Abstract

We have developed a magneto-optical trap that is well suited for high-resolution spectroscopy. It uses a combination of doughnut mode (Laguerre–Gaussian TEM01) and TEM00 cooling beams rather than the usual TEM00 cooling beams. This configuration allows us to tailor the intensity distribution within the magneto-optical trap such that the atoms are cooled from the background vapor by the intense TEM01 beams and then trapped by the weak TEM00 beams. This greatly reduces the magnitude of the ac-Stark shift and the line broadening induced by the cooling lasers, allowing high-resolution spectroscopy to be performed in the presence of the cooling beams.

© 1997 Optical Society of America

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  1. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
    [Crossref] [PubMed]
  2. S. Chu and C. Wieman, eds., feature on laser cooling and trapping of atoms, J. Opt. Soc. Am. B 6, 2020–2278 (1989).
  3. H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 204–286 (1994).
    [Crossref]
  4. M. Zhu, C. W. Oates, and J. L. Hall, “Improved hyperfine measurements of the Na 5P excited-state through frequency-controlled Dopplerless spectroscopy in a Zeeman magneto-optic laser trap,” Opt. Lett. 18, 1186–1188 (1993).
    [Crossref]
  5. C. W. Oates, K. R. Vogel, and J. L. Hall, “High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p2 P3/2  lifetime discrepancy,” Phys. Rev. Lett. 76, 2866–2869 (1996).
    [Crossref] [PubMed]
  6. M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
    [Crossref]
  7. A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, “Cold atoms—a new medium for quantum optics,” Appl. Phys. B 60, 129–134 (1995).
    [Crossref]
  8. C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571–1574 (1990).
    [Crossref] [PubMed]
  9. R. W. Fox, S. L. Gilbert, L. Hollberg, J. H. Marquardt, and H. G. Robinson, “Optical probing of cold trapped atoms,” Opt. Lett. 18, 1456–1458 (1993).
    [Crossref] [PubMed]
  10. A. G. Sinclair, B. D. McDonald, E. Riis, and G. Duxbury, “Double-resonance spectroscopy of laser-cooled Rb atoms,” Opt. Commun. 106, 207–212 (1994). (Note that there are two slight mistakes in the paper. The Rabi frequency is 2α=10.56 MHz(I/mW cm-2), and the saturation intensity should be 156 µW cm-2 ).
    [Crossref]
  11. N. P. Georgiades, E. S. Polzik, and H. J. Kimble, “Two-photon spectroscopy of the 6S1/2–6D5/2  transition of trapped atomic cesium,” Opt. Lett. 19, 1474–1476 (1994).
    [Crossref] [PubMed]
  12. M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996).
    [Crossref]
  13. A. G. Sinclair, E. Riis, and M. J. Snadden, “Improved trapping in a vapor-cell magneto-optic trap with multiple laser frequencies,” J. Opt. Soc. Am. B 11, 2333–2339 (1994).
    [Crossref]
  14. K. E. Gibble, S. Kasapi, and S. Chu, “Improved magneto-optic trapping in a vapor cell,” Opt. Lett. 17, 526–528 (1992).
    [Crossref] [PubMed]
  15. D. Hoffmann, P. Feng, R. S. Williamson, and T. Walker, “Excited-state collisions of trapped Rb-85 atoms,” Phys. Rev. Lett. 69, 753–756 (1992).
    [Crossref] [PubMed]
  16. D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961–964 (1989).
    [Crossref] [PubMed]
  17. W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
    [Crossref] [PubMed]
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    [Crossref]
  21. E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–125 (1991).
    [Crossref]
  22. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
    [Crossref]
  23. C. Tamm and C. O. Weiss, “Bistability and optical switching of spatial patterns in a laser,” J. Opt. Soc. Am. B 7, 1034–1038 (1990).
    [Crossref]
  24. A. E. Siegman, “Defining and measuring laser beam quality,” in Solid State Lasers: New Developments and Applications, M. Ingusico and R. Waleenstein, eds. (Plenum, New York, 1993), pp. 13–28.
  25. F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2  2-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993).
    [Crossref]
  26. S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).
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  28. N. C. Wong and J. L. Hall, “Servo control of amplitude modulation in frequency-modulation spectroscopy: demonstration of shot-noise limited detection,” J. Opt. Soc. Am. B 2, 1527–1533 (1985).
    [Crossref]

1996 (2)

