Abstract

A compact frequency standard based on an expanding cold Cs133 cloud is under development in our laboratory. In a first experiment, Cs cold atoms were prepared by a magneto-optical trap in a vapor cell, and a microwave antenna was used to transmit the radiation for the clock transition. The signal obtained from fluorescence of the expanding cold atoms cloud is used to lock a microwave chain. In this way the overall system stability is evaluated. A theoretical model based on a two-level system interacting with the two microwave pulses enables interpretation for the observed features, especially the poor Ramsey fringes contrast.

© 2008 Optical Society of America

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  1. S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
    [CrossRef]
  2. M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612-615 (1989).
    [CrossRef] [PubMed]
  3. D. W. Sesko and C. E. Wieman, “Observation of the cesium clock transition in laser-cooled atoms,” Opt. Lett. 14, 269-271 (1989).
    [CrossRef] [PubMed]
  4. A. Clairon, C. Salomon, S. Guellati, and W. D. Phillips, “Ramsey resonance in a Zacharias fountain,” Europhys. Lett. 16, 165-170 (1991).
    [CrossRef]
  5. S. T. Müller, D. V. Magalhães, A. Bebeachibuli, M. S. Santos, and V. S. Bagnato, “Demonstration and observation of a frequency standard based on an expanding cold atoms cloud of cesium,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2005), pp. 288-291.
    [CrossRef]
  6. S. Tremine, S. Guerandel, D. Holleville, A. Clairon, and N. Dimarcq, “Development of a compact cold atom clock,” in Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition 2004 (IEEE, 2004), pp. 65-70.
    [CrossRef]
  7. D. V. Magalhães, S. T. Müller, A. Bebeachibuli, R. F. Alves, and V. S. Bagnato, “Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards,” Laser Phys. 16, 1-4 (2006).
    [CrossRef]
  8. F. Teles, D. V. Magalhães, M. S. Santos, G. D. Rovera, and V. S. Bagnato, “Construction and evaluation of the first Brazilian atomic clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1111-1114 (2000).
    [CrossRef]
  9. J. F. Garcia Nava, F. L. Walls, J. H. Shirley, W. D. Lee, and M. C. Delgado Aramburo, “Environmental effects in frequency synthesizers for passive frequency standards,” in Proceedings of IEEE International Frequency Control Symposium (IEEE, 1996), pp. 973-979.
    [CrossRef]
  10. E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.
  11. D. J. Glaze, H. Hellwig, D. W. Allan, and S. Jarvis, “NBS-4 and NBS-6: The NBS primary frequency standards,” Metrologia 13, 17-28 (1977).
    [CrossRef]
  12. J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Hilger, 1989), Vol. 2.
    [CrossRef]
  13. S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1965).
  14. G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887-894 (1998).
    [CrossRef]

2006

D. V. Magalhães, S. T. Müller, A. Bebeachibuli, R. F. Alves, and V. S. Bagnato, “Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards,” Laser Phys. 16, 1-4 (2006).
[CrossRef]

2005

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

2000

F. Teles, D. V. Magalhães, M. S. Santos, G. D. Rovera, and V. S. Bagnato, “Construction and evaluation of the first Brazilian atomic clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1111-1114 (2000).
[CrossRef]

1998

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887-894 (1998).
[CrossRef]

1991

A. Clairon, C. Salomon, S. Guellati, and W. D. Phillips, “Ramsey resonance in a Zacharias fountain,” Europhys. Lett. 16, 165-170 (1991).
[CrossRef]

1989

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612-615 (1989).
[CrossRef] [PubMed]

D. W. Sesko and C. E. Wieman, “Observation of the cesium clock transition in laser-cooled atoms,” Opt. Lett. 14, 269-271 (1989).
[CrossRef] [PubMed]

1977

D. J. Glaze, H. Hellwig, D. W. Allan, and S. Jarvis, “NBS-4 and NBS-6: The NBS primary frequency standards,” Metrologia 13, 17-28 (1977).
[CrossRef]

Abgrall, M.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Allan, D. W.

D. J. Glaze, H. Hellwig, D. W. Allan, and S. Jarvis, “NBS-4 and NBS-6: The NBS primary frequency standards,” Metrologia 13, 17-28 (1977).
[CrossRef]

Alves, R. F.

D. V. Magalhães, S. T. Müller, A. Bebeachibuli, R. F. Alves, and V. S. Bagnato, “Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards,” Laser Phys. 16, 1-4 (2006).
[CrossRef]

Audoin, C.

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887-894 (1998).
[CrossRef]

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Hilger, 1989), Vol. 2.
[CrossRef]

Bagnato, V. S.

