Abstract

Precision studies of stimulated-resonance Raman interactions in a sodium atomic beam were performed with emphasis on Ramsey’s separated-field excitation. Ramsey fringes were obtained for a field separation of up to 30 cm, and the data were consistent with theoretical predictions. Possible applications of this Raman interaction to clock development also were studied by stabilizing a microwave oscillator to a Raman–Ramsey fringe. The resulting oscillator stability of 1.5 × 10−11 for a 1000-sec averaging time compares favorably with commercial cesium clocks when differences in atom transit time and transition frequency are taken into consideration. Finally, potential sources of long-term frequency error, which are important for clock applications, were also partially investigated.

© 1986 Optical Society of America

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  1. J. E. Thomas, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Opt. Lett. 6, 298 (1981).
    [CrossRef] [PubMed]
  2. J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
    [CrossRef]
  3. P. R. Hemmer, S. Ezekiel, and C. C. Leiby, Opt. Lett. 8, 440 (1983).
    [CrossRef] [PubMed]
  4. R. P. Hackel and S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein; M. S. Feld, M. M. Burns, T. V. Kuhl, P. G. Pappas, and D. E. Murnick, Opt. Lett. 5, 79 (1980).
    [CrossRef]
  5. N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1963).
  6. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).
  7. E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, New York, 1970).
  8. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  9. E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1975).
  10. D. J. Glaze, H. Hellwig, D. W. Allen, and S. Jarvis, Metrologia 13, 19 (1977); A. G. Mungall and H. Daams, Metrologia 6, 60 (1970).
    [CrossRef]
  11. R. M. Garvey, H. W. Hellwig, S. Jarvis, and D. J. Wineland, IEEE Trans. Instrum. Meas. IM-27, 349 (1978).
    [CrossRef]
  12. Hewlett-Packard portable cesium clock.
  13. P. R. Hemmer, Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1984).
  14. A. Brillet, Metrologia 17, 147 (1981).
    [CrossRef]
  15. W. Phillips and H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. Prodan, W. Phillips, and H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
    [CrossRef]
  16. J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 54, 1000 (1985), and references therein.
    [CrossRef] [PubMed]
  17. J. Prodan, A. Migdall, and W. D. Phillips, Phys. Rev. Lett. 54, 992 (1985), and references therein; W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, Phys. Rev. Lett. 54, 996 (1985), and references therein.
    [CrossRef] [PubMed]

1985 (2)

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 54, 1000 (1985), and references therein.
[CrossRef] [PubMed]

J. Prodan, A. Migdall, and W. D. Phillips, Phys. Rev. Lett. 54, 992 (1985), and references therein; W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, Phys. Rev. Lett. 54, 996 (1985), and references therein.
[CrossRef] [PubMed]

1983 (1)

1982 (2)

W. Phillips and H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. Prodan, W. Phillips, and H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

1981 (2)

1979 (1)

R. P. Hackel and S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein; M. S. Feld, M. M. Burns, T. V. Kuhl, P. G. Pappas, and D. E. Murnick, Opt. Lett. 5, 79 (1980).
[CrossRef]

1978 (1)

R. M. Garvey, H. W. Hellwig, S. Jarvis, and D. J. Wineland, IEEE Trans. Instrum. Meas. IM-27, 349 (1978).
[CrossRef]

1977 (1)

D. J. Glaze, H. Hellwig, D. W. Allen, and S. Jarvis, Metrologia 13, 19 (1977); A. G. Mungall and H. Daams, Metrologia 6, 60 (1970).
[CrossRef]

Allen, D. W.

D. J. Glaze, H. Hellwig, D. W. Allen, and S. Jarvis, Metrologia 13, 19 (1977); A. G. Mungall and H. Daams, Metrologia 6, 60 (1970).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Bollinger, J. J.

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 54, 1000 (1985), and references therein.
[CrossRef] [PubMed]

Brillet, A.

A. Brillet, Metrologia 17, 147 (1981).
[CrossRef]

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Ezekiel, S.

P. R. Hemmer, S. Ezekiel, and C. C. Leiby, Opt. Lett. 8, 440 (1983).
[CrossRef] [PubMed]

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

J. E. Thomas, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Opt. Lett. 6, 298 (1981).
[CrossRef] [PubMed]

R. P. Hackel and S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein; M. S. Feld, M. M. Burns, T. V. Kuhl, P. G. Pappas, and D. E. Murnick, Opt. Lett. 5, 79 (1980).
[CrossRef]

Garvey, R. M.

R. M. Garvey, H. W. Hellwig, S. Jarvis, and D. J. Wineland, IEEE Trans. Instrum. Meas. IM-27, 349 (1978).
[CrossRef]

Glaze, D. J.