C. W. Oates, K. R. Vogel, and J. L. Hall, “High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p2 P3/2  lifetime discrepancy,” Phys. Rev. Lett. 76, 2866–2869 (1996).
[Crossref] [PubMed]

M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996).
[Crossref]

1995 (1)

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, “Cold atoms—a new medium for quantum optics,” Appl. Phys. B 60, 129–134 (1995).
[Crossref]

1994 (4)

H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 204–286 (1994).
[Crossref]

A. G. Sinclair, B. D. McDonald, E. Riis, and G. Duxbury, “Double-resonance spectroscopy of laser-cooled Rb atoms,” Opt. Commun. 106, 207–212 (1994). (Note that there are two slight mistakes in the paper. The Rabi frequency is 2α=10.56 MHz(I/mW cm-2), and the saturation intensity should be 156 µW cm-2 ).
[Crossref]

A. G. Sinclair, E. Riis, and M. J. Snadden, “Improved trapping in a vapor-cell magneto-optic trap with multiple laser frequencies,” J. Opt. Soc. Am. B 11, 2333–2339 (1994).
[Crossref]

N. P. Georgiades, E. S. Polzik, and H. J. Kimble, “Two-photon spectroscopy of the 6S1/2–6D5/2  transition of trapped atomic cesium,” Opt. Lett. 19, 1474–1476 (1994).
[Crossref] [PubMed]

1993 (5)

M. Zhu, C. W. Oates, and J. L. Hall, “Improved hyperfine measurements of the Na 5P excited-state through frequency-controlled Dopplerless spectroscopy in a Zeeman magneto-optic laser trap,” Opt. Lett. 18, 1186–1188 (1993).
[Crossref]

R. W. Fox, S. L. Gilbert, L. Hollberg, J. H. Marquardt, and H. G. Robinson, “Optical probing of cold trapped atoms,” Opt. Lett. 18, 1456–1458 (1993).
[Crossref] [PubMed]

F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2  2-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993).
[Crossref]

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

1992 (2)

D. Hoffmann, P. Feng, R. S. Williamson, and T. Walker, “Excited-state collisions of trapped Rb-85 atoms,” Phys. Rev. Lett. 69, 753–756 (1992).
[Crossref] [PubMed]

K. E. Gibble, S. Kasapi, and S. Chu, “Improved magneto-optic trapping in a vapor cell,” Opt. Lett. 17, 526–528 (1992).
[Crossref] [PubMed]

1991 (2)

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
[Crossref]

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–125 (1991).
[Crossref]

1990 (2)

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571–1574 (1990).
[Crossref] [PubMed]

C. Tamm and C. O. Weiss, “Bistability and optical switching of spatial patterns in a laser,” J. Opt. Soc. Am. B 7, 1034–1038 (1990).
[Crossref]

1989 (2)

D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961–964 (1989).
[Crossref] [PubMed]

S. Chu and C. Wieman, eds., feature on laser cooling and trapping of atoms, J. Opt. Soc. Am. B 6, 2020–2278 (1989).

1987 (1)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[Crossref] [PubMed]

1985 (1)

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Abramochkin, E.

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–125 (1991).
[Crossref]

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

Bell, A. S.

M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996).
[Crossref]

Biraben, F.

F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2  2-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993).
[Crossref]

Cable, A.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[Crossref] [PubMed]

Chu, S.

K. E. Gibble, S. Kasapi, and S. Chu, “Improved magneto-optic trapping in a vapor cell,” Opt. Lett. 17, 526–528 (1992).
[Crossref] [PubMed]

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
[Crossref]

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[Crossref] [PubMed]

Courty, J. M.

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, “Cold atoms—a new medium for quantum optics,” Appl. Phys. B 60, 129–134 (1995).
[Crossref]

Davis, K. B.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Duxbury, G.

A. G. Sinclair, B. D. McDonald, E. Riis, and G. Duxbury, “Double-resonance spectroscopy of laser-cooled Rb atoms,” Opt. Commun. 106, 207–212 (1994). (Note that there are two slight mistakes in the paper. The Rabi frequency is 2α=10.56 MHz(I/mW cm-2), and the saturation intensity should be 156 µW cm-2 ).
[Crossref]

Felder, R.

F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2  2-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993).
[Crossref]

Feng, P.

D. Hoffmann, P. Feng, R. S. Williamson, and T. Walker, “Excited-state collisions of trapped Rb-85 atoms,” Phys. Rev. Lett. 69, 753–756 (1992).
[Crossref] [PubMed]

Ferguson, A. I.

