Abstract

Doppler cooling on a forbidden transition is studied experimentally and numerically. By quenching the upper level of the cooling transition, the scattering rate is increased, and 106 40Ca atoms have been cooled and trapped in a magneto-optical trap to temperatures of down to 6 μK. A model is developed that describes the cooling method by rate equations. Based on the model, Monte Carlo simulations are performed that show good agreement with the experimental results. Possibilities of reaching high densities and low temperature by optimizing the parameters during the cooling phase are discussed, and the benefit of these ultracold atoms for the accuracy and stability of optical frequency standards is demonstrated.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
  36. L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
    [CrossRef]

2003

2002

G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, “Optical clock with ultracold neutral atoms,” Phys. Rev. Lett. 89, 230801 (2002).
[CrossRef] [PubMed]

2001

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

E. A. Curtis, C. W. Oates, and L. Hollberg, “Quenched narrow-line laser cooling of 40Ca to near the photon recoil limit,” Phys. Rev. A 64, 031403(R) (2001).
[CrossRef]

M. Machholm, P. S. Julienne, and K.-A. Suominen, “Calculations of collisions between cold alkaline earth atoms in a weak laser field,” Phys. Rev. A 64, 033425 (2001).
[CrossRef]

2000

T. Ido, Y. Isoya, and H. Katori, “Optical-dipole trapping of Sr atoms at a high phase-space density,” Phys. Rev. A 61, 061403 (2000).
[CrossRef]

G. Zinner, T. Binnewies, F. Riehle, and E. Tiemann, “Photoassociation of cold Ca atoms,” Phys. Rev. Lett. 85, 2292–2295 (2000).
[CrossRef] [PubMed]

1999

C. W. Oates, F. Bondu, R. W. Fox, and L. Hollberg, “A diode-laser optical frequency standard based on laser-cooled Ca atoms: sub-kilohertz spectroscopy by optical shelving detection,” Eur. Phys. J. D 7, 449–460 (1999).
[CrossRef]

F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke, “The optical calcium frequency standard,” IEEE Trans. Instrum. Meas. IM-48, 613–617 (1999).
[CrossRef]

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, and A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

S. M. Tan, “A computational toolbox for quantum and atom optics,” J. Opt. B 1, 424–432 (1999).
[CrossRef]

H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

1998

F. Ruschewitz, J. L. Peng, H. Hinderthür, N. Schaffrath, K. Sengstock, and W. Ertmer, “Sub-kilohertz optical spectroscopy with a time domain atom interferometer,” Phys. Rev. Lett. 80, 3173–3176 (1998).
[CrossRef]

Y. Castin, J. I. Cirac, and M. Lewenstein, “Reabsorption of light by trapped atoms,” Phys. Rev. Lett. 80, 5305–5308 (1998).
[CrossRef]

1997

W. Rooijakkers, W. Hoogervorst, and W. Vassen, “Laser cooling, friction, and diffusion in a three-level cascade system,” Phys. Rev. A 56, 3083–3092 (1997).
[CrossRef]

1996

J. I. Cirac, M. Lewenstein, and P. Zoller, “Collective laser cooling of trapped atoms,” Europhys. Lett. 35, 647–651 (1996).
[CrossRef]

1993

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

1992

M. Kasevich and S. Chu, “Laser cooling below a photon recoil with three-level atoms,” Phys. Rev. Lett. 69, 1741–1744 (1992).
[CrossRef] [PubMed]

T. Kurosu and F. Shimizu, “Laser cooling and trapping of alkaline earth atoms,” Jpn. J. Appl. Phys., Part 1 31, 908–912 (1992).
[CrossRef]

1991

1989

1988

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

1986

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: observation of quantum jumps,” Phys. Rev. Lett. 56, 2797–2799 (1986).
[CrossRef] [PubMed]

1985

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

1984

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

1980

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

1976

R. Whitley and C. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498–1513 (1976).
[CrossRef]

Arimondo, E.

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, and A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Ashkin, A.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

Aspect, A.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Avrillier, S.

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

Bassi, D.

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

Bergquist, J. C.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

Beverini, N.

