Abstract

We succeeded in measuring phase shift spectra of a micro-sphere cavity coupled with a tapered fiber using a weak coherent probe light at the single photon level. We utilized a tapered fiber with almost no depolarization and constructed a very stable phase shift measurement scheme based on polarization analysis using photon counting. Using a very weak probe light ( = 0.41), we succeeded in observing the transition in the phase shift spectrum between undercoupling and overcoupling (at gap distances of 500 and 100 nm, respectively). We also used quantum state tomography to obtain a ‘purity spectrum’. Even in the overcoupling regime, the average purity was 0.982±0.024 (minimum purity: 0.892), suggesting that the coherence of the fiber–microsphere system was well preserved. Based on these results, we believe this system is applicable to quantum phase gates using single light emitters such as diamond nitrogen vacancy centers.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
    [CrossRef] [PubMed]
  2. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
    [CrossRef] [PubMed]
  3. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996).
    [CrossRef] [PubMed]
  4. J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
    [CrossRef]
  5. H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Polarization-discriminated spectra of a fiber-microsphere system," Appl. Phys. Lett. 89, 121107 (2006).
    [CrossRef]
  6. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003).
    [CrossRef] [PubMed]
  7. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
    [CrossRef]
  8. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002).
    [CrossRef]
  9. H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007).
    [CrossRef]
  10. F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities," Biophys. J. 85, 1974-1979 (2003).
    [CrossRef] [PubMed]
  11. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres," Phys. Rev. A 76, 043837 (2007).
    [CrossRef]
  12. H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
    [CrossRef] [PubMed]
  13. H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Optimized phase switching using a single-atom nonlinearity," J. Opt. B 5, 218-221 (2003).
    [CrossRef]
  14. K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, "Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate," Phys. Rev. A 70, 013810 (2004).
    [CrossRef]
  15. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, "Measurement of conditional phase-shifts for quantum logic," Phys. Rev. Lett. 75, 4710-4713 (1995).
    [CrossRef] [PubMed]
  16. E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
    [CrossRef]
  17. T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, "Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light," N. J. Phys. 8, 184 (2006).
    [CrossRef]
  18. A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
    [CrossRef]
  19. K. Totsuka, and M. Tomita, "Slow and fast light in a microsphere-optical fiber system," J. Opt. Soc. Am. B 23, 2194-2199 (2006).
    [CrossRef]
  20. M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, "Observation of normal and anomalous dispersions in a microsphere taper fiber system," J. Phys. Soc. Jpn. 78, 035001 (2009).
    [CrossRef]
  21. T. Asai, H. Konishi, H. Takashima, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Optical phase shift observed in a resonance mode of a tapered-fiber coupled with a microsphere resonator," in Meeting Abstracts of the Phys. Soc. of Japan, (Academic, Osaka, Japan, 2008) 63, 23pQD-13, pp. 152.
  22. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).
    [CrossRef]
  23. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, "Fano resonance in a multimode tapered fiber coupled with a microspherical cavity," Appl. Phys. Lett. 86, 261106 (2005).
    [CrossRef]
  24. L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, "Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres," Europhys. Lett. 23, 327-334 (1993).
    [CrossRef]
  25. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
    [CrossRef] [PubMed]
  26. N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
    [CrossRef] [PubMed]
  27. A. Yariv, Optical Electronics in Modern Communications, pp. 12 (Oxford, 1997).

2010 (1)

H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
[CrossRef] [PubMed]

2009 (1)

M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, "Observation of normal and anomalous dispersions in a microsphere taper fiber system," J. Phys. Soc. Jpn. 78, 035001 (2009).
[CrossRef]

2007 (2)

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres," Phys. Rev. A 76, 043837 (2007).
[CrossRef]

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007).
[CrossRef]

2006 (3)

H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Polarization-discriminated spectra of a fiber-microsphere system," Appl. Phys. Lett. 89, 121107 (2006).
[CrossRef]

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, "Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light," N. J. Phys. 8, 184 (2006).
[CrossRef]

K. Totsuka, and M. Tomita, "Slow and fast light in a microsphere-optical fiber system," J. Opt. Soc. Am. B 23, 2194-2199 (2006).
[CrossRef]

2005 (1)

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, "Fano resonance in a multimode tapered fiber coupled with a microspherical cavity," Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

2004 (1)

K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, "Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate," Phys. Rev. A 70, 013810 (2004).
[CrossRef]

2003 (4)

