Abstract

We report observation of query pulse length dependent Ramsey interference (QPLD-RI), using pulsed Raman excitation in rubidium vapor. This is observed when a long, attenuated query pulse is used during pulsed Raman excitation. We explain the physical mechanism behind the QPLD-RI using a Bloch vector model. We also use numerical solutions to time-dependent density matrix equations to simulate this interference effect, showing qualitative agreement with experimental results. Presence of such interference could create a potential source of error in a vapor cell Raman clock constructed using frequency-domain Ramsey interference (FDRI).

© 2011 OSA

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  1. N. F. Ramsey, “A molecular beam resonance method with separated oscillating field,” Phys. Rev. 78(6), 695–699 (1950).
    [CrossRef]
  2. M. M. Salour and C. Cohen-Tannoudji, “Observation of Ramsey’s interference fringes in the profile of Doppler-free two-photon resonances,” Phys. Rev. Lett. 38(14), 757–760 (1977).
    [CrossRef]
  3. G. Theobald, V. Giordano, N. Dimatcq, and P. Cerez, “Observation of narrow Ramsey-type resonances in a caesium beam due to Zeeman coherences,” J. Phys. B 24(13), 2957–2966 (1991).
    [CrossRef]
  4. B. Schuh, S. I. Kanorsky, A. Weis, and T. W. Hänsch, “Observation of Ramsey fringes in nonlinear Faraday rotation,” Opt. Commun. 100(5-6), 451–455 (1993).
    [CrossRef]
  5. A. S. Zibrov and A. S. Matsko, “Optical Ramsey fringes induced by Zeeman coherence,” Phys. Rev. A 65(1), 013814 (2001).
    [CrossRef]
  6. A. S. Zibrov, I. Novikova, and A. B. Matsko, “Observation of Ramsey fringes in an atomic cell with buffer gas,” Opt. Lett. 26(17), 1311–1313 (2001).
    [CrossRef] [PubMed]
  7. L. Essen and J. V. L. Parry, “An atomic standard of frequency and time interval: a caesium resonator,” Nature 176(4476), 280–282 (1955).
    [CrossRef]
  8. A. G. Mungall, H. Daams, and J. S. Boulanger, “Design, construction, and performance of the NRC CsVI primary cesium clocks,” Metrolog. 17(4), 123–145 (1981).
    [CrossRef]
  9. C. Audoin, “Caesium beam frequency standards: classical and optically pumped,” Metrolog. 29(2), 113–134 (1992).
    [CrossRef]
  10. J. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48(13), 867–870 (1982).
    [CrossRef]
  11. P. R. Hemmer, S. Ezekiel, and C. C. Leiby., “Stabilization of a microwave oscillator using a resonance Raman transition in a sodium beam,” Opt. Lett. 8(8), 440–442 (1983).
    [CrossRef] [PubMed]
  12. P. R. Hemmer, M. S. Shahriar, H. Lamela-Rivera, S. P. Smith, B. E. Bernacki, and S. Ezekiel, “Semiconductor laser excitation of Ramsey fringes using a Raman transition in a cesium atomic beam,” J. Opt. Soc. Am. B 10(8), 1326–1329 (1993).
    [CrossRef]
  13. T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system,” Phys. Rev. Lett. 94(19), 193002 (2005).
    [CrossRef] [PubMed]
  14. G. S. Pati, K. Salit, R. Tripathi, and M. S. Shahriar, “Demonstration of Raman–Ramsey fringes using time delayed optical pulses in rubidium vapor,” Opt. Commun. 281(18), 4676–4680 (2008).
    [CrossRef]
  15. G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Prospect for development of a pulsed CPT Raman–Ramsey clock using atomic vapor,” Proc. SPIE 7612, 76120D, 76120D-25 (2010).
    [CrossRef]
  16. B. Yan, Y. Ma, and Y. Wang, “Formation of Ramsey fringes based on pulsed coherent light storage,” Phys. Rev. A 79(6), 063820 (2009).
    [CrossRef]
  17. M. Merimaa, T. Lindvall, I. Tittonen, and E. Ikonen, “All-optical atomic clock based on coherent population trapping in Rb,” J. Opt. Soc. Am. B 20(2), 273–279 (2003).
    [CrossRef]
  18. J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81(4), 421–442 (2005).
    [CrossRef]
  19. G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Optical Ramsey interference and its performance in D1 line excitation in rubidium vapor for implementation of a vapor cell clock,” Proc. SPIE 7949, 794910D (2010).
  20. V. Shah, S. Kanppe, P. D. Schwindt, and J. Kitching, “Subpicotesla atomic magnetometry with a microfabricated vapour cell,” Nat. Photonics 1(11), 649–652 (2007).
    [CrossRef]
  21. E. Arimondo, “Coherent population trapping in laser spectroscopy,” in Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 35, pp. 257–354.
  22. M. S. Shahriar, P. R. Hemmer, D. P. Katz, A. Lee, and M. G. Prentiss, “Dark-state-based three-element vector model for the stimulated Raman interaction,” Phys. Rev. A 55(3), 2272–2282 (1997).
    [CrossRef]
  23. P. R. Hemmer, M. S. Shahriar, V. D. Natoli, and S. Ezekiel, “AC Stark shifts in a two-zone Raman interaction,” J. Opt. Soc. Am. B 6(8), 1519–1528 (1989).
    [CrossRef]
  24. P. R. Hemmer, G. P. Ontai, and S. Ezekiel, “Precision studies of stimulated-resonance Raman interactions in an atomic beam,” J. Opt. Soc. Am. B 3(2), 219–230 (1986).
    [CrossRef]
  25. S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced line width reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56(2), R1063–R1066 (1997).
    [CrossRef]
  26. S. J. Park, H. Cho, T. Y. Kwon, and H. S. Lee, “Transient coherence oscillation induced by a detuned Raman field in a rubidium Λ system,” Phys. Rev. A 69(2), 023806 (2004).
    [CrossRef]