Binnewies, T.

G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, “Optical clock with ultracold neutral atoms,” Phys. Rev. Lett. 89, 230801 (2002).
[CrossRef] [PubMed]

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

G. Zinner, T. Binnewies, F. Riehle, and E. Tiemann, “Photoassociation of cold Ca atoms,” Phys. Rev. Lett. 85, 2292–2295 (2000).
[CrossRef] [PubMed]

Bjorkholm, J. E.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

Bollinger, J. J.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

Bondu, F.

C. W. Oates, F. Bondu, R. W. Fox, and L. Hollberg, “A diode-laser optical frequency standard based on laser-cooled Ca atoms: sub-kilohertz spectroscopy by optical shelving detection,” Eur. Phys. J. D 7, 449–460 (1999).
[CrossRef]

Bordé, C. J.

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

Bréant, C.

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

Cable, A.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

Castin, Y.

Y. Castin, J. I. Cirac, and M. Lewenstein, “Reabsorption of light by trapped atoms,” Phys. Rev. Lett. 80, 5305–5308 (1998).
[CrossRef]

Y. Castin, H. Wallis, and J. Dalibard, “Limit of Doppler cooling,” J. Opt. Soc. Am. B 6, 2046–2057 (1989).
[CrossRef]

Chu, S.

M. Kasevich and S. Chu, “Laser cooling below a photon recoil with three-level atoms,” Phys. Rev. Lett. 69, 1741–1744 (1992).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

Cirac, J. I.

Y. Castin, J. I. Cirac, and M. Lewenstein, “Reabsorption of light by trapped atoms,” Phys. Rev. Lett. 80, 5305–5308 (1998).
[CrossRef]

J. I. Cirac, M. Lewenstein, and P. Zoller, “Collective laser cooling of trapped atoms,” Europhys. Lett. 35, 647–651 (1996).
[CrossRef]

Cohen-Tannoudji, C.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Curtis, E. A.

E. A. Curtis, C. W. Oates, and L. Hollberg, “Quenched narrow-line second- and third-stage laser cooling of 40Ca,” J. Opt. Soc. Am. B 20, 977–984 (2003).
[CrossRef]

E. A. Curtis, C. W. Oates, and L. Hollberg, “Quenched narrow-line laser cooling of 40Ca to near the photon recoil limit,” Phys. Rev. A 64, 031403(R) (2001).
[CrossRef]

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

Dagdigian, P. J.

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

Dalibard, J.

Degenhardt, C.

G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, “Optical clock with ultracold neutral atoms,” Phys. Rev. Lett. 89, 230801 (2002).
[CrossRef] [PubMed]

Dehmelt, H.

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: observation of quantum jumps,” Phys. Rev. Lett. 56, 2797–2799 (1986).
[CrossRef] [PubMed]

Diddams, S. A.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

Dinneen, T. P.

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, and A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Drullinger, R. E.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

Ertmer, W.

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

F. Ruschewitz, J. L. Peng, H. Hinderthür, N. Schaffrath, K. Sengstock, and W. Ertmer, “Sub-kilohertz optical spectroscopy with a time domain atom interferometer,” Phys. Rev. Lett. 80, 3173–3176 (1998).
[CrossRef]

H. Wallis and W. Ertmer, “Broadband laser cooling on narrow transitions,” J. Opt. Soc. Am. B 6, 2211–2219 (1989).
[CrossRef]

Fox, R. W.

C. W. Oates, F. Bondu, R. W. Fox, and L. Hollberg, “A diode-laser optical frequency standard based on laser-cooled Ca atoms: sub-kilohertz spectroscopy by optical shelving detection,” Eur. Phys. J. D 7, 449–460 (1999).
[CrossRef]

Gallagher, A.

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, and A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Giammanco, F.

Gilligan, J. M.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

Gould, P. L.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

Hall, J. L.

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, and A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Heinzen, D. J.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

Helmcke, J.

