Abstract

The dipole force experienced by an atom in a nonresonant spatially inhomogeneous light field is quantized by the discrete nature of the photon. We propose to detect this quantization by studying the scattering of slow atoms that pass in the evanescent field of a microsphere whispering gallery mode. This constitutes an inverse Stern–Gerlach experiment in which the atomic deflection is correlated to the state of the scattering field.

© 1994 Optical Society of America

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References

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  1. C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, Les Houches Summer School Proceedings, Session LIII, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), p. 1; W. D. Phillips, ibid, p. 165.
  2. S. Haroche, M. Brune, J. M. Raimond, Eur. Phys. Lett. 14, 19 (1991); B. G. Englert, J. Schwinger, A. O. Barut, M. O. Scully, Eur. Phys. Lett. 14,25 (1991); D. Ivanov, T. A B. Kennedy, Phys. Rev. A 47, 566 (1993).
    [CrossRef] [PubMed]
  3. S. Haroche, J. M Raimond, in Cavity Quantum Electrodynamics, Advances in Atomic, Moleculara and Optical Physics, P. Berman, ed. (Academic, New York, 1994), Suppl. 2, p. 123.
  4. Sh. I. Averbuck, V. M. Akulin, W. P. Schleich, Phys. Rev. Lett. 72, 437 (1994).
    [CrossRef]
  5. V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
    [CrossRef]
  6. L. Collot, V. Lefèvre-Séguin, M. Brune, J. M. Raimond, S. Haroche, Eur. Phys. Lett. 23, 327 (1993).
    [CrossRef]
  7. H. Mabuchi, H. J. Kimble, Opt. Lett. 19,749 (1994).
    [CrossRef] [PubMed]
  8. E. A. Hinds, V. A. Sandoghdar, Phys. Rev. A 43, 398 (1991).
    [CrossRef] [PubMed]
  9. A. Goldberg, H. M. Shey, J. L. Schwartz, Am. J. Phys. 35, 177 (1967).
    [CrossRef]

1994 (2)

Sh. I. Averbuck, V. M. Akulin, W. P. Schleich, Phys. Rev. Lett. 72, 437 (1994).
[CrossRef]

H. Mabuchi, H. J. Kimble, Opt. Lett. 19,749 (1994).
[CrossRef] [PubMed]

1993 (1)

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

1991 (2)

S. Haroche, M. Brune, J. M. Raimond, Eur. Phys. Lett. 14, 19 (1991); B. G. Englert, J. Schwinger, A. O. Barut, M. O. Scully, Eur. Phys. Lett. 14,25 (1991); D. Ivanov, T. A B. Kennedy, Phys. Rev. A 47, 566 (1993).
[CrossRef] [PubMed]

E. A. Hinds, V. A. Sandoghdar, Phys. Rev. A 43, 398 (1991).
[CrossRef] [PubMed]

1989 (1)

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

1967 (1)

A. Goldberg, H. M. Shey, J. L. Schwartz, Am. J. Phys. 35, 177 (1967).
[CrossRef]

Akulin, V. M.

Sh. I. Averbuck, V. M. Akulin, W. P. Schleich, Phys. Rev. Lett. 72, 437 (1994).
[CrossRef]

Averbuck, Sh. I.

Sh. I. Averbuck, V. M. Akulin, W. P. Schleich, Phys. Rev. Lett. 72, 437 (1994).
[CrossRef]

Braginski, V. B.

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Brune, M.

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

S. Haroche, M. Brune, J. M. Raimond, Eur. Phys. Lett. 14, 19 (1991); B. G. Englert, J. Schwinger, A. O. Barut, M. O. Scully, Eur. Phys. Lett. 14,25 (1991); D. Ivanov, T. A B. Kennedy, Phys. Rev. A 47, 566 (1993).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, Les Houches Summer School Proceedings, Session LIII, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), p. 1; W. D. Phillips, ibid, p. 165.

Collot, L.

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

Goldberg, A.

A. Goldberg, H. M. Shey, J. L. Schwartz, Am. J. Phys. 35, 177 (1967).
[CrossRef]

Gorodetsky, M. L.

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Haroche, S.

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

S. Haroche, M. Brune, J. M. Raimond, Eur. Phys. Lett. 14, 19 (1991); B. G. Englert, J. Schwinger, A. O. Barut, M. O. Scully, Eur. Phys. Lett. 14,25 (1991); D. Ivanov, T. A B. Kennedy, Phys. Rev. A 47, 566 (1993).
[CrossRef] [PubMed]

S. Haroche, J. M Raimond, in Cavity Quantum Electrodynamics, Advances in Atomic, Moleculara and Optical Physics, P. Berman, ed. (Academic, New York, 1994), Suppl. 2, p. 123.