D. V. Magalhães, S. T. Müller, A. Bebeachibuli, R. F. Alves, and V. S. Bagnato, “Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards,” Laser Phys. 16, 1-4 (2006).
[CrossRef]

F. Teles, D. V. Magalhães, M. S. Santos, G. D. Rovera, and V. S. Bagnato, “Construction and evaluation of the first Brazilian atomic clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1111-1114 (2000).
[CrossRef]

S. T. Müller, D. V. Magalhães, A. Bebeachibuli, M. S. Santos, and V. S. Bagnato, “Demonstration and observation of a frequency standard based on an expanding cold atoms cloud of cesium,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2005), pp. 288-291.
[CrossRef]

Bebeachibuli, A.

D. V. Magalhães, S. T. Müller, A. Bebeachibuli, R. F. Alves, and V. S. Bagnato, “Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards,” Laser Phys. 16, 1-4 (2006).
[CrossRef]

S. T. Müller, D. V. Magalhães, A. Bebeachibuli, M. S. Santos, and V. S. Bagnato, “Demonstration and observation of a frequency standard based on an expanding cold atoms cloud of cesium,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2005), pp. 288-291.
[CrossRef]

Bize, S.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Cacciapuoti, L.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Chu, S.

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612-615 (1989).
[CrossRef] [PubMed]

Clairon, A.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887-894 (1998).
[CrossRef]

A. Clairon, C. Salomon, S. Guellati, and W. D. Phillips, “Ramsey resonance in a Zacharias fountain,” Europhys. Lett. 16, 165-170 (1991).
[CrossRef]

S. Tremine, S. Guerandel, D. Holleville, A. Clairon, and N. Dimarcq, “Development of a compact cold atom clock,” in Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition 2004 (IEEE, 2004), pp. 65-70.
[CrossRef]

De Voe, R.

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612-615 (1989).
[CrossRef] [PubMed]

Delgado Aramburo, M. C.

J. F. Garcia Nava, F. L. Walls, J. H. Shirley, W. D. Lee, and M. C. Delgado Aramburo, “Environmental effects in frequency synthesizers for passive frequency standards,” in Proceedings of IEEE International Frequency Control Symposium (IEEE, 1996), pp. 973-979.
[CrossRef]

Delporte, J.

E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.

Dick, G. J.

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887-894 (1998).
[CrossRef]

Dimarcq, N.

E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.

S. Tremine, S. Guerandel, D. Holleville, A. Clairon, and N. Dimarcq, “Development of a compact cold atom clock,” in Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition 2004 (IEEE, 2004), pp. 65-70.
[CrossRef]

Esnault, E. X.

E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.

Garcia Nava, J. F.

J. F. Garcia Nava, F. L. Walls, J. H. Shirley, W. D. Lee, and M. C. Delgado Aramburo, “Environmental effects in frequency synthesizers for passive frequency standards,” in Proceedings of IEEE International Frequency Control Symposium (IEEE, 1996), pp. 973-979.
[CrossRef]

Glaze, D. J.

D. J. Glaze, H. Hellwig, D. W. Allan, and S. Jarvis, “NBS-4 and NBS-6: The NBS primary frequency standards,” Metrologia 13, 17-28 (1977).
[CrossRef]

Grünert, J.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Guellati, S.

A. Clairon, C. Salomon, S. Guellati, and W. D. Phillips, “Ramsey resonance in a Zacharias fountain,” Europhys. Lett. 16, 165-170 (1991).
[CrossRef]

Guerandel, S.

S. Tremine, S. Guerandel, D. Holleville, A. Clairon, and N. Dimarcq, “Development of a compact cold atom clock,” in Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition 2004 (IEEE, 2004), pp. 65-70.
[CrossRef]

E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.

Hellwig, H.

D. J. Glaze, H. Hellwig, D. W. Allan, and S. Jarvis, “NBS-4 and NBS-6: The NBS primary frequency standards,” Metrologia 13, 17-28 (1977).
[CrossRef]

Hermann, V.

E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.

Holleville, D.

E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.

S. Tremine, S. Guerandel, D. Holleville, A. Clairon, and N. Dimarcq, “Development of a compact cold atom clock,” in Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition 2004 (IEEE, 2004), pp. 65-70.
[CrossRef]

Jarvis, S.

D. J. Glaze, H. Hellwig, D. W. Allan, and S. Jarvis, “NBS-4 and NBS-6: The NBS primary frequency standards,” Metrologia 13, 17-28 (1977).
[CrossRef]

Kasevich, M.