G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, “Optical clock with ultracold neutral atoms,” Phys. Rev. Lett. 89, 230801 (2002).
[CrossRef] [PubMed]

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke, “The optical calcium frequency standard,” IEEE Trans. Instrum. Meas. IM-48, 613–617 (1999).
[CrossRef]

Hinderthür, H.

F. Ruschewitz, J. L. Peng, H. Hinderthür, N. Schaffrath, K. Sengstock, and W. Ertmer, “Sub-kilohertz optical spectroscopy with a time domain atom interferometer,” Phys. Rev. Lett. 80, 3173–3176 (1998).
[CrossRef]

Hollberg, L.

E. A. Curtis, C. W. Oates, and L. Hollberg, “Quenched narrow-line second- and third-stage laser cooling of 40Ca,” J. Opt. Soc. Am. B 20, 977–984 (2003).
[CrossRef]

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

E. A. Curtis, C. W. Oates, and L. Hollberg, “Quenched narrow-line laser cooling of 40Ca to near the photon recoil limit,” Phys. Rev. A 64, 031403(R) (2001).
[CrossRef]

C. W. Oates, F. Bondu, R. W. Fox, and L. Hollberg, “A diode-laser optical frequency standard based on laser-cooled Ca atoms: sub-kilohertz spectroscopy by optical shelving detection,” Eur. Phys. J. D 7, 449–460 (1999).
[CrossRef]

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

Hoogervorst, W.

W. Rooijakkers, W. Hoogervorst, and W. Vassen, “Laser cooling, friction, and diffusion in a three-level cascade system,” Phys. Rev. A 56, 3083–3092 (1997).
[CrossRef]

Ido, T.

T. Ido, Y. Isoya, and H. Katori, “Optical-dipole trapping of Sr atoms at a high phase-space density,” Phys. Rev. A 61, 061403 (2000).
[CrossRef]

H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Isoya, Y.

T. Ido, Y. Isoya, and H. Katori, “Optical-dipole trapping of Sr atoms at a high phase-space density,” Phys. Rev. A 61, 061403 (2000).
[CrossRef]

H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Itano, W. M.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

Ivanov, E. N.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

Julienne, P. S.

M. Machholm, P. S. Julienne, and K.-A. Suominen, “Calculations of collisions between cold alkaline earth atoms in a weak laser field,” Phys. Rev. A 64, 033425 (2001).
[CrossRef]

Kaiser, R.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Kasevich, M.

M. Kasevich and S. Chu, “Laser cooling below a photon recoil with three-level atoms,” Phys. Rev. Lett. 69, 1741–1744 (1992).
[CrossRef] [PubMed]

Katori, H.

T. Ido, Y. Isoya, and H. Katori, “Optical-dipole trapping of Sr atoms at a high phase-space density,” Phys. Rev. A 61, 061403 (2000).
[CrossRef]

H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Kurosu, T.

T. Kurosu and F. Shimizu, “Laser cooling and trapping of alkaline earth atoms,” Jpn. J. Appl. Phys., Part 1 31, 908–912 (1992).
[CrossRef]

Kuwata-Gonokami, M.

H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Lett, P. D.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

Lewenstein, M.

Y. Castin, J. I. Cirac, and M. Lewenstein, “Reabsorption of light by trapped atoms,” Phys. Rev. Lett. 80, 5305–5308 (1998).
[CrossRef]

J. I. Cirac, M. Lewenstein, and P. Zoller, “Collective laser cooling of trapped atoms,” Europhys. Lett. 35, 647–651 (1996).
[CrossRef]

Lipphardt, B.

F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke, “The optical calcium frequency standard,” IEEE Trans. Instrum. Meas. IM-48, 613–617 (1999).
[CrossRef]

Maccioni, E.

Machholm, M.

M. Machholm, P. S. Julienne, and K.-A. Suominen, “Calculations of collisions between cold alkaline earth atoms in a weak laser field,” Phys. Rev. A 64, 033425 (2001).
[CrossRef]

Mehlstäubler, T. E.

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

Metcalf, H. J.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

Moore, F. L.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

Nagourney, W.

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: observation of quantum jumps,” Phys. Rev. Lett. 56, 2797–2799 (1986).
[CrossRef] [PubMed]

Oates, C. W.