M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996).
[Crossref]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Fox, R. W.

Gallagher, A.

D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961–964 (1989).
[Crossref] [PubMed]

Georgiades, N. P.

Giacobino, E.

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, “Cold atoms—a new medium for quantum optics,” Appl. Phys. B 60, 129–134 (1995).
[Crossref]

Gibble, K. E.

Gilbert, S. L.

Hall, J. L.

C. W. Oates, K. R. Vogel, and J. L. Hall, “High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p2 P3/2  lifetime discrepancy,” Phys. Rev. Lett. 76, 2866–2869 (1996).
[Crossref] [PubMed]

M. Zhu, C. W. Oates, and J. L. Hall, “Improved hyperfine measurements of the Na 5P excited-state through frequency-controlled Dopplerless spectroscopy in a Zeeman magneto-optic laser trap,” Opt. Lett. 18, 1186–1188 (1993).
[Crossref]

N. C. Wong and J. L. Hall, “Servo control of amplitude modulation in frequency-modulation spectroscopy: demonstration of shot-noise limited detection,” J. Opt. Soc. Am. B 2, 1527–1533 (1985).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Hoffmann, D.

D. Hoffmann, P. Feng, R. S. Williamson, and T. Walker, “Excited-state collisions of trapped Rb-85 atoms,” Phys. Rev. Lett. 69, 753–756 (1992).
[Crossref] [PubMed]

Hollberg, L.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Joffe, M. A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

Kasapi, S.

K. E. Gibble, S. Kasapi, and S. Chu, “Improved magneto-optic trapping in a vapor cell,” Opt. Lett. 17, 526–528 (1992).
[Crossref] [PubMed]

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
[Crossref]

Kasevich, M.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
[Crossref]

Ketterle, W.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

Kimble, H. J.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Lambrecht, A.

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, “Cold atoms—a new medium for quantum optics,” Appl. Phys. B 60, 129–134 (1995).
[Crossref]

Marquardt, J. H.

Martin, A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

McDonald, B. D.

A. G. Sinclair, B. D. McDonald, E. Riis, and G. Duxbury, “Double-resonance spectroscopy of laser-cooled Rb atoms,” Opt. Commun. 106, 207–212 (1994). (Note that there are two slight mistakes in the paper. The Rabi frequency is 2α=10.56 MHz(I/mW cm-2), and the saturation intensity should be 156 µW cm-2 ).
[Crossref]

Metcalf, H.

H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 204–286 (1994).
[Crossref]

Millerioux, Y.

F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2  2-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993).
[Crossref]

Moler, K.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
[Crossref]

Monroe, C.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571–1574 (1990).
[Crossref] [PubMed]

D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961–964 (1989).
[Crossref] [PubMed]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Nez, F.

F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2  2-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993).
[Crossref]

Oates, C. W.

C. W. Oates, K. R. Vogel, and J. L. Hall, “High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p2 P3/2  lifetime discrepancy,” Phys. Rev. Lett. 76, 2866–2869 (1996).
[Crossref] [PubMed]

M. Zhu, C. W. Oates, and J. L. Hall, “Improved hyperfine measurements of the Na 5P excited-state through frequency-controlled Dopplerless spectroscopy in a Zeeman magneto-optic laser trap,” Opt. Lett. 18, 1186–1188 (1993).
[Crossref]

Polzik, E. S.

Prentiss, M.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[Crossref] [PubMed]

Pritchard, D. E.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[Crossref] [PubMed]

Raab, E. L.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[Crossref] [PubMed]

Reynaud, S.

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, “Cold atoms—a new medium for quantum optics,” Appl. Phys. B 60, 129–134 (1995).
[Crossref]

Riis, E.

M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996).
[Crossref]

A. G. Sinclair, B. D. McDonald, E. Riis, and G. Duxbury, “Double-resonance spectroscopy of laser-cooled Rb atoms,” Opt. Commun. 106, 207–212 (1994). (Note that there are two slight mistakes in the paper. The Rabi frequency is 2α=10.56 MHz(I/mW cm-2), and the saturation intensity should be 156 µW cm-2 ).
[Crossref]

A. G. Sinclair, E. Riis, and M. J. Snadden, “Improved trapping in a vapor-cell magneto-optic trap with multiple laser frequencies,” J. Opt. Soc. Am. B 11, 2333–2339 (1994).
[Crossref]

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
[Crossref]

Robinson, H.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571–1574 (1990).
[Crossref] [PubMed]

Robinson, H. G.