2010 (2)

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Prospect for development of a pulsed CPT Raman–Ramsey clock using atomic vapor,” Proc. SPIE 7612, 76120D, 76120D-25 (2010).
[CrossRef]

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Optical Ramsey interference and its performance in D1 line excitation in rubidium vapor for implementation of a vapor cell clock,” Proc. SPIE 7949, 794910D (2010).

2009 (1)

B. Yan, Y. Ma, and Y. Wang, “Formation of Ramsey fringes based on pulsed coherent light storage,” Phys. Rev. A 79(6), 063820 (2009).
[CrossRef]

2008 (1)

G. S. Pati, K. Salit, R. Tripathi, and M. S. Shahriar, “Demonstration of Raman–Ramsey fringes using time delayed optical pulses in rubidium vapor,” Opt. Commun. 281(18), 4676–4680 (2008).
[CrossRef]

2007 (1)

V. Shah, S. Kanppe, P. D. Schwindt, and J. Kitching, “Subpicotesla atomic magnetometry with a microfabricated vapour cell,” Nat. Photonics 1(11), 649–652 (2007).
[CrossRef]

2005 (2)

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81(4), 421–442 (2005).
[CrossRef]

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system,” Phys. Rev. Lett. 94(19), 193002 (2005).
[CrossRef] [PubMed]

2004 (1)

S. J. Park, H. Cho, T. Y. Kwon, and H. S. Lee, “Transient coherence oscillation induced by a detuned Raman field in a rubidium Λ system,” Phys. Rev. A 69(2), 023806 (2004).
[CrossRef]

2003 (1)

2001 (2)

A. S. Zibrov, I. Novikova, and A. B. Matsko, “Observation of Ramsey fringes in an atomic cell with buffer gas,” Opt. Lett. 26(17), 1311–1313 (2001).
[CrossRef] [PubMed]

A. S. Zibrov and A. S. Matsko, “Optical Ramsey fringes induced by Zeeman coherence,” Phys. Rev. A 65(1), 013814 (2001).
[CrossRef]

1997 (2)

M. S. Shahriar, P. R. Hemmer, D. P. Katz, A. Lee, and M. G. Prentiss, “Dark-state-based three-element vector model for the stimulated Raman interaction,” Phys. Rev. A 55(3), 2272–2282 (1997).
[CrossRef]

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced line width reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56(2), R1063–R1066 (1997).
[CrossRef]

1993 (2)

1992 (1)

C. Audoin, “Caesium beam frequency standards: classical and optically pumped,” Metrolog. 29(2), 113–134 (1992).
[CrossRef]

1991 (1)

G. Theobald, V. Giordano, N. Dimatcq, and P. Cerez, “Observation of narrow Ramsey-type resonances in a caesium beam due to Zeeman coherences,” J. Phys. B 24(13), 2957–2966 (1991).
[CrossRef]

1989 (1)

1986 (1)

1983 (1)

1982 (1)

J. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48(13), 867–870 (1982).
[CrossRef]