E. A. Curtis, C. W. Oates, and L. Hollberg, “Quenched narrow-line second- and third-stage laser cooling of 40Ca,” J. Opt. Soc. Am. B 20, 977–984 (2003).
[CrossRef]

E. A. Curtis, C. W. Oates, and L. Hollberg, “Quenched narrow-line laser cooling of 40Ca to near the photon recoil limit,” Phys. Rev. A 64, 031403(R) (2001).
[CrossRef]

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

C. W. Oates, F. Bondu, R. W. Fox, and L. Hollberg, “A diode-laser optical frequency standard based on laser-cooled Ca atoms: sub-kilohertz spectroscopy by optical shelving detection,” Eur. Phys. J. D 7, 449–460 (1999).
[CrossRef]

Pasternack, L.

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

Peng, J. L.

F. Ruschewitz, J. L. Peng, H. Hinderthür, N. Schaffrath, K. Sengstock, and W. Ertmer, “Sub-kilohertz optical spectroscopy with a time domain atom interferometer,” Phys. Rev. Lett. 80, 3173–3176 (1998).
[CrossRef]

Phillips, W. D.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

Rafac, R. J.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

Raizen, M. G.

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

Rasel, E. M.

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

Riehle, F.

G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, “Optical clock with ultracold neutral atoms,” Phys. Rev. Lett. 89, 230801 (2002).
[CrossRef] [PubMed]

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

G. Zinner, T. Binnewies, F. Riehle, and E. Tiemann, “Photoassociation of cold Ca atoms,” Phys. Rev. Lett. 85, 2292–2295 (2000).
[CrossRef] [PubMed]

F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke, “The optical calcium frequency standard,” IEEE Trans. Instrum. Meas. IM-48, 613–617 (1999).
[CrossRef]

Robinson, H. G.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

Rooijakkers, W.

W. Rooijakkers, W. Hoogervorst, and W. Vassen, “Laser cooling, friction, and diffusion in a three-level cascade system,” Phys. Rev. A 56, 3083–3092 (1997).
[CrossRef]

Ruschewitz, F.

F. Ruschewitz, J. L. Peng, H. Hinderthür, N. Schaffrath, K. Sengstock, and W. Ertmer, “Sub-kilohertz optical spectroscopy with a time domain atom interferometer,” Phys. Rev. Lett. 80, 3173–3176 (1998).
[CrossRef]

Salomon, C.

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

Sandberg, J.

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: observation of quantum jumps,” Phys. Rev. Lett. 56, 2797–2799 (1986).
[CrossRef] [PubMed]

Schaffrath, N.

F. Ruschewitz, J. L. Peng, H. Hinderthür, N. Schaffrath, K. Sengstock, and W. Ertmer, “Sub-kilohertz optical spectroscopy with a time domain atom interferometer,” Phys. Rev. Lett. 80, 3173–3176 (1998).
[CrossRef]

Schnatz, H.

F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke, “The optical calcium frequency standard,” IEEE Trans. Instrum. Meas. IM-48, 613–617 (1999).
[CrossRef]

Scoles, G.

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

Sengstock, K.

F. Ruschewitz, J. L. Peng, H. Hinderthür, N. Schaffrath, K. Sengstock, and W. Ertmer, “Sub-kilohertz optical spectroscopy with a time domain atom interferometer,” Phys. Rev. Lett. 80, 3173–3176 (1998).
[CrossRef]

Sesko, D.

Shimizu, F.

T. Kurosu and F. Shimizu, “Laser cooling and trapping of alkaline earth atoms,” Jpn. J. Appl. Phys., Part 1 31, 908–912 (1992).
[CrossRef]

Silver, D. M.

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

Sterr, U.

G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, “Optical clock with ultracold neutral atoms,” Phys. Rev. Lett. 89, 230801 (2002).
[CrossRef] [PubMed]

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

Stroud, C.

R. Whitley and C. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498–1513 (1976).
[CrossRef]

Strumia, F.

Suominen, K.-A.