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Optimized phase switching using a single-atom nonlinearity," J. Opt. B 5, 218-221 (2003).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef] [PubMed]

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

2002 (2)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002).
[CrossRef]

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
[CrossRef]

2001 (2)

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).
[CrossRef]

2000 (1)

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

1997 (2)

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

1996 (2)

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996).
[CrossRef] [PubMed]

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
[CrossRef] [PubMed]

1995 (2)

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, "Measurement of conditional phase-shifts for quantum logic," Phys. Rev. Lett. 75, 4710-4713 (1995).
[CrossRef] [PubMed]

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
[CrossRef] [PubMed]

1993 (1)

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, "Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres," Europhys. Lett. 23, 327-334 (1993).
[CrossRef]

Agha, I. H.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres," Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Arnold, S.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
[CrossRef] [PubMed]

Asai, T.

H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
[CrossRef] [PubMed]

Beveratos, A.

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
[CrossRef]

Birks, T. A.

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

Braun, D.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Brouri, R.

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
[CrossRef]

Brune, M.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, "Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres," Europhys. Lett. 23, 327-334 (1993).
[CrossRef]

Buck, J. R.

J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Cai, M.

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

Cheung, G.

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

Chiba, A.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, "Fano resonance in a multimode tapered fiber coupled with a microspherical cavity," Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Collot, L.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, "Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres," Europhys. Lett. 23, 327-334 (1993).
[CrossRef]

Connolly, J.

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
[CrossRef] [PubMed]

Dubreuil, N.

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
[CrossRef] [PubMed]

Foster, M. A.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres," Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Fujiwara, H.

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007).
[CrossRef]

H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Polarization-discriminated spectra of a fiber-microsphere system," Appl. Phys. Lett. 89, 121107 (2006).
[CrossRef]

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, "Fano resonance in a multimode tapered fiber coupled with a microspherical cavity," Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Fujiwara, M.

H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
[CrossRef] [PubMed]

Gacoin, T.

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
[CrossRef]

Gaeta, A. L.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres," Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Gorodetsky, M. L.

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996).
[CrossRef] [PubMed]

Grangier, P.

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
[CrossRef]

Griffel, G.

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
[CrossRef] [PubMed]

Hare, J.

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
[CrossRef] [PubMed]

Haroche, S.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, "Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres," Europhys. Lett. 23, 327-334 (1993).
[CrossRef]

Hofmann, H. F.

K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, "Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate," Phys. Rev. A 70, 013810 (2004).
[CrossRef]

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Optimized phase switching using a single-atom nonlinearity," J. Opt. B 5, 218-221 (2003).
[CrossRef]

Hood, C. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, "Measurement of conditional phase-shifts for quantum logic," Phys. Rev. Lett. 75, 4710-4713 (1995).
[CrossRef] [PubMed]

Hotta, J.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, "Fano resonance in a multimode tapered fiber coupled with a microspherical cavity," Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Ilchenko, V. S.

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996).
[CrossRef] [PubMed]

Jacques, F.

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

James, D. F. V.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Kimble, H. J.

J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, "Measurement of conditional phase-shifts for quantum logic," Phys. Rev. Lett. 75, 4710-4713 (1995).
[CrossRef] [PubMed]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002).
[CrossRef]

Knight, J. C.

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
[CrossRef] [PubMed]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef]

Kojima, K.

K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, "Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate," Phys. Rev. A 70, 013810 (2004).
[CrossRef]

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Optimized phase switching using a single-atom nonlinearity," J. Opt. B 5, 218-221 (2003).
[CrossRef]

Konishi, H.

H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Polarization-discriminated spectra of a fiber-microsphere system," Appl. Phys. Lett. 89, 121107 (2006).
[CrossRef]

Kuhn, S.

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
[CrossRef]

Kwiat, P. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Ladd, T. D.

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, "Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light," N. J. Phys. 8, 184 (2006).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef]

Lange, W.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, "Measurement of conditional phase-shifts for quantum logic," Phys. Rev. Lett. 75, 4710-4713 (1995).
[CrossRef] [PubMed]

Lefevre, V.

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
[CrossRef] [PubMed]

Lefevreseguin, V.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, "Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres," Europhys. Lett. 23, 327-334 (1993).
[CrossRef]

Leventhal, D. K.

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
[CrossRef] [PubMed]

Libchaber, A.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Mabuchi, H.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, "Measurement of conditional phase-shifts for quantum logic," Phys. Rev. Lett. 75, 4710-4713 (1995).
[CrossRef] [PubMed]

Matsumoto, T.