Hinds, E. A.

E. A. Hinds, V. A. Sandoghdar, Phys. Rev. A 43, 398 (1991).
[CrossRef] [PubMed]

Ilchenko, V. S.

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Kimble, H. J.

Lefèvre-Séguin, V.

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

Mabuchi, H.

Raimond, J. M

S. Haroche, J. M Raimond, in Cavity Quantum Electrodynamics, Advances in Atomic, Moleculara and Optical Physics, P. Berman, ed. (Academic, New York, 1994), Suppl. 2, p. 123.

Raimond, J. M.

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

S. Haroche, M. Brune, J. M. Raimond, Eur. Phys. Lett. 14, 19 (1991); B. G. Englert, J. Schwinger, A. O. Barut, M. O. Scully, Eur. Phys. Lett. 14,25 (1991); D. Ivanov, T. A B. Kennedy, Phys. Rev. A 47, 566 (1993).
[CrossRef] [PubMed]

Sandoghdar, V. A.

E. A. Hinds, V. A. Sandoghdar, Phys. Rev. A 43, 398 (1991).
[CrossRef] [PubMed]

Schleich, W. P.

Sh. I. Averbuck, V. M. Akulin, W. P. Schleich, Phys. Rev. Lett. 72, 437 (1994).
[CrossRef]

Schwartz, J. L.

A. Goldberg, H. M. Shey, J. L. Schwartz, Am. J. Phys. 35, 177 (1967).
[CrossRef]

Shey, H. M.

A. Goldberg, H. M. Shey, J. L. Schwartz, Am. J. Phys. 35, 177 (1967).
[CrossRef]

Am. J. Phys. (1)

A. Goldberg, H. M. Shey, J. L. Schwartz, Am. J. Phys. 35, 177 (1967).
[CrossRef]

Eur. Phys. Lett. (2)

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

S. Haroche, M. Brune, J. M. Raimond, Eur. Phys. Lett. 14, 19 (1991); B. G. Englert, J. Schwinger, A. O. Barut, M. O. Scully, Eur. Phys. Lett. 14,25 (1991); D. Ivanov, T. A B. Kennedy, Phys. Rev. A 47, 566 (1993).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Lett. A (1)

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Phys. Rev. A (1)

E. A. Hinds, V. A. Sandoghdar, Phys. Rev. A 43, 398 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

Sh. I. Averbuck, V. M. Akulin, W. P. Schleich, Phys. Rev. Lett. 72, 437 (1994).
[CrossRef]

Other (2)

C. Cohen-Tannoudji, in Fundamental Systems in Quantum Optics, Les Houches Summer School Proceedings, Session LIII, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), p. 1; W. D. Phillips, ibid, p. 165.

S. Haroche, J. M Raimond, in Cavity Quantum Electrodynamics, Advances in Atomic, Moleculara and Optical Physics, P. Berman, ed. (Academic, New York, 1994), Suppl. 2, p. 123.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the proposed experiment: atoms are released from the MOT and fall into the small space between diaphragm D and microsphere S. They are deflected by the evanescent field of a WGM at the sphere’s equator. The deflection angles, quantized by the discrete nature of the photon field, are revealed by the ring-shaped distribution of the atoms in a horizontal plane below S. (b) Simplified two-dimensional schematic showing a classical atomic trajectory in the xOz meridian plane of the microsphere.

Fig. 2
Fig. 2

Plots of the total effective potential experienced by the atom in the z = 0 plane for n = 0, 1, 2, 3,4 photons stored in the WGM. The strong attractive region near x = 0 is due to the van der Waals force’s pulling the atom to the sphere, and the repulsive contributions for x > 50 nm are due to the optical dipole force (blue detuning δ = 8Ωmax).

Fig. 3
Fig. 3

(a) Distribution of atomic deflection angles for n = 0, 1, 2, 3,4 photons, calculated by solving the atomic wave equation in the optical plus van der Waals potential (δ = 8Ωmax, v = 3 m/s, Δvt = 1.6 cm/s; diaphragm D cuts off atoms falling at x > 140 nm from S). The patterns corresponding to successive n values are clearly resolved. (b) The same distribution as in (a) when the WGM stores a coherent state with two photons on average in the mode (tcavw/v)

Equations (2)

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Ω ( r , θ ) = Ω max exp ( - r - R L ) exp ( - N R π θ 2 / λ 2 ) ,
i u τ = - 2 2 M 2 u x 2 + V ( x , τ ) u .

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