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612-615 (1989).
[CrossRef] [PubMed]

Laurent, P.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887-894 (1998).
[CrossRef]

Lee, W. D.

J. F. Garcia Nava, F. L. Walls, J. H. Shirley, W. D. Lee, and M. C. Delgado Aramburo, “Environmental effects in frequency synthesizers for passive frequency standards,” in Proceedings of IEEE International Frequency Control Symposium (IEEE, 1996), pp. 973-979.
[CrossRef]

Lemonde, P.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Luiten, A.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Magalhães, D. V.

D. V. Magalhães, S. T. Müller, A. Bebeachibuli, R. F. Alves, and V. S. Bagnato, “Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards,” Laser Phys. 16, 1-4 (2006).
[CrossRef]

F. Teles, D. V. Magalhães, M. S. Santos, G. D. Rovera, and V. S. Bagnato, “Construction and evaluation of the first Brazilian atomic clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1111-1114 (2000).
[CrossRef]

S. T. Müller, D. V. Magalhães, A. Bebeachibuli, M. S. Santos, and V. S. Bagnato, “Demonstration and observation of a frequency standard based on an expanding cold atoms cloud of cesium,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2005), pp. 288-291.
[CrossRef]

Makdissi, A.

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887-894 (1998).
[CrossRef]

Maksimovic, I.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Marion, H.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Müller, S. T.

D. V. Magalhães, S. T. Müller, A. Bebeachibuli, R. F. Alves, and V. S. Bagnato, “Comparative short-term stability for a Cs beam and an expanding cold atomic cloud of Cs used as atomic frequency standards,” Laser Phys. 16, 1-4 (2006).
[CrossRef]

S. T. Müller, D. V. Magalhães, A. Bebeachibuli, M. S. Santos, and V. S. Bagnato, “Demonstration and observation of a frequency standard based on an expanding cold atoms cloud of cesium,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2005), pp. 288-291.
[CrossRef]

Pereira dos Santos, F.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Perrin, S.

E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.

Phillips, W. D.

A. Clairon, C. Salomon, S. Guellati, and W. D. Phillips, “Ramsey resonance in a Zacharias fountain,” Europhys. Lett. 16, 165-170 (1991).
[CrossRef]

Ramo, S.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1965).

Riis, E.

M. Kasevich, E. Riis, S. Chu, and R. De Voe, “Rf spectroscopy in an atomic fountain,” Phys. Rev. Lett. 63, 612-615 (1989).
[CrossRef] [PubMed]

Rosenbusch, P.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Rovera, G. D.

F. Teles, D. V. Magalhães, M. S. Santos, G. D. Rovera, and V. S. Bagnato, “Construction and evaluation of the first Brazilian atomic clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1111-1114 (2000).
[CrossRef]

Salomon, C.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

A. Clairon, C. Salomon, S. Guellati, and W. D. Phillips, “Ramsey resonance in a Zacharias fountain,” Europhys. Lett. 16, 165-170 (1991).
[CrossRef]

Santarelli, G.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

G. Santarelli, C. Audoin, A. Makdissi, P. Laurent, G. J. Dick, and A. Clairon, “Frequency stability degradation of oscillator slaved to a periodically interrogated atomic resonator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887-894 (1998).
[CrossRef]

Santos, M. S.

F. Teles, D. V. Magalhães, M. S. Santos, G. D. Rovera, and V. S. Bagnato, “Construction and evaluation of the first Brazilian atomic clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1111-1114 (2000).
[CrossRef]

S. T. Müller, D. V. Magalhães, A. Bebeachibuli, M. S. Santos, and V. S. Bagnato, “Demonstration and observation of a frequency standard based on an expanding cold atoms cloud of cesium,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2005), pp. 288-291.
[CrossRef]

Sesko, D. W.

Shirley, J. H.

J. F. Garcia Nava, F. L. Walls, J. H. Shirley, W. D. Lee, and M. C. Delgado Aramburo, “Environmental effects in frequency synthesizers for passive frequency standards,” in Proceedings of IEEE International Frequency Control Symposium (IEEE, 1996), pp. 973-979.
[CrossRef]

Teles, F.

F. Teles, D. V. Magalhães, M. S. Santos, G. D. Rovera, and V. S. Bagnato, “Construction and evaluation of the first Brazilian atomic clock,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1111-1114 (2000).
[CrossRef]

Tobar, M.

S. Bize, P. Laurent, M. Abgrall, H. Marion, I. Maksimovic, L. Cacciapuoti, J. Grünert, C. Vian, F. Pereira dos Santos, P. Rosenbusch, P. Lemonde, G. Santarelli, P. Wolf, A. Clairon, A. Luiten, M. Tobar, and C. Salomon, “Cold atom clocks and applications,” J. Phys. B 38, S449-S468 (2005).
[CrossRef]

Tremine, S.