M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, "Observation of normal and anomalous dispersions in a microsphere taper fiber system," J. Phys. Soc. Jpn. 78, 035001 (2009).
[CrossRef]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef]

Morris, N.

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
[CrossRef] [PubMed]

Munro, W. J.

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, "Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light," N. J. Phys. 8, 184 (2006).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Nemoto, K.

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, "Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light," N. J. Phys. 8, 184 (2006).
[CrossRef]

Okawachi, Y.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres," Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Okishio, M.

M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, "Observation of normal and anomalous dispersions in a microsphere taper fiber system," J. Phys. Soc. Jpn. 78, 035001 (2009).
[CrossRef]

Painter, O.

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef] [PubMed]

Poizat, J. P.

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
[CrossRef]

Raimond, J. M.

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, "Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres," Europhys. Lett. 23, 327-334 (1993).
[CrossRef]

Sandoghdar, V.

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
[CrossRef] [PubMed]

Sasaki, K.

H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
[CrossRef] [PubMed]

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007).
[CrossRef]

H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Polarization-discriminated spectra of a fiber-microsphere system," Appl. Phys. Lett. 89, 121107 (2006).
[CrossRef]

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, "Fano resonance in a multimode tapered fiber coupled with a microspherical cavity," Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, "Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate," Phys. Rev. A 70, 013810 (2004).
[CrossRef]

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Optimized phase switching using a single-atom nonlinearity," J. Opt. B 5, 218-221 (2003).
[CrossRef]

Savchenkov, A. A.

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996).
[CrossRef] [PubMed]

Sercel, P. C.

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

Serpenguzel, A.

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
[CrossRef] [PubMed]

Sharping, J. E.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres," Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002).
[CrossRef]

Takahashi, M.

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007).
[CrossRef]

Takashima, H.

H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
[CrossRef] [PubMed]

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007).
[CrossRef]

Takeuchi, S.

H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
[CrossRef] [PubMed]

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007).
[CrossRef]

H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Polarization-discriminated spectra of a fiber-microsphere system," Appl. Phys. Lett. 89, 121107 (2006).
[CrossRef]

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, "Fano resonance in a multimode tapered fiber coupled with a microspherical cavity," Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, "Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate," Phys. Rev. A 70, 013810 (2004).
[CrossRef]

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Optimized phase switching using a single-atom nonlinearity," J. Opt. B 5, 218-221 (2003).
[CrossRef]

Taskent, D.

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
[CrossRef] [PubMed]

Teraoka, I.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Tomita, M.

M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, "Observation of normal and anomalous dispersions in a microsphere taper fiber system," J. Phys. Soc. Jpn. 78, 035001 (2009).
[CrossRef]

K. Totsuka, and M. Tomita, "Slow and fast light in a microsphere-optical fiber system," J. Opt. Soc. Am. B 23, 2194-2199 (2006).
[CrossRef]

Totsuka, K.

M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, "Observation of normal and anomalous dispersions in a microsphere taper fiber system," J. Phys. Soc. Jpn. 78, 035001 (2009).
[CrossRef]

K. Totsuka, and M. Tomita, "Slow and fast light in a microsphere-optical fiber system," J. Opt. Soc. Am. B 23, 2194-2199 (2006).
[CrossRef]

Toubaru, K.

H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
[CrossRef] [PubMed]

Turchette, Q. A.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, "Measurement of conditional phase-shifts for quantum logic," Phys. Rev. Lett. 75, 4710-4713 (1995).
[CrossRef] [PubMed]

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002).
[CrossRef]

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

van Loock, P.

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, "Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light," N. J. Phys. 8, 184 (2006).
[CrossRef]

Vollmer, F.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

White, A. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Yamamoto, Y.

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, "Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light," N. J. Phys. 8, 184 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

H. Konishi, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Polarization-discriminated spectra of a fiber-microsphere system," Appl. Phys. Lett. 89, 121107 (2006).
[CrossRef]

H. Takashima, H. Fujiwara, S. Takeuchi, K. Sasaki, and M. Takahashi, "Fiber-microsphere laser with a submicrometer sol-gel silica glass layer codoped with erbium, aluminum, and phosphorus," Appl. Phys. Lett. 90, 101103 (2007).
[CrossRef]

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, "Fano resonance in a multimode tapered fiber coupled with a microspherical cavity," Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Biophys. J. (1)

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Eur. Phys. J. D (1)