Sesko, D.

D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961–964 (1989).
[Crossref] [PubMed]

Siegman, A. E.

A. E. Siegman, “Defining and measuring laser beam quality,” in Solid State Lasers: New Developments and Applications, M. Ingusico and R. Waleenstein, eds. (Plenum, New York, 1993), pp. 13–28.

A. E. Siegman, Lasers, 1st ed. (Oxford U. Press, Oxford, 1986).

Sinclair, A. G.

A. G. Sinclair, B. D. McDonald, E. Riis, and G. Duxbury, “Double-resonance spectroscopy of laser-cooled Rb atoms,” Opt. Commun. 106, 207–212 (1994). (Note that there are two slight mistakes in the paper. The Rabi frequency is 2α=10.56 MHz(I/mW cm-2), and the saturation intensity should be 156 µW cm-2 ).
[Crossref]

A. G. Sinclair, E. Riis, and M. J. Snadden, “Improved trapping in a vapor-cell magneto-optic trap with multiple laser frequencies,” J. Opt. Soc. Am. B 11, 2333–2339 (1994).
[Crossref]

Snadden, M. J.

M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996).
[Crossref]

A. G. Sinclair, E. Riis, and M. J. Snadden, “Improved trapping in a vapor-cell magneto-optic trap with multiple laser frequencies,” J. Opt. Soc. Am. B 11, 2333–2339 (1994).
[Crossref]

Sobelman, I. I.

I. I. Sobelman, Atomic Spectra and Radiative Transitions (Springer-Verlag, Berlin, 1979).

Stenholm, S.

S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).

Swann, W.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571–1574 (1990).
[Crossref] [PubMed]

Tamm, C.

van der Straten, P.

H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 204–286 (1994).
[Crossref]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

Vogel, K. R.

C. W. Oates, K. R. Vogel, and J. L. Hall, “High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p2 P3/2  lifetime discrepancy,” Phys. Rev. Lett. 76, 2866–2869 (1996).
[Crossref] [PubMed]

Volostnikov, V.

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–125 (1991).
[Crossref]

Walker, T.

D. Hoffmann, P. Feng, R. S. Williamson, and T. Walker, “Excited-state collisions of trapped Rb-85 atoms,” Phys. Rev. Lett. 69, 753–756 (1992).
[Crossref] [PubMed]

D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961–964 (1989).
[Crossref] [PubMed]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Weiss, C. O.

Weiss, D. S.

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
[Crossref]

Wieman, C.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571–1574 (1990).
[Crossref] [PubMed]

D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961–964 (1989).
[Crossref] [PubMed]

Williamson, R. S.

D. Hoffmann, P. Feng, R. S. Williamson, and T. Walker, “Excited-state collisions of trapped Rb-85 atoms,” Phys. Rev. Lett. 69, 753–756 (1992).
[Crossref] [PubMed]

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

Wong, N. C.

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Orlando, Fla., 1991).

Zhu, M.

Appl. Phys. B (2)

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, “Cold atoms—a new medium for quantum optics,” Appl. Phys. B 60, 129–134 (1995).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

J. Opt. Soc. Am. B (4)

Opt. Commun. (5)

A. G. Sinclair, B. D. McDonald, E. Riis, and G. Duxbury, “Double-resonance spectroscopy of laser-cooled Rb atoms,” Opt. Commun. 106, 207–212 (1994). (Note that there are two slight mistakes in the paper. The Rabi frequency is 2α=10.56 MHz(I/mW cm-2), and the saturation intensity should be 156 µW cm-2 ).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular-momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–125 (1991).
[Crossref]

M. J. Snadden, A. S. Bell, E. Riis, and A. I. Ferguson, “Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser,” Opt. Commun. 125, 70–76 (1996).
[Crossref]

F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination of the hyperfine components of the 5S1/2–5D3/2  2-photon transitions in rubidium,” Opt. Commun. 102, 432–438 (1993).
[Crossref]

Opt. Lett. (4)

Phys. Rep. (1)

H. Metcalf and P. van der Straten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 204–286 (1994).
[Crossref]

Phys. Rev. Lett. (7)

C. W. Oates, K. R. Vogel, and J. L. Hall, “High precision linewidth measurement of laser-cooled atoms: resolution of the Na 3p2 P3/2  lifetime discrepancy,” Phys. Rev. Lett. 76, 2866–2869 (1996).
[Crossref] [PubMed]

