Abstract

We demonstrate a novel variable beam splitter using a tripod-linkage of atomic states, the physics of which is based on the laser control of the non-adiabatic coupling between two degenerate dark states. This coupling and the splitting ratio is determined by the time delay of the interaction induced by two of the laser beams.

© 1999 Optical Society of America

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References

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  1. P. R. Berman, Atom Interferornetry, (Academic Press, 1997).
  2. R. Deutschmann, W. Ertmer, and H. Wallis, “Reflection and diffraction of atomic de broglie waves by an evanescent laser wave,” Phys. Rev. A 47, 2169–2185 (1993).
    [CrossRef] [PubMed]
  3. S. Glasgow, P. Meystre, M. Wilkens, and E.M. Wright, “Theory of an atomic beam splitter based on velocity-tuned resonances,” Phys. Rev. A 43, 2455–2463 (1991).
    [CrossRef] [PubMed]
  4. T. Pfau, C. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-optical beam splitter for atoms,“ Phys. Rev. Lett. 71, 3427–3430 (1993).
    [CrossRef] [PubMed]
  5. M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
    [CrossRef] [PubMed]
  6. P. Marte, P. Zoller, and J. L. Hall, “Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems,” Phys. Rev. A 44, 4118–4121 (1991).
    [CrossRef] [PubMed]
  7. M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563–2566 (1994).
    [CrossRef] [PubMed]
  8. U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990).
    [CrossRef]
  9. K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1026 (1998).
    [CrossRef]
  10. R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. 155, 144–154 (1998).
    [CrossRef]
  11. R. Unanyan, B. W. Shore, and K. Bergmann, Phys. Rev. A submitted.
  12. H. Theuer and K. Bergmann, “Atomic beam deflection by coherent momentum transfer and the dependence on small magnetic fields,” Eur. Phys. J. D 2, 279–289 (1998).
    [CrossRef]

1998 (3)

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1026 (1998).
[CrossRef]

R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. 155, 144–154 (1998).
[CrossRef]

H. Theuer and K. Bergmann, “Atomic beam deflection by coherent momentum transfer and the dependence on small magnetic fields,” Eur. Phys. J. D 2, 279–289 (1998).
[CrossRef]

1994 (1)

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563–2566 (1994).
[CrossRef] [PubMed]

1993 (2)

R. Deutschmann, W. Ertmer, and H. Wallis, “Reflection and diffraction of atomic de broglie waves by an evanescent laser wave,” Phys. Rev. A 47, 2169–2185 (1993).
[CrossRef] [PubMed]

T. Pfau, C. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-optical beam splitter for atoms,“ Phys. Rev. Lett. 71, 3427–3430 (1993).
[CrossRef] [PubMed]

1991 (3)

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

P. Marte, P. Zoller, and J. L. Hall, “Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems,” Phys. Rev. A 44, 4118–4121 (1991).
[CrossRef] [PubMed]

S. Glasgow, P. Meystre, M. Wilkens, and E.M. Wright, “Theory of an atomic beam splitter based on velocity-tuned resonances,” Phys. Rev. A 43, 2455–2463 (1991).
[CrossRef] [PubMed]

1990 (1)

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990).
[CrossRef]

Adams, C. S.

T. Pfau, C. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-optical beam splitter for atoms,“ Phys. Rev. Lett. 71, 3427–3430 (1993).
[CrossRef] [PubMed]

Bergmann, K.

H. Theuer and K. Bergmann, “Atomic beam deflection by coherent momentum transfer and the dependence on small magnetic fields,” Eur. Phys. J. D 2, 279–289 (1998).
[CrossRef]

R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. 155, 144–154 (1998).
[CrossRef]

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1026 (1998).
[CrossRef]

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990).
[CrossRef]

R. Unanyan, B. W. Shore, and K. Bergmann, Phys. Rev. A submitted.

Berman, P. R.

P. R. Berman, Atom Interferornetry, (Academic Press, 1997).

Chu, S.

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563–2566 (1994).
[CrossRef] [PubMed]

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

Deutschmann, R.

R. Deutschmann, W. Ertmer, and H. Wallis, “Reflection and diffraction of atomic de broglie waves by an evanescent laser wave,” Phys. Rev. A 47, 2169–2185 (1993).
[CrossRef] [PubMed]

Ertmer, W.