M. Machholm, P. S. Julienne, and K.-A. Suominen, “Calculations of collisions between cold alkaline earth atoms in a weak laser field,” Phys. Rev. A 64, 033425 (2001).
[CrossRef]

Tan, S. M.

S. M. Tan, “A computational toolbox for quantum and atom optics,” J. Opt. B 1, 424–432 (1999).
[CrossRef]

Tiemann, E.

G. Zinner, T. Binnewies, F. Riehle, and E. Tiemann, “Photoassociation of cold Ca atoms,” Phys. Rev. Lett. 85, 2292–2295 (2000).
[CrossRef] [PubMed]

Trebst, T.

F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke, “The optical calcium frequency standard,” IEEE Trans. Instrum. Meas. IM-48, 613–617 (1999).
[CrossRef]

Udem, T.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

Van Lerberghe, A.

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

Vansteenkiste, N.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Vassen, W.

W. Rooijakkers, W. Hoogervorst, and W. Vassen, “Laser cooling, friction, and diffusion in a three-level cascade system,” Phys. Rev. A 56, 3083–3092 (1997).
[CrossRef]

Vissani, G.

Vogel, K. R.

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, and A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

Walker, T.

Wallis, H.

Watts, R. N.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

Westbrook, C. I.

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

Whitley, R.

R. Whitley and C. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498–1513 (1976).
[CrossRef]

Wieman, C.

Wilpers, G.

G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, “Optical clock with ultracold neutral atoms,” Phys. Rev. Lett. 89, 230801 (2002).
[CrossRef] [PubMed]

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

Wineland, D. J.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

Yarkony, D. R.

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

Zinner, G.

G. Zinner, T. Binnewies, F. Riehle, and E. Tiemann, “Photoassociation of cold Ca atoms,” Phys. Rev. Lett. 85, 2292–2295 (2000).
[CrossRef] [PubMed]

F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke, “The optical calcium frequency standard,” IEEE Trans. Instrum. Meas. IM-48, 613–617 (1999).
[CrossRef]

Zoller, P.

J. I. Cirac, M. Lewenstein, and P. Zoller, “Collective laser cooling of trapped atoms,” Europhys. Lett. 35, 647–651 (1996).
[CrossRef]

Eur. Phys. J. D

C. W. Oates, F. Bondu, R. W. Fox, and L. Hollberg, “A diode-laser optical frequency standard based on laser-cooled Ca atoms: sub-kilohertz spectroscopy by optical shelving detection,” Eur. Phys. J. D 7, 449–460 (1999).
[CrossRef]

Europhys. Lett.

J. I. Cirac, M. Lewenstein, and P. Zoller, “Collective laser cooling of trapped atoms,” Europhys. Lett. 35, 647–651 (1996).
[CrossRef]

IEEE J. Quantum Electron.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, T. Udem, H. G. Robinson, J. C. Bergquist, R. J. Rafac, W. M. Itano, R. E. Drullinger, and D. J. Wineland, “Optical frequency standards and measurements,” IEEE J. Quantum Electron. 37, 1502–1513 (2001).
[CrossRef]

IEEE Trans. Instrum. Meas.

F. Riehle, H. Schnatz, B. Lipphardt, G. Zinner, T. Trebst, and J. Helmcke, “The optical calcium frequency standard,” IEEE Trans. Instrum. Meas. IM-48, 613–617 (1999).
[CrossRef]

J. Opt. B

S. M. Tan, “A computational toolbox for quantum and atom optics,” J. Opt. B 1, 424–432 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

Jpn. J. Appl. Phys., Part 1

T. Kurosu and F. Shimizu, “Laser cooling and trapping of alkaline earth atoms,” Jpn. J. Appl. Phys., Part 1 31, 908–912 (1992).
[CrossRef]

Phys. Rev. A

R. Whitley and C. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498–1513 (1976).
[CrossRef]

W. Rooijakkers, W. Hoogervorst, and W. Vassen, “Laser cooling, friction, and diffusion in a three-level cascade system,” Phys. Rev. A 56, 3083–3092 (1997).
[CrossRef]