D. J. Glaze, H. Hellwig, D. W. Allen, and S. Jarvis, Metrologia 13, 19 (1977); A. G. Mungall and H. Daams, Metrologia 6, 60 (1970).
[CrossRef]

Hackel, R. P.

R. P. Hackel and S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein; M. S. Feld, M. M. Burns, T. V. Kuhl, P. G. Pappas, and D. E. Murnick, Opt. Lett. 5, 79 (1980).
[CrossRef]

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1975).

Hellwig, H.

D. J. Glaze, H. Hellwig, D. W. Allen, and S. Jarvis, Metrologia 13, 19 (1977); A. G. Mungall and H. Daams, Metrologia 6, 60 (1970).
[CrossRef]

Hellwig, H. W.

R. M. Garvey, H. W. Hellwig, S. Jarvis, and D. J. Wineland, IEEE Trans. Instrum. Meas. IM-27, 349 (1978).
[CrossRef]

Hemmer, P. R.

P. R. Hemmer, S. Ezekiel, and C. C. Leiby, Opt. Lett. 8, 440 (1983).
[CrossRef] [PubMed]

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

P. R. Hemmer, Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1984).

Itano, W. M.

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 54, 1000 (1985), and references therein.
[CrossRef] [PubMed]

Jarvis, S.

R. M. Garvey, H. W. Hellwig, S. Jarvis, and D. J. Wineland, IEEE Trans. Instrum. Meas. IM-27, 349 (1978).
[CrossRef]

D. J. Glaze, H. Hellwig, D. W. Allen, and S. Jarvis, Metrologia 13, 19 (1977); A. G. Mungall and H. Daams, Metrologia 6, 60 (1970).
[CrossRef]

Leiby, C. C.

Merzbacher, E.

E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, New York, 1970).

Metcalf, H.

W. Phillips and H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. Prodan, W. Phillips, and H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

Migdall, A.

J. Prodan, A. Migdall, and W. D. Phillips, Phys. Rev. Lett. 54, 992 (1985), and references therein; W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, Phys. Rev. Lett. 54, 996 (1985), and references therein.
[CrossRef] [PubMed]

Phillips, W.

W. Phillips and H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. Prodan, W. Phillips, and H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

Phillips, W. D.

J. Prodan, A. Migdall, and W. D. Phillips, Phys. Rev. Lett. 54, 992 (1985), and references therein; W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, Phys. Rev. Lett. 54, 996 (1985), and references therein.
[CrossRef] [PubMed]

Picard, R. H.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

J. E. Thomas, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Opt. Lett. 6, 298 (1981).
[CrossRef] [PubMed]

Prestage, J. D.

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 54, 1000 (1985), and references therein.
[CrossRef] [PubMed]

Prodan, J.

J. Prodan, A. Migdall, and W. D. Phillips, Phys. Rev. Lett. 54, 992 (1985), and references therein; W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, Phys. Rev. Lett. 54, 996 (1985), and references therein.
[CrossRef] [PubMed]

Ramsey, N. F.

N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1963).

Thomas, J. E.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

J. E. Thomas, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Opt. Lett. 6, 298 (1981).
[CrossRef] [PubMed]

Willis, C. R.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

J. E. Thomas, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Opt. Lett. 6, 298 (1981).
[CrossRef] [PubMed]

Wineland, D. J.

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 54, 1000 (1985), and references therein.
[CrossRef] [PubMed]

R. M. Garvey, H. W. Hellwig, S. Jarvis, and D. J. Wineland, IEEE Trans. Instrum. Meas. IM-27, 349 (1978).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1975).

IEEE Trans. Instrum. Meas. (1)

R. M. Garvey, H. W. Hellwig, S. Jarvis, and D. J. Wineland, IEEE Trans. Instrum. Meas. IM-27, 349 (1978).
[CrossRef]

Metrologia (2)

A. Brillet, Metrologia 17, 147 (1981).
[CrossRef]

D. J. Glaze, H. Hellwig, D. W. Allen, and S. Jarvis, Metrologia 13, 19 (1977); A. G. Mungall and H. Daams, Metrologia 6, 60 (1970).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (5)

R. P. Hackel and S. Ezekiel, Phys. Rev. Lett. 42, 1736 (1979), and references therein; M. S. Feld, M. M. Burns, T. V. Kuhl, P. G. Pappas, and D. E. Murnick, Opt. Lett. 5, 79 (1980).
[CrossRef]

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

W. Phillips and H. Metcalf, Phys. Rev. Lett. 48, 596 (1982); J. Prodan, W. Phillips, and H. Metcalf, Phys. Rev. Lett. 49, 1149 (1982).
[CrossRef]

J. J. Bollinger, J. D. Prestage, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 54, 1000 (1985), and references therein.
[CrossRef] [PubMed]

J. Prodan, A. Migdall, and W. D. Phillips, Phys. Rev. Lett. 54, 992 (1985), and references therein; W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, Phys. Rev. Lett. 54, 996 (1985), and references therein.
[CrossRef] [PubMed]

Other (7)

Hewlett-Packard portable cesium clock.