1981 (1)

A. G. Mungall, H. Daams, and J. S. Boulanger, “Design, construction, and performance of the NRC CsVI primary cesium clocks,” Metrolog. 17(4), 123–145 (1981).
[CrossRef]

1977 (1)

M. M. Salour and C. Cohen-Tannoudji, “Observation of Ramsey’s interference fringes in the profile of Doppler-free two-photon resonances,” Phys. Rev. Lett. 38(14), 757–760 (1977).
[CrossRef]

1955 (1)

L. Essen and J. V. L. Parry, “An atomic standard of frequency and time interval: a caesium resonator,” Nature 176(4476), 280–282 (1955).
[CrossRef]

1950 (1)

N. F. Ramsey, “A molecular beam resonance method with separated oscillating field,” Phys. Rev. 78(6), 695–699 (1950).
[CrossRef]

Audoin, C.

C. Audoin, “Caesium beam frequency standards: classical and optically pumped,” Metrolog. 29(2), 113–134 (1992).
[CrossRef]

Bashkansky, M.

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Prospect for development of a pulsed CPT Raman–Ramsey clock using atomic vapor,” Proc. SPIE 7612, 76120D, 76120D-25 (2010).
[CrossRef]

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Optical Ramsey interference and its performance in D1 line excitation in rubidium vapor for implementation of a vapor cell clock,” Proc. SPIE 7949, 794910D (2010).

Bernacki, B. E.

Boulanger, J. S.

A. G. Mungall, H. Daams, and J. S. Boulanger, “Design, construction, and performance of the NRC CsVI primary cesium clocks,” Metrolog. 17(4), 123–145 (1981).
[CrossRef]

Brandt, S.

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced line width reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56(2), R1063–R1066 (1997).
[CrossRef]

Cerez, P.

G. Theobald, V. Giordano, N. Dimatcq, and P. Cerez, “Observation of narrow Ramsey-type resonances in a caesium beam due to Zeeman coherences,” J. Phys. B 24(13), 2957–2966 (1991).
[CrossRef]

Cho, H.

S. J. Park, H. Cho, T. Y. Kwon, and H. S. Lee, “Transient coherence oscillation induced by a detuned Raman field in a rubidium Λ system,” Phys. Rev. A 69(2), 023806 (2004).
[CrossRef]

Clairon, A.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system,” Phys. Rev. Lett. 94(19), 193002 (2005).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

M. M. Salour and C. Cohen-Tannoudji, “Observation of Ramsey’s interference fringes in the profile of Doppler-free two-photon resonances,” Phys. Rev. Lett. 38(14), 757–760 (1977).
[CrossRef]

Daams, H.

A. G. Mungall, H. Daams, and J. S. Boulanger, “Design, construction, and performance of the NRC CsVI primary cesium clocks,” Metrolog. 17(4), 123–145 (1981).
[CrossRef]

de Clercq, E.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system,” Phys. Rev. Lett. 94(19), 193002 (2005).
[CrossRef] [PubMed]

Dimarcq, N.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system,” Phys. Rev. Lett. 94(19), 193002 (2005).
[CrossRef] [PubMed]

Dimatcq, N.

G. Theobald, V. Giordano, N. Dimatcq, and P. Cerez, “Observation of narrow Ramsey-type resonances in a caesium beam due to Zeeman coherences,” J. Phys. B 24(13), 2957–2966 (1991).
[CrossRef]

Essen, L.

L. Essen and J. V. L. Parry, “An atomic standard of frequency and time interval: a caesium resonator,” Nature 176(4476), 280–282 (1955).
[CrossRef]

Ezekiel, S.

Fatemi, F. K.

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Prospect for development of a pulsed CPT Raman–Ramsey clock using atomic vapor,” Proc. SPIE 7612, 76120D, 76120D-25 (2010).
[CrossRef]

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Optical Ramsey interference and its performance in D1 line excitation in rubidium vapor for implementation of a vapor cell clock,” Proc. SPIE 7949, 794910D (2010).

Giordano, V.

G. Theobald, V. Giordano, N. Dimatcq, and P. Cerez, “Observation of narrow Ramsey-type resonances in a caesium beam due to Zeeman coherences,” J. Phys. B 24(13), 2957–2966 (1991).
[CrossRef]

Guerandel, S.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system,” Phys. Rev. Lett. 94(19), 193002 (2005).
[CrossRef] [PubMed]

Hänsch, T. W.

