Abstract

Two new schemes for achieving optical Ramsey resonance by use of gratings are suggested. They do not need a coincidence of the gratings’ period with the laser wavelength and permit the same gratings to be used for arbitrary optical transition. A theoretical description for the Gaussian shapes of laser beams and for arbitrary saturation is given.

© 2004 Optical Society of America

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References

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  1. N. F. Ramsey, “A molecular beam resonance method with separated oscillating fields,” Phys. Rev. 78, 695–699 (1950).
    [CrossRef]
  2. Ye. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “Nonlinear Ramsey resonance in the optical region,” Appl. Phys. 9, 171–174 (1976).
    [CrossRef]
  3. Ch. J. Bordé, “Sur les franges de Ramsey en spectroscopie sans elargissement Doppler,” C. R. Seances Acad. Sci., Ser. B 284, 101–107 (1977).
  4. Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
    [CrossRef]
  5. Ch. J. Bordé, N. Courtier, F. du Burck, A. N. Goncharov, and M. Gorlicki, “Molecular interferometry experiment,” Phys. Lett. A 188, 187–197 (1994).
    [CrossRef]
  6. F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).
  7. Y. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “The resonance of two-photon absorption in separated optical fields,” Appl. Phys. 11, 201–202 (1976).
    [CrossRef]
  8. L. F. Constantin, R. J. Butcher, P. E. Durand, A. Amy-Klein, and Ch. Chardonnet, “2.3-kHz two-photon Ramsey fringes at 30 THz,” Phys. Rev. A 60, R753–R756 (1999).
    [CrossRef]
  9. C. Grain, A. Shelkovnikov, A. Amy-Klein, R. J. Butcher, and Chr. Chardonnet, “High-sensitivity detection of two-photon Ramsey fringes at 30 THz by frequency-comb assisted stimulated emission,” IEEE J. Quantum Electron. 38, 1406–1411 (2002).
    [CrossRef]
  10. G. Kramer, “Linear optical ‘Ramsey’ resonance by means of a spatially modulated molecular beam,” J. Opt. Soc. Am. 68, 1634–1635 (1978).
  11. G. Kramer, C. O. Weiss, and B. Lipphardt, “Coherent frequency measurements of the hfs-resolved methane line,” in Frequency Standards and Metrology, A. De Marchi, ed. (Springer-Verlag, Berlin, 1989), pp. 181–186.
  12. G. Kramer, “The photon recoil effect in the linear optical Ramsey resonance,” in Frequency Standards and Metrology, P. Gill, ed. (World Scientific, Singapore, 2002), pp. 507–509.
  13. D. D. Krylova, “The line shape of linear optical Ramsey resonance,” Opt. Commun. 212, 317–334 (2002).
    [CrossRef]
  14. B. Ya. Dubetsky, “Nonlinear resonances in a system of separated optical fields taking into account the recoil effect and the quadratic Doppler effect,” Sov. J. Quantum Electron. 13, 772–781 (1983).
    [CrossRef]
  15. G. Kramer and D. N. Ghost Roy, “Linear optical Ramsey resonance,” presented at the Conference on Precision Electromagnetic Measurements, Braunschweig, Germany, June 23–27, 1980.

2002

C. Grain, A. Shelkovnikov, A. Amy-Klein, R. J. Butcher, and Chr. Chardonnet, “High-sensitivity detection of two-photon Ramsey fringes at 30 THz by frequency-comb assisted stimulated emission,” IEEE J. Quantum Electron. 38, 1406–1411 (2002).
[CrossRef]

D. D. Krylova, “The line shape of linear optical Ramsey resonance,” Opt. Commun. 212, 317–334 (2002).
[CrossRef]

1999

L. F. Constantin, R. J. Butcher, P. E. Durand, A. Amy-Klein, and Ch. Chardonnet, “2.3-kHz two-photon Ramsey fringes at 30 THz,” Phys. Rev. A 60, R753–R756 (1999).
[CrossRef]

1996

F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).

1994

Ch. J. Bordé, N. Courtier, F. du Burck, A. N. Goncharov, and M. Gorlicki, “Molecular interferometry experiment,” Phys. Lett. A 188, 187–197 (1994).
[CrossRef]

1984

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

1983

B. Ya. Dubetsky, “Nonlinear resonances in a system of separated optical fields taking into account the recoil effect and the quadratic Doppler effect,” Sov. J. Quantum Electron. 13, 772–781 (1983).
[CrossRef]

1978

G. Kramer, “Linear optical ‘Ramsey’ resonance by means of a spatially modulated molecular beam,” J. Opt. Soc. Am. 68, 1634–1635 (1978).

