Abstract

The external fields of optical whispering gallery modes may be used to confine atoms in stable orbits around a dielectric microsphere. As an example, a toroidal dipole-force trap (atom gallery) for three-level atoms is investigated, and the possibility of achieving an atomic (matter–wave) resonator is discussed. The extremely small electromagnetic mode volumes and high Q’s of the whispering gallery modes should permit a circulating photon to be repeatedly absorbed and reemitted by a trapped whispering atom.

© 1994 Optical Society of America

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  1. V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett A 137, 393 (1989); “Optical whispering-gallery microresonators,” Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).
    [CrossRef]
  2. L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993).
    [CrossRef]
  3. G. S. Agarwal, S. Duttagupta, Opt. Commun. 93, 173 (1992).
    [CrossRef]
  4. H. J. Kimble, H. Mabuchi, A. B. Matsko, S. P. Vyatchanin, unpublished data.
  5. P. W. Barber, R. K. Chang, eds., Optical Effects Associated With Small Particles (World Scientific, Singapore, 1988).
  6. See session QTuC inQuantum Electronics and Laser Science, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 45–49.
  7. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
    [CrossRef]
  8. Y. B. Ovchinnikov, S. V. Shulga, V. I. Balykin, J. Phys. B 24, 3173 (1991).
    [CrossRef]
  9. H. J. Kimble, in Cavity Quantum Electrodynamics, Advances in Atomic, Molecular, and Optical Physics, Supplement 2, P. R. Berman, ed. (Academic, San Diego, Calif., 1994).
  10. V. I. Balykin, V. S. Letokhov, Appl. Phys. B 48, 517 (1989).
    [CrossRef]
  11. H. Wallis, J. Dalibard, C. Cohen-Tannoudji, Appl. Phys. B 54, 407 (1992).
    [CrossRef]
  12. C. Cohen-Tannoudji, W. D. Phillips, Phys. Today 43(10), 33 (1990); S. Chu, Science 253, 861 (1991).
    [CrossRef] [PubMed]
  13. S. Haroche, in Fundamental Systems in Quantum Optics, Les Houches Summer School Session LIII, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (Elsevier, Amsterdam, 1992), p. 771.
  14. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom–Photon Interactions (Wiley, New York, 1992).
  15. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 554.
  16. M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
    [CrossRef]

1993

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

1992

G. S. Agarwal, S. Duttagupta, Opt. Commun. 93, 173 (1992).
[CrossRef]

H. Wallis, J. Dalibard, C. Cohen-Tannoudji, Appl. Phys. B 54, 407 (1992).
[CrossRef]

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
[CrossRef]

1991

Y. B. Ovchinnikov, S. V. Shulga, V. I. Balykin, J. Phys. B 24, 3173 (1991).
[CrossRef]

1990

C. Cohen-Tannoudji, W. D. Phillips, Phys. Today 43(10), 33 (1990); S. Chu, Science 253, 861 (1991).
[CrossRef] [PubMed]

1989

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett A 137, 393 (1989); “Optical whispering-gallery microresonators,” Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).
[CrossRef]

V. I. Balykin, V. S. Letokhov, Appl. Phys. B 48, 517 (1989).
[CrossRef]

1970

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, S. Duttagupta, Opt. Commun. 93, 173 (1992).
[CrossRef]

Ashkin, A.

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Balykin, V. I.

Y. B. Ovchinnikov, S. V. Shulga, V. I. Balykin, J. Phys. B 24, 3173 (1991).
[CrossRef]

V. I. Balykin, V. S. Letokhov, Appl. Phys. B 48, 517 (1989).
[CrossRef]

Bloch, D.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
[CrossRef]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett A 137, 393 (1989); “Optical whispering-gallery microresonators,” Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).
[CrossRef]

Brune, M.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Chevrollier, M.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
[CrossRef]

Cohen-Tannoudji, C.

H. Wallis, J. Dalibard, C. Cohen-Tannoudji, Appl. Phys. B 54, 407 (1992).
[CrossRef]

C. Cohen-Tannoudji, W. D. Phillips, Phys. Today 43(10), 33 (1990); S. Chu, Science 253, 861 (1991).
[CrossRef] [PubMed]

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom–Photon Interactions (Wiley, New York, 1992).

Collot, L.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Dalibard, J.

H. Wallis, J. Dalibard, C. Cohen-Tannoudji, Appl. Phys. B 54, 407 (1992).
[CrossRef]

Ducloy, M.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
[CrossRef]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom–Photon Interactions (Wiley, New York, 1992).

Duttagupta, S.

G. S. Agarwal, S. Duttagupta, Opt. Commun. 93, 173 (1992).
[CrossRef]

Fichet, M.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
[CrossRef]

Gorodetsky, M. L.

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett A 137, 393 (1989); “Optical whispering-gallery microresonators,” Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom–Photon Interactions (Wiley, New York, 1992).

Haroche, S.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

S. Haroche, in Fundamental Systems in Quantum Optics, Les Houches Summer School Session LIII, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (Elsevier, Amsterdam, 1992), p. 771.

Ilchenko, V. S.

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett A 137, 393 (1989); “Optical whispering-gallery microresonators,” Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).
[CrossRef]

Kimble, H. J.