M. Machholm, P. S. Julienne, and K.-A. Suominen, “Calculations of collisions between cold alkaline earth atoms in a weak laser field,” Phys. Rev. A 64, 033425 (2001).
[CrossRef]

T. Ido, Y. Isoya, and H. Katori, “Optical-dipole trapping of Sr atoms at a high phase-space density,” Phys. Rev. A 61, 061403 (2000).
[CrossRef]

T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, and A. Gallagher, “Cold collisions of Sr*-Sr in a magneto-optical trap,” Phys. Rev. A 59, 1216–1222 (1999).
[CrossRef]

W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland, “Quantum projection noise: population fluctuations in two-level systems,” Phys. Rev. A 47, 3554–3570 (1993).
[CrossRef] [PubMed]

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

E. A. Curtis, C. W. Oates, and L. Hollberg, “Quenched narrow-line laser cooling of 40Ca to near the photon recoil limit,” Phys. Rev. A 64, 031403(R) (2001).
[CrossRef]

Phys. Rev. Lett.

W. Nagourney, J. Sandberg, and H. Dehmelt, “Shelved optical electron amplifier: observation of quantum jumps,” Phys. Rev. Lett. 56, 2797–2799 (1986).
[CrossRef] [PubMed]

G. Wilpers, T. Binnewies, C. Degenhardt, U. Sterr, J. Helmcke, and F. Riehle, “Optical clock with ultracold neutral atoms,” Phys. Rev. Lett. 89, 230801 (2002).
[CrossRef] [PubMed]

Y. Castin, J. I. Cirac, and M. Lewenstein, “Reabsorption of light by trapped atoms,” Phys. Rev. Lett. 80, 5305–5308 (1998).
[CrossRef]

G. Zinner, T. Binnewies, F. Riehle, and E. Tiemann, “Photoassociation of cold Ca atoms,” Phys. Rev. Lett. 85, 2292–2295 (2000).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould, and H. J. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

M. Kasevich and S. Chu, “Laser cooling below a photon recoil with three-level atoms,” Phys. Rev. Lett. 69, 1741–1744 (1992).
[CrossRef] [PubMed]

F. Ruschewitz, J. L. Peng, H. Hinderthür, N. Schaffrath, K. Sengstock, and W. Ertmer, “Sub-kilohertz optical spectroscopy with a time domain atom interferometer,” Phys. Rev. Lett. 80, 3173–3176 (1998).
[CrossRef]

T. Binnewies, G. Wilpers, U. Sterr, F. Riehle, J. Helmcke, T. E. Mehlstäubler, E. M. Rasel, and W. Ertmer, “Doppler cooling and trapping on forbidden transitions,” Phys. Rev. Lett. 87, 123002 (2001).
[CrossRef] [PubMed]

H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116–1119 (1999).
[CrossRef]

Other

R. L. Kurucz, “Semiempirical calculations of gf values for the iron group,” Trans. IAU XXB, 168–172 (1988).

V. Pal’chikov, Institute of Metrology for Time and Space at National Research Institute for Physical-Technical and Radiotechnical Measurements, Mendeleevo, Russia (personal communication, 2002).

P. R. Berman, ed., Atom Interferometry (Academic, New York, 1997).

G. Wilpers, C. Degenhardt, T. Binnewies, A. Chernyshov, F. Riehle, J. Helmcke, and U. Sterr, “Improvement of the fractional uncertainty of a neutral atom calcium optical frequency standard to 2×10−14,” Appl. Phys. B (to be published).

G. Wilpers, “Ein Optisches Frequenznormal mit kalten und ultrakalten Atomen,” PTB-Bericht PTB-Opt-66, Ph.D. dissertation (Physikalisch-Technische Bundesanstalt, University of Hannover, Braunschweig, 2002).

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Figures (16)

Fig. 1
Fig. 1

Excerpt of the level scheme of calcium showing the transitions with corresponding A factors that are relevant for the cooling.

Fig. 2
Fig. 2

Three-level atom with fast decay from the excited state interacting with two laser fields.

Fig. 3
Fig. 3

Quench transitions to the Zeeman substates with the relevant Clebsch–Gordan coefficients.