1977

Ch. J. Bordé, “Sur les franges de Ramsey en spectroscopie sans elargissement Doppler,” C. R. Seances Acad. Sci., Ser. B 284, 101–107 (1977).

1976

Ye. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “Nonlinear Ramsey resonance in the optical region,” Appl. Phys. 9, 171–174 (1976).
[CrossRef]

Y. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “The resonance of two-photon absorption in separated optical fields,” Appl. Phys. 11, 201–202 (1976).
[CrossRef]

1950

N. F. Ramsey, “A molecular beam resonance method with separated oscillating fields,” Phys. Rev. 78, 695–699 (1950).
[CrossRef]

Amy-Klein, A.

C. Grain, A. Shelkovnikov, A. Amy-Klein, R. J. Butcher, and Chr. Chardonnet, “High-sensitivity detection of two-photon Ramsey fringes at 30 THz by frequency-comb assisted stimulated emission,” IEEE J. Quantum Electron. 38, 1406–1411 (2002).
[CrossRef]

L. F. Constantin, R. J. Butcher, P. E. Durand, A. Amy-Klein, and Ch. Chardonnet, “2.3-kHz two-photon Ramsey fringes at 30 THz,” Phys. Rev. A 60, R753–R756 (1999).
[CrossRef]

Avrillier, S.

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

Baklanov, Y. V.

Y. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “The resonance of two-photon absorption in separated optical fields,” Appl. Phys. 11, 201–202 (1976).
[CrossRef]

Baklanov, Ye. V.

Ye. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “Nonlinear Ramsey resonance in the optical region,” Appl. Phys. 9, 171–174 (1976).
[CrossRef]

Bassi, D.

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

Bordé, Ch.

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

Bordé, Ch. J.

Ch. J. Bordé, N. Courtier, F. du Burck, A. N. Goncharov, and M. Gorlicki, “Molecular interferometry experiment,” Phys. Lett. A 188, 187–197 (1994).
[CrossRef]

Ch. J. Bordé, “Sur les franges de Ramsey en spectroscopie sans elargissement Doppler,” C. R. Seances Acad. Sci., Ser. B 284, 101–107 (1977).

Bréant, Ch.

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

Butcher, R. J.

C. Grain, A. Shelkovnikov, A. Amy-Klein, R. J. Butcher, and Chr. Chardonnet, “High-sensitivity detection of two-photon Ramsey fringes at 30 THz by frequency-comb assisted stimulated emission,” IEEE J. Quantum Electron. 38, 1406–1411 (2002).
[CrossRef]

L. F. Constantin, R. J. Butcher, P. E. Durand, A. Amy-Klein, and Ch. Chardonnet, “2.3-kHz two-photon Ramsey fringes at 30 THz,” Phys. Rev. A 60, R753–R756 (1999).
[CrossRef]

Chardonnet, Ch.

L. F. Constantin, R. J. Butcher, P. E. Durand, A. Amy-Klein, and Ch. Chardonnet, “2.3-kHz two-photon Ramsey fringes at 30 THz,” Phys. Rev. A 60, R753–R756 (1999).
[CrossRef]

Chardonnet, Chr.

C. Grain, A. Shelkovnikov, A. Amy-Klein, R. J. Butcher, and Chr. Chardonnet, “High-sensitivity detection of two-photon Ramsey fringes at 30 THz by frequency-comb assisted stimulated emission,” IEEE J. Quantum Electron. 38, 1406–1411 (2002).
[CrossRef]

Chebotaev, V. P.

Y. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “The resonance of two-photon absorption in separated optical fields,” Appl. Phys. 11, 201–202 (1976).
[CrossRef]

Ye. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “Nonlinear Ramsey resonance in the optical region,” Appl. Phys. 9, 171–174 (1976).
[CrossRef]

Constantin, L. F.

L. F. Constantin, R. J. Butcher, P. E. Durand, A. Amy-Klein, and Ch. Chardonnet, “2.3-kHz two-photon Ramsey fringes at 30 THz,” Phys. Rev. A 60, R753–R756 (1999).
[CrossRef]

Courtier, N.

Ch. J. Bordé, N. Courtier, F. du Burck, A. N. Goncharov, and M. Gorlicki, “Molecular interferometry experiment,” Phys. Lett. A 188, 187–197 (1994).
[CrossRef]

du Burck, F.

Ch. J. Bordé, N. Courtier, F. du Burck, A. N. Goncharov, and M. Gorlicki, “Molecular interferometry experiment,” Phys. Lett. A 188, 187–197 (1994).
[CrossRef]

Dubetsky, B. Ya.