H. J. Kimble, H. Mabuchi, A. B. Matsko, S. P. Vyatchanin, unpublished data.

H. J. Kimble, in Cavity Quantum Electrodynamics, Advances in Atomic, Molecular, and Optical Physics, Supplement 2, P. R. Berman, ed. (Academic, San Diego, Calif., 1994).

Lefèvre-Seguin, V.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Letokhov, V. S.

V. I. Balykin, V. S. Letokhov, Appl. Phys. B 48, 517 (1989).
[CrossRef]

Mabuchi, H.

H. J. Kimble, H. Mabuchi, A. B. Matsko, S. P. Vyatchanin, unpublished data.

Matsko, A. B.

H. J. Kimble, H. Mabuchi, A. B. Matsko, S. P. Vyatchanin, unpublished data.

Oria, M.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
[CrossRef]

Ovchinnikov, Y. B.

Y. B. Ovchinnikov, S. V. Shulga, V. I. Balykin, J. Phys. B 24, 3173 (1991).
[CrossRef]

Phillips, W. D.

C. Cohen-Tannoudji, W. D. Phillips, Phys. Today 43(10), 33 (1990); S. Chu, Science 253, 861 (1991).
[CrossRef] [PubMed]

Rahmat, G.

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
[CrossRef]

Raimond, J. M.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Shulga, S. V.

Y. B. Ovchinnikov, S. V. Shulga, V. I. Balykin, J. Phys. B 24, 3173 (1991).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 554.

Vyatchanin, S. P.

H. J. Kimble, H. Mabuchi, A. B. Matsko, S. P. Vyatchanin, unpublished data.

Wallis, H.

H. Wallis, J. Dalibard, C. Cohen-Tannoudji, Appl. Phys. B 54, 407 (1992).
[CrossRef]

Appl. Phys. B

V. I. Balykin, V. S. Letokhov, Appl. Phys. B 48, 517 (1989).
[CrossRef]

H. Wallis, J. Dalibard, C. Cohen-Tannoudji, Appl. Phys. B 54, 407 (1992).
[CrossRef]

Europhys. Lett.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

J. Phys. B

Y. B. Ovchinnikov, S. V. Shulga, V. I. Balykin, J. Phys. B 24, 3173 (1991).
[CrossRef]

J. Phys. II

M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, M. Ducloy, J. Phys. II (Paris) 2, 631 (1992).
[CrossRef]

Opt. Commun.

G. S. Agarwal, S. Duttagupta, Opt. Commun. 93, 173 (1992).
[CrossRef]

Phys. Lett A

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett A 137, 393 (1989); “Optical whispering-gallery microresonators,” Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).
[CrossRef]

Phys. Rev. Lett.

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Phys. Today

C. Cohen-Tannoudji, W. D. Phillips, Phys. Today 43(10), 33 (1990); S. Chu, Science 253, 861 (1991).
[CrossRef] [PubMed]

Other

S. Haroche, in Fundamental Systems in Quantum Optics, Les Houches Summer School Session LIII, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (Elsevier, Amsterdam, 1992), p. 771.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom–Photon Interactions (Wiley, New York, 1992).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 554.

H. J. Kimble, in Cavity Quantum Electrodynamics, Advances in Atomic, Molecular, and Optical Physics, Supplement 2, P. R. Berman, ed. (Academic, San Diego, Calif., 1994).

H. J. Kimble, H. Mabuchi, A. B. Matsko, S. P. Vyatchanin, unpublished data.

P. W. Barber, R. K. Chang, eds., Optical Effects Associated With Small Particles (World Scientific, Singapore, 1988).

See session QTuC inQuantum Electronics and Laser Science, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 45–49.

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Figures (3)

Fig. 1
Fig. 1

Level diagram for an atom interacting with WGM’s of frequencies ωa and ωb The first-order light shifts are indicated.

Fig. 2
Fig. 2

Two-dimensional potential for atomic motion in the (ρ, z) plane around a sphere of radius R, where ρ is the radial and z is the axial coordinate. The ρ axis ranges from ρ1 = R + 0.0006 μm to ρ2 = R + 0.5006 μm, the z axis from −2 to 2 μm (centered at zero), and the height of the potential from −1 to +1 μK. The detunings of the WGM’s used are δ1/2π = −2.2 × 1012 Hz, δ2/2π = 2.3 × 1012 Hz. Note that the mode structure of the sphere does not permit |δ1| = |δ2| exactly. Maximum Rabi frequencies in the well region of the external field are Ω 1 * / 2 π = 3.45 × 10 8 Hz , Ω 2 * / 2 π = 3.58 × 10 8 Hz .

Fig. 3
Fig. 3

Coupling coefficient g/γ at r = (R, θ/2) versus size parameter x = 2πR/λ for the cesium D2 transition at λ = 852.36 nm ( m F = F = 4 m F = F = 5 ) interacting with WGM’s in microspheres of various size.

Equations (1)

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E r ( r , θ , ϕ ) = - l ( l + 1 ) P l m ( cos θ ) j l ( k l p r ) k l p r × exp ( i m ϕ - i ω l p t ) , E θ ( r , θ , ϕ ) = - P l m ( cos θ ) θ [ k l p r j l ( k l p r ) ] k l p r × exp ( i m ϕ - i ω l p t ) , E ϕ ( r , θ , ϕ ) = - i m sin θ P l m ( cos θ ) [ k l p r j l ( k l p r ) ] k l p r × exp ( i m ϕ - i ω l p t ) ,

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