A. Beveratos, S. Kuhn, R. Brouri, T. Gacoin, J. P. Poizat, and P. Grangier, "Room temperature stable single photon source," Eur. Phys. J. D 18, 191-196 (2002).
[CrossRef]

Europhys. Lett. (1)

L. Collot, V. Lefevreseguin, M. Brune, J. M. Raimond, and S. Haroche, "Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres," Europhys. Lett. 23, 327-334 (1993).
[CrossRef]

J. Opt. B (1)

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, "Optimized phase switching using a single-atom nonlinearity," J. Opt. B 5, 218-221 (2003).
[CrossRef]

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

K. Totsuka, and M. Tomita, "Slow and fast light in a microsphere-optical fiber system," J. Opt. Soc. Am. B 23, 2194-2199 (2006).
[CrossRef]

J. Phys. Soc. Jpn. (1)

M. Tomita, M. Okishio, T. Matsumoto, and K. Totsuka, "Observation of normal and anomalous dispersions in a microsphere taper fiber system," J. Phys. Soc. Jpn. 78, 035001 (2009).
[CrossRef]

N. J. Phys. (1)

T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, "Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light," N. J. Phys. 8, 184 (2006).
[CrossRef]

Nature (2)

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002).
[CrossRef]

Opt. Express (1)

H. Takashima, T. Asai, K. Toubaru, M. Fujiwara, K. Sasaki, and S. Takeuchi, "Fiber-microsphere system at cryogenic temperatures toward cavity QED using diamond NV centers," Opt. Express 18, 15169-15173 (2010).
[CrossRef] [PubMed]

Opt. Lett. (6)

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, and V. Lefevre, "Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres," Opt. Lett. 20, 813-815 (1995).
[CrossRef] [PubMed]

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

G. Griffel, S. Arnold, D. Taskent, A. Serpenguzel, J. Connolly, and N. Morris, "Morphology-dependent resonances of a microsphere-optical fiber system," Opt. Lett. 21, 695-697 (1996).
[CrossRef] [PubMed]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996).
[CrossRef] [PubMed]

Phys. Rev. A (4)

J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, "Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate," Phys. Rev. A 70, 013810 (2004).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres," Phys. Rev. A 76, 043837 (2007).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, "Measurement of conditional phase-shifts for quantum logic," Phys. Rev. Lett. 75, 4710-4713 (1995).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef] [PubMed]

Other (2)

T. Asai, H. Konishi, H. Takashima, H. Fujiwara, S. Takeuchi, and K. Sasaki, "Optical phase shift observed in a resonance mode of a tapered-fiber coupled with a microsphere resonator," in Meeting Abstracts of the Phys. Soc. of Japan, (Academic, Osaka, Japan, 2008) 63, 23pQD-13, pp. 152.

A. Yariv, Optical Electronics in Modern Communications, pp. 12 (Oxford, 1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Experimental setup. HWP: half wave plate; QWP: quarter wave plate; PBS: polarizing beam splitter; SMF: single mode fiber; PD: photodiode; PZT: piezoelectric transducer; SPCM: single photon counting module.

Fig. 2
Fig. 2

(a) Minimum transmittance, (c) phase shift, and (e) purity spectra obtained at a gap distance of 500 nm; (b), (d), and (f) spectra obtained at a gap distance of 100 nm. Solid curves in (a) to (d) are theoretical fits based on coupled-mode theory.

Fig. 3
Fig. 3

Dependences of (red) minimum transmittance and (green) quality factor on gap distance. Black arrows indicate gap distances used to measure the spectra in Fig. 2.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

A X ( ω ) A 0 X ( ω ) = 1 γ [ y x e i ϕ 1 x y e i ϕ ] = T ( ω ) e i θ ( ω ) ,
A 0 X ( ω ) A X ( ω ) = T a l l T X ( ω ) e i θ X ( ω ) A 0 X ( ω ) , A 0 Y ( ω ) A Y ( ω ) = T all A 0 Y ( ω )
θ X ( ω ) = Tan 1 ( S 3 ( ω ) S 2 ( ω ) ) Arg A 0 X + Arg A 0 Y
I P ( ω ) = | A P ( ω ) | 2 2 η = 1 2 η | A X ( ω ) + A Y ( ω ) 2 | 2
ρ ^ = 1 2 ( I ^ + S 1 S 0 Z ^ + S 2 S 0 X ^ S 3 S 0 Y ^ ) .
p ( ω ) = Tr [ ρ ^ ( ω ) 2 ] .

Metrics