B. Schuh, S. I. Kanorsky, A. Weis, and T. W. Hänsch, “Observation of Ramsey fringes in nonlinear Faraday rotation,” Opt. Commun. 100(5-6), 451–455 (1993).
[CrossRef]

Hemmer, P. R.

Holleville, D.

T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, and A. Clairon, “High contrast Ramsey fringes with coherent-population-trapping pulses in a double lambda atomic system,” Phys. Rev. Lett. 94(19), 193002 (2005).
[CrossRef] [PubMed]

Ikonen, E.

Kanorsky, S. I.

B. Schuh, S. I. Kanorsky, A. Weis, and T. W. Hänsch, “Observation of Ramsey fringes in nonlinear Faraday rotation,” Opt. Commun. 100(5-6), 451–455 (1993).
[CrossRef]

Kanppe, S.

V. Shah, S. Kanppe, P. D. Schwindt, and J. Kitching, “Subpicotesla atomic magnetometry with a microfabricated vapour cell,” Nat. Photonics 1(11), 649–652 (2007).
[CrossRef]

Katz, D. P.

M. S. Shahriar, P. R. Hemmer, D. P. Katz, A. Lee, and M. G. Prentiss, “Dark-state-based three-element vector model for the stimulated Raman interaction,” Phys. Rev. A 55(3), 2272–2282 (1997).
[CrossRef]

Kitching, J.

V. Shah, S. Kanppe, P. D. Schwindt, and J. Kitching, “Subpicotesla atomic magnetometry with a microfabricated vapour cell,” Nat. Photonics 1(11), 649–652 (2007).
[CrossRef]

Kwon, T. Y.

S. J. Park, H. Cho, T. Y. Kwon, and H. S. Lee, “Transient coherence oscillation induced by a detuned Raman field in a rubidium Λ system,” Phys. Rev. A 69(2), 023806 (2004).
[CrossRef]

Lamela-Rivera, H.

Lee, A.

M. S. Shahriar, P. R. Hemmer, D. P. Katz, A. Lee, and M. G. Prentiss, “Dark-state-based three-element vector model for the stimulated Raman interaction,” Phys. Rev. A 55(3), 2272–2282 (1997).
[CrossRef]

Lee, H. S.

S. J. Park, H. Cho, T. Y. Kwon, and H. S. Lee, “Transient coherence oscillation induced by a detuned Raman field in a rubidium Λ system,” Phys. Rev. A 69(2), 023806 (2004).
[CrossRef]

Leiby, C. C.

P. R. Hemmer, S. Ezekiel, and C. C. Leiby., “Stabilization of a microwave oscillator using a resonance Raman transition in a sodium beam,” Opt. Lett. 8(8), 440–442 (1983).
[CrossRef] [PubMed]

J. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48(13), 867–870 (1982).
[CrossRef]

Lindvall, T.

Ma, Y.

B. Yan, Y. Ma, and Y. Wang, “Formation of Ramsey fringes based on pulsed coherent light storage,” Phys. Rev. A 79(6), 063820 (2009).
[CrossRef]

Matsko, A. B.

Matsko, A. S.

A. S. Zibrov and A. S. Matsko, “Optical Ramsey fringes induced by Zeeman coherence,” Phys. Rev. A 65(1), 013814 (2001).
[CrossRef]

Merimaa, M.

Meschede, D.

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced line width reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56(2), R1063–R1066 (1997).
[CrossRef]

Mungall, A. G.

A. G. Mungall, H. Daams, and J. S. Boulanger, “Design, construction, and performance of the NRC CsVI primary cesium clocks,” Metrolog. 17(4), 123–145 (1981).
[CrossRef]

Nagel, A.

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced line width reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56(2), R1063–R1066 (1997).
[CrossRef]

Natoli, V. D.

Novikova, I.

Ontai, G. P.

Park, S. J.

S. J. Park, H. Cho, T. Y. Kwon, and H. S. Lee, “Transient coherence oscillation induced by a detuned Raman field in a rubidium Λ system,” Phys. Rev. A 69(2), 023806 (2004).
[CrossRef]

Parry, J. V. L.

L. Essen and J. V. L. Parry, “An atomic standard of frequency and time interval: a caesium resonator,” Nature 176(4476), 280–282 (1955).
[CrossRef]

Pati, G. S.

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Prospect for development of a pulsed CPT Raman–Ramsey clock using atomic vapor,” Proc. SPIE 7612, 76120D, 76120D-25 (2010).
[CrossRef]

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Optical Ramsey interference and its performance in D1 line excitation in rubidium vapor for implementation of a vapor cell clock,” Proc. SPIE 7949, 794910D (2010).