R. Deutschmann, W. Ertmer, and H. Wallis, “Reflection and diffraction of atomic de broglie waves by an evanescent laser wave,” Phys. Rev. A 47, 2169–2185 (1993).
[CrossRef] [PubMed]

Fleischhauer, M.

R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. 155, 144–154 (1998).
[CrossRef]

Gaubatz, U.

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990).
[CrossRef]

Glasgow, S.

S. Glasgow, P. Meystre, M. Wilkens, and E.M. Wright, “Theory of an atomic beam splitter based on velocity-tuned resonances,” Phys. Rev. A 43, 2455–2463 (1991).
[CrossRef] [PubMed]

Hall, J. L.

P. Marte, P. Zoller, and J. L. Hall, “Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems,” Phys. Rev. A 44, 4118–4121 (1991).
[CrossRef] [PubMed]

Kasapi, S.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

Kasevich, M.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

Kurtsiefer, C.

T. Pfau, C. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-optical beam splitter for atoms,“ Phys. Rev. Lett. 71, 3427–3430 (1993).
[CrossRef] [PubMed]

Marte, P.

P. Marte, P. Zoller, and J. L. Hall, “Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems,” Phys. Rev. A 44, 4118–4121 (1991).
[CrossRef] [PubMed]

Meystre, P.

S. Glasgow, P. Meystre, M. Wilkens, and E.M. Wright, “Theory of an atomic beam splitter based on velocity-tuned resonances,” Phys. Rev. A 43, 2455–2463 (1991).
[CrossRef] [PubMed]

Mlynek, J.

T. Pfau, C. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-optical beam splitter for atoms,“ Phys. Rev. Lett. 71, 3427–3430 (1993).
[CrossRef] [PubMed]

Moler, K.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

Pfau, T.

T. Pfau, C. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-optical beam splitter for atoms,“ Phys. Rev. Lett. 71, 3427–3430 (1993).
[CrossRef] [PubMed]

Riis, E.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

Rudecki, P.

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990).
[CrossRef]

Schiemann, S.

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990).
[CrossRef]

Shore, B. W.

R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. 155, 144–154 (1998).
[CrossRef]

R. Unanyan, B. W. Shore, and K. Bergmann, Phys. Rev. A submitted.

Shore, B.W.

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1026 (1998).
[CrossRef]

Sigel, M.

T. Pfau, C. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-optical beam splitter for atoms,“ Phys. Rev. Lett. 71, 3427–3430 (1993).
[CrossRef] [PubMed]

Theuer, H.

H. Theuer and K. Bergmann, “Atomic beam deflection by coherent momentum transfer and the dependence on small magnetic fields,” Eur. Phys. J. D 2, 279–289 (1998).
[CrossRef]

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1026 (1998).
[CrossRef]

Unanyan, R.

R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. 155, 144–154 (1998).
[CrossRef]

R. Unanyan, B. W. Shore, and K. Bergmann, Phys. Rev. A submitted.

Wallis, H.

R. Deutschmann, W. Ertmer, and H. Wallis, “Reflection and diffraction of atomic de broglie waves by an evanescent laser wave,” Phys. Rev. A 47, 2169–2185 (1993).
[CrossRef] [PubMed]

Weiss, D. S.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

Weitz, M.

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563–2566 (1994).
[CrossRef] [PubMed]

Wilkens, M.

S. Glasgow, P. Meystre, M. Wilkens, and E.M. Wright, “Theory of an atomic beam splitter based on velocity-tuned resonances,” Phys. Rev. A 43, 2455–2463 (1991).
[CrossRef] [PubMed]

Wright, E.M.

S. Glasgow, P. Meystre, M. Wilkens, and E.M. Wright, “Theory of an atomic beam splitter based on velocity-tuned resonances,” Phys. Rev. A 43, 2455–2463 (1991).
[CrossRef] [PubMed]

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

Young, B. C.

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563–2566 (1994).
[CrossRef] [PubMed]

Zoller, P.