B. Ya. Dubetsky, “Nonlinear resonances in a system of separated optical fields taking into account the recoil effect and the quadratic Doppler effect,” Sov. J. Quantum Electron. 13, 772–781 (1983).
[CrossRef]

Ye. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “Nonlinear Ramsey resonance in the optical region,” Appl. Phys. 9, 171–174 (1976).
[CrossRef]

Y. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “The resonance of two-photon absorption in separated optical fields,” Appl. Phys. 11, 201–202 (1976).
[CrossRef]

Durand, P. E.

L. F. Constantin, R. J. Butcher, P. E. Durand, A. Amy-Klein, and Ch. Chardonnet, “2.3-kHz two-photon Ramsey fringes at 30 THz,” Phys. Rev. A 60, R753–R756 (1999).
[CrossRef]

Goncharov, A. N.

Ch. J. Bordé, N. Courtier, F. du Burck, A. N. Goncharov, and M. Gorlicki, “Molecular interferometry experiment,” Phys. Lett. A 188, 187–197 (1994).
[CrossRef]

Gorlicki, M.

Ch. J. Bordé, N. Courtier, F. du Burck, A. N. Goncharov, and M. Gorlicki, “Molecular interferometry experiment,” Phys. Lett. A 188, 187–197 (1994).
[CrossRef]

Grain, C.

C. Grain, A. Shelkovnikov, A. Amy-Klein, R. J. Butcher, and Chr. Chardonnet, “High-sensitivity detection of two-photon Ramsey fringes at 30 THz by frequency-comb assisted stimulated emission,” IEEE J. Quantum Electron. 38, 1406–1411 (2002).
[CrossRef]

Helmcke, J.

F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).

Kramer, G.

G. Kramer, “Linear optical ‘Ramsey’ resonance by means of a spatially modulated molecular beam,” J. Opt. Soc. Am. 68, 1634–1635 (1978).

Krylova, D. D.

D. D. Krylova, “The line shape of linear optical Ramsey resonance,” Opt. Commun. 212, 317–334 (2002).
[CrossRef]

Lipphardt, B.

F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).

Ramsey, N. F.

N. F. Ramsey, “A molecular beam resonance method with separated oscillating fields,” Phys. Rev. 78, 695–699 (1950).
[CrossRef]

Riehle, F.

F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).

Salomon, Ch.

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

Schnatz, H.

F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).

Scoles, G.

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

Shelkovnikov, A.

C. Grain, A. Shelkovnikov, A. Amy-Klein, R. J. Butcher, and Chr. Chardonnet, “High-sensitivity detection of two-photon Ramsey fringes at 30 THz by frequency-comb assisted stimulated emission,” IEEE J. Quantum Electron. 38, 1406–1411 (2002).
[CrossRef]

VanLerberghe, A.

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

Zeiske, K.

F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).

Zinner, G.

F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).

Appl. Phys.

Ye. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “Nonlinear Ramsey resonance in the optical region,” Appl. Phys. 9, 171–174 (1976).
[CrossRef]

Y. V. Baklanov, B. Ya. Dubetsky, and V. P. Chebotaev, “The resonance of two-photon absorption in separated optical fields,” Appl. Phys. 11, 201–202 (1976).
[CrossRef]

C. R. Seances Acad. Sci., Ser. B

Ch. J. Bordé, “Sur les franges de Ramsey en spectroscopie sans elargissement Doppler,” C. R. Seances Acad. Sci., Ser. B 284, 101–107 (1977).

IEEE J. Quantum Electron.

C. Grain, A. Shelkovnikov, A. Amy-Klein, R. J. Butcher, and Chr. Chardonnet, “High-sensitivity detection of two-photon Ramsey fringes at 30 THz by frequency-comb assisted stimulated emission,” IEEE J. Quantum Electron. 38, 1406–1411 (2002).
[CrossRef]

J. Opt. Soc. Am.

G. Kramer, “Linear optical ‘Ramsey’ resonance by means of a spatially modulated molecular beam,” J. Opt. Soc. Am. 68, 1634–1635 (1978).

Laser Phys.

F. Riehle, H. Schnatz, G. Zinner, K. Zeiske, B. Lipphardt, and J. Helmcke, “Calcium optical frequency standard based on atom interferometry,” Laser Phys. 6, 237–243 (1996).

Opt. Commun.

D. D. Krylova, “The line shape of linear optical Ramsey resonance,” Opt. Commun. 212, 317–334 (2002).
[CrossRef]

Phys. Lett. A

Ch. J. Bordé, N. Courtier, F. du Burck, A. N. Goncharov, and M. Gorlicki, “Molecular interferometry experiment,” Phys. Lett. A 188, 187–197 (1994).
[CrossRef]

Phys. Rev.