G. S. Pati, K. Salit, R. Tripathi, and M. S. Shahriar, “Demonstration of Raman–Ramsey fringes using time delayed optical pulses in rubidium vapor,” Opt. Commun. 281(18), 4676–4680 (2008).
[CrossRef]

Picard, R. H.

J. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48(13), 867–870 (1982).
[CrossRef]

Prentiss, M. G.

M. S. Shahriar, P. R. Hemmer, D. P. Katz, A. Lee, and M. G. Prentiss, “Dark-state-based three-element vector model for the stimulated Raman interaction,” Phys. Rev. A 55(3), 2272–2282 (1997).
[CrossRef]

Ramsey, N. F.

N. F. Ramsey, “A molecular beam resonance method with separated oscillating field,” Phys. Rev. 78(6), 695–699 (1950).
[CrossRef]

Salit, K.

G. S. Pati, K. Salit, R. Tripathi, and M. S. Shahriar, “Demonstration of Raman–Ramsey fringes using time delayed optical pulses in rubidium vapor,” Opt. Commun. 281(18), 4676–4680 (2008).
[CrossRef]

Salour, M. M.

M. M. Salour and C. Cohen-Tannoudji, “Observation of Ramsey’s interference fringes in the profile of Doppler-free two-photon resonances,” Phys. Rev. Lett. 38(14), 757–760 (1977).
[CrossRef]

Schuh, B.

B. Schuh, S. I. Kanorsky, A. Weis, and T. W. Hänsch, “Observation of Ramsey fringes in nonlinear Faraday rotation,” Opt. Commun. 100(5-6), 451–455 (1993).
[CrossRef]

Schwindt, P. D.

V. Shah, S. Kanppe, P. D. Schwindt, and J. Kitching, “Subpicotesla atomic magnetometry with a microfabricated vapour cell,” Nat. Photonics 1(11), 649–652 (2007).
[CrossRef]

Shah, V.

V. Shah, S. Kanppe, P. D. Schwindt, and J. Kitching, “Subpicotesla atomic magnetometry with a microfabricated vapour cell,” Nat. Photonics 1(11), 649–652 (2007).
[CrossRef]

Shahriar, M. S.

G. S. Pati, K. Salit, R. Tripathi, and M. S. Shahriar, “Demonstration of Raman–Ramsey fringes using time delayed optical pulses in rubidium vapor,” Opt. Commun. 281(18), 4676–4680 (2008).
[CrossRef]

M. S. Shahriar, P. R. Hemmer, D. P. Katz, A. Lee, and M. G. Prentiss, “Dark-state-based three-element vector model for the stimulated Raman interaction,” Phys. Rev. A 55(3), 2272–2282 (1997).
[CrossRef]

P. R. Hemmer, M. S. Shahriar, H. Lamela-Rivera, S. P. Smith, B. E. Bernacki, and S. Ezekiel, “Semiconductor laser excitation of Ramsey fringes using a Raman transition in a cesium atomic beam,” J. Opt. Soc. Am. B 10(8), 1326–1329 (1993).
[CrossRef]

P. R. Hemmer, M. S. Shahriar, V. D. Natoli, and S. Ezekiel, “AC Stark shifts in a two-zone Raman interaction,” J. Opt. Soc. Am. B 6(8), 1519–1528 (1989).
[CrossRef]

Shahriar, S.

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Optical Ramsey interference and its performance in D1 line excitation in rubidium vapor for implementation of a vapor cell clock,” Proc. SPIE 7949, 794910D (2010).

G. S. Pati, F. K. Fatemi, M. Bashkansky, and S. Shahriar, “Prospect for development of a pulsed CPT Raman–Ramsey clock using atomic vapor,” Proc. SPIE 7612, 76120D, 76120D-25 (2010).
[CrossRef]

Smith, S. P.

Theobald, G.

G. Theobald, V. Giordano, N. Dimatcq, and P. Cerez, “Observation of narrow Ramsey-type resonances in a caesium beam due to Zeeman coherences,” J. Phys. B 24(13), 2957–2966 (1991).
[CrossRef]

Thomas, J.

J. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48(13), 867–870 (1982).
[CrossRef]

Tittonen, I.

Tripathi, R.