P. Marte, P. Zoller, and J. L. Hall, “Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems,” Phys. Rev. A 44, 4118–4121 (1991).
[CrossRef] [PubMed]

Eur. Phys. J. D (1)

H. Theuer and K. Bergmann, “Atomic beam deflection by coherent momentum transfer and the dependence on small magnetic fields,” Eur. Phys. J. D 2, 279–289 (1998).
[CrossRef]

J. Chem. Phys. (1)

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields,” J. Chem. Phys. 92, 5363–5376 (1990).
[CrossRef]

Opt. Commun. (1)

R. Unanyan, M. Fleischhauer, B. W. Shore, and K. Bergmann, “Robust creation and phase-sensitive probing of superposition states via stimulated raman adiabatic passage (STIRAP) with degenerate dark states,” Opt. Commun. 155, 144–154 (1998).
[CrossRef]

Phys. Rev. A (3)

P. Marte, P. Zoller, and J. L. Hall, “Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems,” Phys. Rev. A 44, 4118–4121 (1991).
[CrossRef] [PubMed]

R. Deutschmann, W. Ertmer, and H. Wallis, “Reflection and diffraction of atomic de broglie waves by an evanescent laser wave,” Phys. Rev. A 47, 2169–2185 (1993).
[CrossRef] [PubMed]

S. Glasgow, P. Meystre, M. Wilkens, and E.M. Wright, “Theory of an atomic beam splitter based on velocity-tuned resonances,” Phys. Rev. A 43, 2455–2463 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

T. Pfau, C. Kurtsiefer, C. S. Adams, M. Sigel, and J. Mlynek, “Magneto-optical beam splitter for atoms,“ Phys. Rev. Lett. 71, 3427–3430 (1993).
[CrossRef] [PubMed]

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu, and E.M. Wright, “Atomic velocity selection using stimulated raman transitions,” Phys. Rev. Lett. 66, 2297–2300 (1991).
[CrossRef] [PubMed]

M. Weitz, B. C. Young, and S. Chu, “Atomic interferometer based on adiabatic population transfer,” Phys. Rev. Lett. 73, 2563–2566 (1994).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

K. Bergmann, H. Theuer, and B.W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1026 (1998).
[CrossRef]

Other (2)

R. Unanyan, B. W. Shore, and K. Bergmann, Phys. Rev. A submitted.

P. R. Berman, Atom Interferornetry, (Academic Press, 1997).

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Figures (3)

Figure 1.
Figure 1.

(a) The relevant level scheme for the realization of the beam splitter using the tripod-linkage system. Initially only the state 3 P 0 is populated. (b) The geometry of the setup.

Figure 2.
Figure 2.

Variation of the profiles of the metastable neon atomic beam with the relative displacement of the σ-polarized Stokes-laser beams. From top to bottom the displacement is +250 μm, +50 μm, 0 μm, -150 μm and -250 μm. The diameter of the laser beams is 0.6 mm. The solid lines result from a fit to the data.

Figure 3.
Figure 3.

(a) Intensity of the two components of the coherently split atomic beam as a function of the displacement D of the σ --Stokes laser measured in units of the laser beam width 2ω 0 ≈ 0.6mm. The open circles give the flux of atoms in state ∣3-⟩ (M = +1) while the dots refer to state ∣3+⟩ (M = -1). The sum of both count rates is also shown (triangles). The relevant laser powers are PP = 46 mW, PS = 34 mW corresponding to Ω P ≈ 100 MHz and Ω± ≈ 30 MHz. (b) Numerical simulation for the intensities of both beam splitter channels as a function of D. The gray line gives the total population in the 3 P 2 state.

Equations (14)

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E P = e z Re E π ( x ) e i ( k π y ω π t )
E S 1 = Re E + ( x ) e i ( k σ z ω σ t ) e + E S 2 = Re E ( x ) e i ( + k σ z ω σ t ) e
E π ( x ) = E 0 exp [ ( x x 0 ) 2 ω 0 2 ] E ± ( x ) = E 1 exp [ ( x ± x 1 ) 2 ω 1 2 ]
1 = 3 P 0 , M = 0 , p x , p y ħ k π , p z
2 = 3 P 1 , M = 0 , p x , p y , p z
3 = 3 P 2 , M = 1 , p x , p y , p z ħ k σ
3 + = 3 P 2 , M = 1 , p x , p y , p z + ħ k σ .
Φ 1 = cos θ 1 sin θ ( sin φ 3 + cos φ 3 + )
Φ 2 = cos φ 3 sin φ 3 +
tan φ = Ω + Ω and tan θ = Ω π Ω + 2 + Ω 2 .
Ψ = B 1 Φ 1 + B 2 Φ 2 .
B 1 = cos γ B 2 = sin γ
γ = + φ ˙ ( τ ) sin θ ( τ ) .
Ψ 1 = sin γ 3 + cos γ 3 + or Ψ 2 = cos γ 3 sin γ 3 +

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