P. R. Hemmer, Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1984).

N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1963).

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, New York, 1970).

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1975).

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Figures (19)

Fig. 1
Fig. 1

Schematic of a laser-induced resonance Raman interaction.

Fig. 2
Fig. 2

(a) Effects of correlated laser jitter. (b) Schematic of Raman separated-field excitation.

Fig. 3
Fig. 3

Time dependence of final-state population for two-level and Raman interactions.

Fig. 4
Fig. 4

Fringe line shape calculated for Raman separated-field excitation when the field separation L is three times the (rectangular) laser-beam widths l.

Fig. 5
Fig. 5

Dependence of relative phases on path length for two optical excitation fields (dotted curves).

Fig. 6
Fig. 6

Effect of velocity averaging on Raman–Ramsey-fringe line shapes (a) when ϕ = 0, (b) when ϕ = π/2.

Fig. 7
Fig. 7

Schematic of experimental setup used to observe Raman–Ramsey fringes.

Fig. 8
Fig. 8

(a) Data showing Raman dips superimposed upon 10-MHz-wide D1 fluorescence line shape. (b) Expanded scan showing Raman dips and Ramsey fringes (arrow) for L = 15 cm. (c) Expanded scan of Ramsey fringes. Dotted curve is theory.

Fig. 9
Fig. 9

Data showing Raman–Ramsey fringes obtained by using laser intensities well above saturation. Dotted curve is theory including a v4 velocity weighting.

Fig. 10
Fig. 10

(a) Typical Raman–Ramsey-fringe line shapes (and photocathode current levels) used for clock applications. (b) Discriminant of fringes in (a) obtained by using frequency modulation.

Fig. 11
Fig. 11

Schematic of experimental setup used to demonstrate applications of the Raman interaction to clock development.

Fig. 12
Fig. 12

Allan variance plot showing measured fractional frequency stability σy(τ) as a function of averaging time τ. Upper dashed line, shot-noise prediction; lower dashed line, projected stability if cesium were used in place of sodium; triangles, specifications for H-P portable cesium clock.

Fig. 13
Fig. 13

Data showing the effects of misalignments of ω1 and ω2 away from copropagating for three cases: (a) when ω2 is misaligned 0.1 mrad upstream (toward the atomic-beam source), (b) when ω1 and ω2 are copropagating, (c) when ω2 is misaligned 0.1 mrad down-stream. Schematic diagrams alongside each trace illustrate the experimental conditions.

Fig. 14
Fig. 14

(a) Schematic diagram illustrating the use of an E/O to induce optical phase shifts. (b) Data showing the effects of optical phase shifts induced by various applied E/O voltages.

Fig. 15
Fig. 15

(a) Schematic showing the use of a translating corner reflector (path-length adjust) to induce path-length phase shifts. (b) Schematic showing a standing-wave scheme for controlling path-length phase shifts. (c) Data obtained using the setup described by (a) for various path-length increments. (d) Data obtained using the setup described by (b) for the same path-length increments as in (c).

Fig. 16
Fig. 16

(a) Schematic showing experimental technique for locking ω1 off resonance. (b) Data showing single-zone Raman line shapes superimposed upon fluorescence backgrounds for various ω1 detunings. (c) Theoretical Raman line shapes calculated using density-matrix equations for the same ω1 detunings as in (b).

Fig. 17
Fig. 17

Plot of quadratic m = 0, Δm = 0 magnetic Zeeman shift versus m = 1, Δm = 0 shift (circles). Straight-line plot shows square root of m = 0 shift versus m = 1 shift.

Fig. 18
Fig. 18

Schematic showing how path-length-dependent phase shifts can be induced by atomic-beam misalignments.

Fig. 19
Fig. 19

Partial energy-level diagram for sodium.

