Abstract

We present what we believe to be the first experimental results on resonant amplification of Berry’s phase/geometrical phase. A small-signal magnification factor of 6 was obtained using a 50–50 fiber-optic coupler to construct a ring resonator containing a three-dimensional fiber helix. This enhancement can be exploited when Berry’s phase is used in fiber-optic and other sensors or as a means for performing quantum computation.

© 2010 Optical Society of America

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References

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2007 (1)

2006 (2)

2005 (2)

2004 (3)

2002 (1)

2001 (1)

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[CrossRef] [PubMed]

2000 (4)

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401–403 (2000).
[CrossRef]

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, “Geometric quantum computation using nuclear magnetic resonance,” Nature 403, 869–871 (2000).
[CrossRef] [PubMed]

P. Senthilkumaran, G. Thursby, and B. Culshaw, “Fiber optic tunable loop mirror using Berry's geometric phase,” Opt. Lett. 25, 533–535 (2000).
[CrossRef]

P. Senthilkumaran, B. Culshaw, and G. Thursby, “Fiber-optic Sagnac interferometer for the observation of Berry’s topological phase,” J. Opt. Soc. Am. B 17, 1914–1919 (2000).
[CrossRef]

1999 (2)

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

J. E. Heebner and R. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
[CrossRef]

1998 (1)

1997 (1)

E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
[CrossRef]

1988 (1)

P. Yeh, Optical Waves in Layered Media (Wiley, 1988), Chaps. 4 and 7.

1986 (1)

A. Tomita and R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

1984 (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392, 45–57 (1984).
[CrossRef]

Ankiewicz, A.

Berry, M. V.

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392, 45–57 (1984).
[CrossRef]

Boyd, R.

Castagnoli, G.

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, “Geometric quantum computation using nuclear magnetic resonance,” Nature 403, 869–871 (2000).
[CrossRef] [PubMed]

Chen, Y.

Chiao, R. Y.

A. Tomita and R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

Chu, S. T.

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401–403 (2000).
[CrossRef]

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Cirac, J. I.

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[CrossRef] [PubMed]

Culshaw, B.

Duan, L. -M.

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[CrossRef] [PubMed]

Dulashko, Y.

Dultz, W.

E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
[CrossRef]

Ekert, A.

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, “Geometric quantum computation using nuclear magnetic resonance,” Nature 403, 869–871 (2000).
[CrossRef] [PubMed]

Frins, E. M.

E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
[CrossRef]

Golub, I.

Hale, A.

Heebner, J. E.

Ippen, E.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Jiang, X.

Jones, J. A.

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, “Geometric quantum computation using nuclear magnetic resonance,” Nature 403, 869–871 (2000).
[CrossRef] [PubMed]

Kaneko, T.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Kokubun, Y.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Kuzyk, M.

Little, B. E.

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401–403 (2000).
[CrossRef]

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Martinelli, M.

Melloni, A.

Morichetti, F.

Pan, W.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Ripin, D.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Senthilkumaran, P.

Simova, E.

Sumetsky, M.

Thursby, G.

Tomita, A.

A. Tomita and R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

Tong, L.

Vedral, V.

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, “Geometric quantum computation using nuclear magnetic resonance,” Nature 403, 869–871 (2000).
[CrossRef] [PubMed]

Vienne, G.

Wassmann, F.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988), Chaps. 4 and 7.

Zoller, P.

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[CrossRef] [PubMed]

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (2)

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401–403 (2000).
[CrossRef]

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nature (1)

J. A. Jones, V. Vedral, A. Ekert, and G. Castagnoli, “Geometric quantum computation using nuclear magnetic resonance,” Nature 403, 869–871 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

E. M. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fiber ring interferometer,” Opt. Commun. 136, 354–356 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (7)

Phys. Rev. Lett. (1)

A. Tomita and R. Y. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392, 45–57 (1984).
[CrossRef]

Science (1)

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[CrossRef] [PubMed]

Other (1)

P. Yeh, Optical Waves in Layered Media (Wiley, 1988), Chaps. 4 and 7.

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Figures (5)

Fig. 1
Fig. 1

(a) Accumulation of Berry’s phase by multiple helically wound fiber stretches. (b) Amplification of Berry’s phase by placing a fiber helix in a RR.

Fig. 2
Fig. 2

Amplification factor of Berry’s phase (solid curve) by a RR with R = r 2 = 0.5 as a function of single-pass Berry’s phase (or, equivalently, off-resonance frequency). The dashed curve exhibits amplification when the resonance is shifted by 10° phase.

Fig. 3
Fig. 3

Measured polarization rotation angle/Berry’s phase (solid curve) as a function of helix pitch. The dashed line is a theoretical curve.

Fig. 4
Fig. 4

Intensity distribution of the light exiting the RR containing a helix as a function of the output polarizer angle. Each point is time averaged measurement over 1 min. For a single pass, the fiber helix rotates a linearly polarized input light by 10°.

Fig. 5
Fig. 5

Output Berry’s phase for a simple helix (dashed curve) and for the helix in a RR (solid curve) as a function of theoretical single-pass Berry’s phase.

Equations (2)

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φ B = 2 π ( 1 p / s ) ,
φ B   out = 2 tan 1 ( 1 + r 1 r tan φ B 2 ) .

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