Fig. 4
Fig. 4

Influence of the magnetic field in a MOT on the resonance condition. In the upper part, the position-dependent Zeeman shift of the levels and the region of resonance with the broadened and detuned laser is shown. The lower part depicts the corresponding scattering force.

Fig. 5
Fig. 5

Velocity distribution of the precooled atoms (curve a) and after 25 ms of cooling on the narrow line (curve b).

Fig. 6
Fig. 6

Quenching of excited atoms by a pulse of the 453-nm laser as a function of the laser detuning Δq. The solid curve shows a Gaussian curve fitted to the data.

Fig. 7
Fig. 7

Remaining fraction of excited atoms as a function of the pulse length tq of the 453-nm quench laser.

Fig. 8
Fig. 8

Transfer efficiency η (circles) and 1-D rms velocity vrms (squares) as a function of the cooling time tc. Filled symbols are experimental data with the experimental efficiency scaled up by a factor of 3.5, and open symbols are results from simulations. The graph shows results similar to the ones in Fig. 3 in Ref. 13, where the simulation is based on slightly different experimental values.

Fig. 9
Fig. 9

Dependency of the velocity width vrms (squares) and the efficiency η (triangles) on the detuning δ. The filled symbols are experimental data, and the open symbols are simulation results. Here the experimental efficiency is scaled up by a factor of 5.

Fig. 10
Fig. 10

Simulated cooling results with and without polarization effects. Open triangles denote the initial velocity distribution, and squares (circles) are with a polarized (unpolarized) quench laser obtained after 25 ms of cooling.

Fig. 11
Fig. 11

Cooling without a magnetic field in the presence of gravity. Size (circles) and velocity (squares) versus quench-laser power Pq for an initial velocity distribution of vrms=0.07 m/s with experimental laser parameters and δ=-2π×60 kHz. The open (filled) symbols denote data for the z (x) direction.

Fig. 12
Fig. 12

Simulation results of the evolution of the velocity distribution as a function of the cooling time in a horizontal two-dimensional optical molasses with no quench laser. Initial width vrms=7 cm/s, laser detuning δ=-2π×2 kHz. The times from back to front are 0 ms, 5 ms, 10 ms, 20 ms, 40 ms, and 60 ms.

Fig. 13
Fig. 13

Simulated spatial and velocity spread after 25 ms of cooling versus magnetic field gradient for a starting distribution of vrms=0.72 m/s from the broad-line MOT. Filled (open) symbols along the x (z) direction.

Fig. 14
Fig. 14

Transfer efficiency from the broad-line MOT with (initial vrms=0.72 m/s) versus magnetic field gradient.

Fig. 15
Fig. 15

Simulated phase-space density ζ per unit phase-space volume h3 and per atom after 25 ms of cooling versus magnetic field gradient dB/dz for an initial distribution of vrms=0.07 m/s.

Fig. 16
Fig. 16

Optical Ramsey fringes obtained with an ensemble of calcium atoms at a temperature of 10 μK as a function of the laser detuning.30 The gray curve shows the expected envelope. The contrast is ∼70% of what can at best be reached with atoms at rest. The data show a signal-to-noise ratio of 30 that was obtained at a cycle rate of 4.5 per second, and 15 cycles were averaged per point.

Equations (15)

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TD=Γ2kB,
dρdt=-i[H,ρ]-C(ρ).
C(ρ)=kCkρCk-12 CkCkρ-12 ρCkCk,
VAL=-d01  E01-d12  E12.
Ωij=dijEij/=Iij2I0,ij1/2Aji,
I0,ij=πhc3λij3 Aji
Γ1eff=Γ1+r12,
r12=Ω122Γ2Γ224δ122+Γ22.
Ω01=I2I0Γ1+r12Δ1/2A10,
r01=Ω012/Γ1eff.
ρ11=r012r01+r12+Γ1,
rscat=(Γ1+r12)ρ11.
δ-1.8(Γ1k1vr)1/2,
δ-Δ+kvs=gJμBzmaxdB/dz.
amaxv022zmax.

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