Equations (23)

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ψ ( r , t ) = a 1 ( t ) u 1 ( r ) exp [ - i ( 1 / ) t ] + a 2 ( t ) u 2 ( r ) exp [ - i ( 2 / ) t ] + a 3 ( t ) u 3 ( r ) exp [ - i ( 3 / ) t ] ,
E ( r , t ) = ½ [ E 1 ( r ) exp ( - i ω 1 t ) + c . c . ] + ½ [ E 2 ( r ) exp ( - i ω 2 t ) + c . c . ] ,
a ˙ 1 = ½ i Ω 1 * exp ( i δ 1 t ) a 2 , a ˙ 2 = ½ i Ω 1 exp ( - i δ 1 t ) a 1 + ½ i Ω 2 exp ( - i δ 2 t ) a 3 - ½ γ 2 a 2 , a ˙ 3 = ½ i Ω 2 * exp ( i δ 2 t ) a 2 .
δ 1 = ω 1 - ( 2 - 1 ) / , δ 2 = ω 2 - ( 2 - 3 ) / .
Ω 1 = ( μ 21 · E 1 ) / , Ω 2 = ( μ 23 · E 2 ) / ,
a 2 = i Ω 1 γ 2 exp ( - i δ 1 t ) a 1 + i Ω 2 γ 2 exp ( - i δ 2 t ) a 3 .
a ˙ 1 = - 1 2 Ω 1 2 γ 2 a 1 - 1 2 Ω 1 * Ω 2 γ 2 exp [ i ( δ 1 - δ 2 ) t ] a 3 , a ˙ 3 = - 1 2 Ω 2 2 γ 2 a 3 - 1 2 Ω 1 Ω 2 * γ 2 exp [ - i ( δ 1 - δ 2 ) t ] a 1 .
a ˙ 1 = - ½ γ 1 a 1 + ½ i Ω 3 * exp ( i δ 3 t ) a 3 , a ˙ 3 = - ½ γ 3 a 3 + ½ i Ω 3 exp ( - i δ 3 t ) a 1 .
γ 1 eff = Ω 1 2 / γ 2 , γ 3 eff = Ω 2 2 / γ 2 , Ω 3 eff = Ω 1 Ω 2 * / γ 2 .
a ˙ 1 = - ½ γ 1 eff a 1 - ½ ( Ω 3 eff ) * exp [ i ( δ 1 - δ 2 ) t ] a 3 , a ˙ 3 = - ½ γ 3 eff a 3 - ½ ( Ω 3 eff ) exp [ - i ( δ 1 - δ 2 ) t ] a 1 .
a 3 ( t ) 2 = 1 2 Ω 3 2 ( Ω 3 2 + δ 3 2 ) exp ( - γ t ) { 1 - cos [ ( Ω 3 2 + δ 3 2 ) 1 / 2 t ] } .
a 1 ( 0 ) = 1 , a 3 ( 0 ) = 0.
a 3 ( t ) 2 = - 1 2 Ω 3 eff 2 Ω 3 eff 2 - ( δ 1 - δ 2 ) 2 exp ( - γ t eff ) × ( 1 - cosh { [ Ω 3 eff 2 - ( δ 1 - δ 2 ) 2 ] 1 / 2 t } ) ,
a 3 ( t ) 2 = 1 4 Ω 3 eff 2 Ω 3 eff 2 - ( δ 1 - δ 2 ) 2 × [ 1 - 2 exp ( - γ eff t ) + exp ( - 2 γ eff t ) ] .
a 1 ( t ) 1 , a 3 ( t ) 0.
a ˙ 1 = 0 , a ˙ 3 = - 1 2 Ω 1 ( v t ) Ω 2 * ( v t ) γ 2 exp [ - i ( δ 1 - δ 2 ) t ] .
a 3 2 = | 1 2 - Ω 1 ( v t ) Ω 2 * ( v t ) γ 2 exp [ - i ( δ 1 - δ 2 ) t ] d t | 2 .
a 3 2 = 1 2 | Ω 1 Ω 2 * γ 2 | 2 τ 2 [ sin ( 1 / 2 ) ( δ 1 - δ 2 ) τ ( 1 / 2 ) ( δ 1 - δ 2 ) τ ] 2 × { 1 + cos [ ( δ 1 - δ 2 ) T - ϕ ] } .
exp ( i ϕ ) = ( Ω 1 B Ω 2 B * / Ω 1 A Ω 2 A * ) ,
ϕ = - i log ( Ω 1 B Ω 2 B * / Ω 1 A Ω 2 A * ) ,
Ω 1 E 1 exp ( i k 1 n 1 z ) , Ω 2 E 2 exp ( i k 2 n 2 z ) ,
ϕ = k 1 ( n 1 B z B - n 1 A z A ) - k 2 ( n 2 B z B - n 2 A z A ) ,
ϕ = n ( k 1 - k 2 ) ( Z B - Z A ) .

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