N. F. Ramsey, “A molecular beam resonance method with separated oscillating fields,” Phys. Rev. 78, 695–699 (1950).
[CrossRef]

Phys. Rev. A

Ch. Bordé, Ch. Salomon, S. Avrillier, A. VanLerberghe, Ch. Bréant, D. Bassi, and G. Scoles, “Optical Ramsey fringes with traveling waves,” Phys. Rev. A 30, 1836–1848 (1984).
[CrossRef]

L. F. Constantin, R. J. Butcher, P. E. Durand, A. Amy-Klein, and Ch. Chardonnet, “2.3-kHz two-photon Ramsey fringes at 30 THz,” Phys. Rev. A 60, R753–R756 (1999).
[CrossRef]

Sov. J. Quantum Electron.

B. Ya. Dubetsky, “Nonlinear resonances in a system of separated optical fields taking into account the recoil effect and the quadratic Doppler effect,” Sov. J. Quantum Electron. 13, 772–781 (1983).
[CrossRef]

Other

G. Kramer and D. N. Ghost Roy, “Linear optical Ramsey resonance,” presented at the Conference on Precision Electromagnetic Measurements, Braunschweig, Germany, June 23–27, 1980.

G. Kramer, C. O. Weiss, and B. Lipphardt, “Coherent frequency measurements of the hfs-resolved methane line,” in Frequency Standards and Metrology, A. De Marchi, ed. (Springer-Verlag, Berlin, 1989), pp. 181–186.

G. Kramer, “The photon recoil effect in the linear optical Ramsey resonance,” in Frequency Standards and Metrology, P. Gill, ed. (World Scientific, Singapore, 2002), pp. 507–509.

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Figures (4)

Fig. 1
Fig. 1

Shadow function of a grating.

Fig. 2
Fig. 2

Schematic of ORR that uses two gratings. The molecular beam is passing through two laser fields (with wavelength λ) and gratings with period λ1 that are separated in space. The final ORR signal is dependent not on the position of each grating but only on the distance between them, D. Therefore both gratings can be situated in many places (i.e., l0 can be negative and D can be larger than L).

Fig. 3
Fig. 3

Functions R(α, 1) and Q(α) from relation (4) for LORR with two gratings for the condition k1D=2k0L.

Fig. 4
Fig. 4

Functions R(α, 1) and Q(α) from relation (4) for ORR with a grating on the surface of a nozzle for the condition l=L/2.

Equations (22)

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

S(Ω)=N-dθxdθy0v3dvW0(v)F{k1[x0+θx(l+l0)]-β1}F{k1[x0+θx(l+l0+D)]-β2}dx0dy0×-cos α1 cos α2+sin α1 sin α2 cos(ΩL/v)+5πΩavsin(ΩL/v)sin α2×sin α1-2α1(1-cos α1),
α1(θx, θy, v; x0, y0)=αvcos[k(x0+θxl)]×exp-(kaθx)24-(y0+lθy)2a2,
α2(θx, θy, v; x0, y0)=αvcos{k[x0+θx(l+L)]+φ}×exp-(kaθx)24-[y0+(l+L)θy]2a2,
S(Ω)0v3dvW0(v)R(α/v, 1)cos(ΩL/v)-5πΩavsin(ΩL/v)Q(α/v),
R(α/v, ξ)=k  dθxdθydx0dy0F{k1[x0+θx(l+l0)]-β1}F{k1[x0+θx(l+l0+D)]-β2}sin α1 sin(ξα2),
Q(x)=-R(x, 1)+201dξR(x, ξ).
k1D=(2n+1)kL,
R(x, ξ)=4π2kX0-dθxdθydy0J2n+1(A)J2n+1(B),
A=x exp-(kaθx)24exp-y02a2,
B=ξx exp-(kaθx)24exp-(y0-Lθy)2a2,
β1-β2=(2n+1)φ+sπ,s=0,1,2
D/L=(2n+1)λ/λ1.
S(Ω)=N-dθxdθy0v3dvW0(v)F(k1x0-β)×dx0dy0sin α1 sin α2 cos(ΩL/v)+5πΩ a/v sin(ΩL/v)sin α2×sin α1-2α1(1-cos α1)
2(p-n)l=(2n+1)L,p>n,
sk1=2k(p-n),s=1,2,3.
R(α, ξ)=1p-n1πk1X0-dθxdθydy0J2p+1(A)J2n+1(B),
A=αvexp-(kaθx)24exp-y02a2,
B=ξαvexp-(kaθx)24exp-(y0-Lθy)2a2.
2(p-n)λ1λβ-(2n+1)φ=qπ,q=0,1,2.
2(p-n)β=sπ,φ=qπ,s,q=0,1,2.
R(α, ξ)=1/2 sin[(p-n)kd]×-dθxdθydy0J2p+1(A)J2n+1(B),
d=λ2s+1/2p-n,s=0,1,2.

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