G. S. Pati, K. Salit, R. Tripathi, and M. S. Shahriar, “Demonstration of Raman–Ramsey fringes using time delayed optical pulses in rubidium vapor,” Opt. Commun. 281(18), 4676–4680 (2008).
[CrossRef]

Vanier, J.

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81(4), 421–442 (2005).
[CrossRef]

Wang, Y.

B. Yan, Y. Ma, and Y. Wang, “Formation of Ramsey fringes based on pulsed coherent light storage,” Phys. Rev. A 79(6), 063820 (2009).
[CrossRef]

Weis, A.

B. Schuh, S. I. Kanorsky, A. Weis, and T. W. Hänsch, “Observation of Ramsey fringes in nonlinear Faraday rotation,” Opt. Commun. 100(5-6), 451–455 (1993).
[CrossRef]

Willis, C. R.

J. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, and C. R. Willis, “Observation of Ramsey fringes using a stimulated resonance Raman transition in a sodium atomic beam,” Phys. Rev. Lett. 48(13), 867–870 (1982).
[CrossRef]

Wynands, R.

S. Brandt, A. Nagel, R. Wynands, and D. Meschede, “Buffer-gas-induced line width reduction of coherent dark resonances to below 50 Hz,” Phys. Rev. A 56(2), R1063–R1066 (1997).
[CrossRef]

Yan, B.

B. Yan, Y. Ma, and Y. Wang, “Formation of Ramsey fringes based on pulsed coherent light storage,” Phys. Rev. A 79(6), 063820 (2009).
[CrossRef]

Zanon, T.

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

(a) Raman excitation in a three-level Λ-system: ω1 and ω2 correspond the frequencies of the Raman beams, Δ and δ correspond to the difference (or two-photon) and average frequency detuning, respectively (b) repeated sequence of Raman pulse (RP) used in generating Ramsey interference.

Fig. 2
Fig. 2

Bloch vector model showing the dynamics of a three-level Λ-system during pulsed Raman excitation. The figures show the BVs (a) after interaction with the first Raman/CPT pulse (dotted blue arrow: start of BV; solid blue arrow: end state of BV) (b) during free evolution time, T, and (c) after interaction with the second Raman (or detection) pulse.

Fig. 3
Fig. 3

Plots showing oscillations in BV components R2 and R3 as a function of τ2 for Δ = 10 KHz, α = 0.1 Δ and T = 100 μs.

Fig. 4
Fig. 4

Numerical solutions showing (a) FDRI obtained by using the pulse parameters as described in the text, (b) QPLD-RI corresponding to different values of Δ, as a function of the query pulse duration.

Fig. 5
Fig. 5

Experimental setup for Ramsey interference consisting of an injection-locked diode laser, AOM for generating Raman beams and a buffer gas filled Rb cell. FCL: fiber collimating lens, FCP: fiber coupler, NDF: neutral density filter, OF: optical fiber, P: prism (out-of-plane as discussed in the text), PP: prism polarizer, PBS: polarizing beam splitter, PD: photodiode, and HWP: half-wave plate.

Fig. 6
Fig. 6

(a) Experimentally observed FDRI using Raman excitation in the (0-0) ground-state ‘clock transition’ in 85Rb vapor, (b) second-order magnetic field, B dependence of FDRI.

Fig. 7
Fig. 7

(a) Experimentally observed QPLD-RI for different values of Δ as shown in the figure, (b) magnetic field dependence of QPLD-RI for Δ ≈ 0. The horizontal axis shows the whole pulse sequence.

Fig. 8
Fig. 8

Numerical results showing change in (a) central FDRI fringe width and (b) slope at the fringe center as a function of query pulse duration, τ2.

Fig. 9
Fig. 9

Numerical results showing (a) light shift in central fringe for δ = -Γ, and (b) variation in light shift as a function of τ2 corresponding to δ = −1.5Γ.

Equations (4)

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R ˙ = Q × R α R +α e ^ 3
R ( τ 2 )=[ [ sin( Δ.( τ 2 +T ) )cosθ.sin( Δ.( τ 2 +θ ) ) ] e α τ 2 + sin2θ 2 ] e ^ 2 + [ [ cos( Δ.( τ 2 +T ) )cosθ.cos( Δ.( τ 2 +θ ) ) ] e α τ 2 + 1+cos2θ 2 ] e ^ 3
ρ ˜ ˙ = i [ H ˜ , ρ ˜ ]+ ρ ˜ ˙ decay
H ˜ =( 0 Ω 1 2 0 Ω 1 2 δ Ω 2 2 0 Ω 2 2 Δ )

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