (2000).
[CrossRef]

Rudolph, W.

R. J. Jones, J.-C. Diels, J. Jasapara, and W. Rudolph, "Stabilization of the frequency, phase, and repetition rate of an ultra-short pulse train to a Fabry-Perot reference cavity," Opt. Commun. 175, 409-418 (2000).
[CrossRef]

Saha, P.

P. Fritschel, G. González, B. Lantz, P. Saha, and M. Zucker, "High power interferometric phase measurement limited by quantum noise and application to detection of gravitational waves," Phys. Rev. Lett. 80, 3181-3184 (1998).
[CrossRef]

Sappey, A.

Schlosser, N.

P. Grangier, G. Reymond, and N. Schlosser, "Implementations of quantum computing using cavity quantum electrodynamics schemes," Fortschr. Phys. 48, 859-874 (2000).
[CrossRef]

Sekiguchi, H.

Semenov, A. A.

M. Khanbekyan, L. Knöll, A. A. Semenov, W. Vogel, and D.-G. Welsch, "Quantum-state extraction from high-Q cavities," Phys. Rev. A 69, 043807 (2004).

Settersten, T.

Sones, B. A.

Thompson, R. J.

Ueda, A.

Ueda, K.

Uehara, N.

Vogel, W.

M. Khanbekyan, L. Knöll, A. A. Semenov, W. Vogel, and D.-G. Welsch, "Quantum-state extraction from high-Q cavities," Phys. Rev. A 69, 043807 (2004).

Welsch, D.-G.

M. Khanbekyan, L. Knöll, A. A. Semenov, W. Vogel, and D.-G. Welsch, "Quantum-state extraction from high-Q cavities," Phys. Rev. A 69, 043807 (2004).

Ye, J.

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors loss, phase shifts, and mode structure in an optical cavity," Phys. Rev. A 64, 033804 (2001).

J. Ye and T. W. Lynn, "Applications of optical cavities in modern atomic, molecular, and optical physics," in Advances in Atomic Molecular and Optical Physics, B.Bederson and H.Walther, eds. (Academic, 2003), p. 1.

Zucker, M.

P. Fritschel, G. González, B. Lantz, P. Saha, and M. Zucker, "High power interferometric phase measurement limited by quantum noise and application to detection of gravitational waves," Phys. Rev. Lett. 80, 3181-3184 (1998).
[CrossRef]

Appl. Opt. (1)

Fortschr. Phys. (1)

P. Grangier, G. Reymond, and N. Schlosser, "Implementations of quantum computing using cavity quantum electrodynamics schemes," Fortschr. Phys. 48, 859-874 (2000).
[CrossRef]

Opt. Commun. (1)

R. J. Jones, J.-C. Diels, J. Jasapara, and W. Rudolph, "Stabilization of the frequency, phase, and repetition rate of an ultra-short pulse train to a Fabry-Perot reference cavity," Opt. Commun. 175, 409-418 (2000).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

P. Fritschel, G. González, B. Lantz, P. Saha, and M. Zucker, "High power interferometric phase measurement limited by quantum noise and application to detection of gravitational waves," Phys. Rev. Lett. 80, 3181-3184 (1998).
[CrossRef]

Phys. Scr. (1)

H. J. Kimble, "Strong interaction of single atoms and photons in cavity QED," Phys. Scr. , T76, 127-137 (1998).
[CrossRef]

Other (6)

M. Khanbekyan, L. Knöll, A. A. Semenov, W. Vogel, and D.-G. Welsch, "Quantum-state extraction from high-Q cavities," Phys. Rev. A 69, 043807 (2004).

J. Ye and T. W. Lynn, "Applications of optical cavities in modern atomic, molecular, and optical physics," in Advances in Atomic Molecular and Optical Physics, B.Bederson and H.Walther, eds. (Academic, 2003), p. 1.

H. A. Bachor and T. C. Ralph, A Guide to Experiments in Quantum Optics, 2nd ed. (Wiley, 2004), p. 124.
[CrossRef]

Y. Honda, "Review talk of laser wire in cavity," presented at the International Linear Collider European Regional Meeting and ILC-BDIR, London, U.K., 20-23 June 2005.

We get this error range by taking a maximum value that can cover both error ranges of the two transmitted ratios.

C. J. Hood, H. J. Kimble, and J. Ye, "Characterization of high-finesse mirrors loss, phase shifts, and mode structure in an optical cavity," Phys. Rev. A 64, 033804 (2001).

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Figures (4)

Fig. 1
Fig. 1

Schematic of an optical cavity and its transmissions and reflections.

Fig. 2
Fig. 2

(Color online) Setup for the left-side incident beam (similar to the right-side incident beam). PBS, polarizing beam splitter; HP, half-wave plate; D1 and D2, two photodetectors.

Fig. 3
Fig. 3

(Color online) Reflected and transmitted spectra of the cavity TEM 00 mode for a right-side incident beam (the mode-matching factor ε = 0.652 ). (a) Original outputs by detectors D1 and D2 and (b) converted perfect-mode-matching TEM 00 spectra (normalized to 1).

Fig. 4
Fig. 4

Higher-order transverse modes. (a)–(e) Zeroth- to fourth-order modes, and the mode-matching factor is determined as 0.652.

Tables (2)

Tables Icon

Table 1 Reflectivities and Transmittances for Right Incident Beam

Tables Icon

Table 2 Reflectivities and Transmittances for Left Incident Beam

Equations (8)

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( r , L ) = P ref L P in L = [ ( R 1 R 2 + l 1 R 2 ) ( 1 R 1 R 2 ) ] 2 ,
( t , L ) = P trans L P in L = [ ( 1 R 1 l 1 ) ( 1 R 2 l 2 ) ( 1 R 1 R 2 ) ] 2 .
( r , R ) = P ref R P in R = [ ( R 2 R 1 + l 2 R 1 ) ( 1 R 1 R 2 ) ] 2 .
l 1 = 1 R 1 ( r , L ) ( 1 R 1 R 2 ) R 2 ,
l 2 = 1 R 2 ( r , R ) ( 1 R 1 R 2 ) R 1 .
( 1 R 2 ) ( r , L ) R 1 + ( 1 R 1 ) ( r , R ) R 2 ( 1 R 1 R 2 ) × [ P L P R + ( 1 t ) R 1 R 2 ] = 0.
( 1 R 2 ) ( r , L ) + ( 1 R 1 ) ( r , R ) ( 1 R 1 R 2 ) × [ ( r , L ) ( r , R ) + ( 1 t ) ] = 0.
F = 2 π / ( 2 R 1 R 2 ) .

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