S. Tremine, S. Guerandel, D. Holleville, A. Clairon, and N. Dimarcq, “Development of a compact cold atom clock,” in Proceedings of the 2004 IEEE International Frequency Control Symposium and Exposition 2004 (IEEE, 2004), pp. 65-70.
[CrossRef]

E. X. Esnault, S. Perrin, S. Tremine, S. Guerandel, D. Holleville, N. Dimarcq, V. Hermann, and J. Delporte, “Stability of the compact cold atom clock HORACE,” in Proceedings of the 2007 IEEE International Frequency Control Symposium, 2007 (IEEE, 2007), pp. 1342-1345.

Van Duzer, T.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1965).

Vanier, J.

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards (Hilger, 1989), Vol. 2.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

(a) Schematic of the experimental setup. (b) Energy levels for the D 2 line of Cs atoms.

Fig. 2
Fig. 2

Temporal sequence applied to the experiment. The time duration of each stage (in milliseconds) is marked at the top. MOT operation is composed of a trapping laser, a repumper laser, and a magnetic field.

Fig. 3
Fig. 3

Observed resonance for the clock transition using a Rabi pulse for interrogation. The full half-maximum width is close to 40 Hz .

Fig. 4
Fig. 4

Allan standard deviation of the system when locked to an Agilent 5071A primary standard.

Fig. 5
Fig. 5

Ramsey fringes superimposed to the Rabi profile.

Fig. 6
Fig. 6

Diagram showing the angles and the distances between the antenna and the spatial distribution of the atoms used in the simulation.

Fig. 7
Fig. 7

Theoretical fringes when a rest cloud of atoms is considered and compared to the fringes superimposed to the Rabi profile. The experimental data shows the importance to consider the relative motion of atoms with the microwave field profile.

Fig. 8
Fig. 8

Comparison between the simulation and the experimental Ramsey fringes. The central fringes are in quite good agreement. Due to the signal-to-noise ratio, the lateral fringes are less observable in the data. The above data is a result from a single scan, when an average procedure is considered the obtained error bars are presented in a few points in order to provide the type of sensitivity involved in the experiment.

Fig. 9
Fig. 9

Comparison between the simulation and the experimental Rabi profile. The simulation was obtained through the procedure described in the text with 12 ms of time interaction.

Fig. 10
Fig. 10

Comparison between the simulation and the experimental Rabi profile. The simulation was obtained through the procedure described in the text with 15 ms of time interaction.

Equations (10)

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B = j I o μ o 2 π r e j 2 π r λ [ cos ( π 4 cos α ) cos ( π 4 ) sin α ] ,
( a 1 ( τ , T , τ ) a 2 ( τ , T , τ ) a 3 ( τ , T , τ ) ) = R 2 ( b 3 , b 4 , Ω 0 , τ ) R ( 0 , 0 , Ω 0 , T ) R 1 ( b 1 , b 2 , Ω 0 , τ ) ( 0 0 a 3 ( 0 ) ) .
R 1 ( b 1 , b 2 , Ω 0 , τ ) = ( cos Ω 1 τ + b 1 2 Ω 1 2 β ( Ω 0 Ω 1 ) sin Ω 1 τ + b 1 b 2 Ω 1 2 β b 1 Ω 0 Ω 1 2 β ( b 2 Ω 1 ) sin Ω 1 τ ( Ω 0 Ω 1 ) sin Ω 1 τ + b 1 b 2 Ω 1 2 β cos Ω 1 τ + b 2 2 Ω 1 2 β ( b 1 Ω 1 ) sin Ω 1 τ b 2 Ω 0 Ω 1 2 β b 1 Ω 0 Ω 1 2 β + ( b 2 Ω 1 ) sin Ω 1 τ ( b 1 Ω 1 ) sin Ω 1 τ b 2 Ω 0 Ω 1 2 β 1 b 2 Ω 1 2 β ) ,
P ( τ , r , α ) = 1 2 ( 1 a 3 ( τ , T , τ ) a 3 ( 0 ) ) .
d N = 2 π R 2 n ( R ) sin θ d θ d R ,
n ( R ) = n o e R 2 W 2 ,
r 2 = d 2 + R 2 2 d R cos θ ,
cos α = R sin θ r ,
sin α = d R cos θ r .
P = 0 0 π d N ( R ) n o P ( τ , R , θ ) d θ d R ,

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