M. Kasevich, D. S. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, “Atomic velocity selection using stimulated Raman transitions,” Phys. Rev. Lett. 66, 2267–2300 (1991).
[Crossref]

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, “Trapping of neutral sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[Crossref] [PubMed]

C. Monroe, W. Swann, H. Robinson, and C. Wieman, “Very cold trapped atoms in a vapor cell,” Phys. Rev. Lett. 65, 1571–1574 (1990).
[Crossref] [PubMed]

D. Hoffmann, P. Feng, R. S. Williamson, and T. Walker, “Excited-state collisions of trapped Rb-85 atoms,” Phys. Rev. Lett. 69, 753–756 (1992).
[Crossref] [PubMed]

D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman, “Collisional losses from a light-force atom trap,” Phys. Rev. Lett. 63, 961–964 (1989).
[Crossref] [PubMed]

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

Other (5)

A. Yariv, Optical Electronics, 4th ed. (Saunders, Orlando, Fla., 1991).

A. E. Siegman, Lasers, 1st ed. (Oxford U. Press, Oxford, 1986).

S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).

I. I. Sobelman, Atomic Spectra and Radiative Transitions (Springer-Verlag, Berlin, 1979).

A. E. Siegman, “Defining and measuring laser beam quality,” in Solid State Lasers: New Developments and Applications, M. Ingusico and R. Waleenstein, eds. (Plenum, New York, 1993), pp. 13–28.

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Figures (9)

Fig. 1
Fig. 1

HG and LG TEM01 modes resolved into components.

Fig. 2
Fig. 2

Experimental setup, showing the production of the HG TEM01 mode in a ring cavity and its conversion into a LG TEM01 mode by a pair of cylindrical lenses. The other beams that are used to produce and probe the MOT are shown. AOM's, acousto-optic modulators; EOM, electro-optic modulator; M. L., mode locked.

Fig. 3
Fig. 3

Some LG modes produced experimentally by off-axis excitation of a ring cavity. Below each intensity image is shown the interference pattern produced by overlapping a TEM00 mode with the generated mode. The angle between the dark spokes represents an azimuthal phase shift of 2π in the LG mode. The images were captured with a CCD camera, and are all to the same scale.

Fig. 4
Fig. 4

Atomic clouds within the MOT: (a) a conventional MOT produced with TEM00 beams, (b) a MOT produced with only the LG TEM01 beams, showing that the trap is not well defined, (c) a MOT produced with the LG TEM01 beam with an additional, weak TEM00 beam to give a well-compressed trap containing a large number of atoms, and (d) a MOT produced with only the weak TEM00 beam.

Fig. 5
Fig. 5

The MOT is loaded with the cooling and trapping beams and the magnetic field on. It is then probed with the mode-locked laser for 15 ms. The magnetic field and the bright cooling beam are then switched off while the remaining trapping light is further detuned from resonance. The atoms are then further cooled in optical molasses for 10 ms. The trapping light is then fully switched off, and the atoms are probed once more with the mode-locked laser. This allows any frequency shift induced by the MOT to be observed by comparison of the two signals produced by the mode-locked laser.

Fig. 6
Fig. 6

Two traces are shown in each set of experimental results. The upper traces show spectra of the 5S–5D two-photon transition in 85Rb when the MOT was on, and the lower traces show the spectra when the MOT was off. The five strongest lines correspond to transitions to 5D5/2 and are labeled with the initial and the final F quantum numbers. (a) Results for conventional TEM00 mode trapping; while the cooling lasers were on, the two-photon transition was shifted 2 MHz higher in frequency as well as being broadened. (b) Result for trapping with LG TEM01 and weak TEM00 beams. There is no frequency shift greater than our resolution of 100 kHz.

Fig. 7
Fig. 7

While the mode-locked laser was frequency stabilized to the F=35 component of the 5S1/2–5D5/2 two-photon transition, an AOM was used to scan another beam relative to the lock point when the MOT was off. This allowed the ac-Stark shift to be measured as a function of the experimental conditions. This figure shows several such scans when the intensity of the central TEM00 trapping beam was varied. The AOM is driven at a frequency comparable with the mode-locked laser's repetition rate of 80.30 MHz. If there is no ac-Stark shift, the probe beam is resonant with the two-photon transition when the AOM runs at 80.30 MHz.

Fig. 8
Fig. 8

ac-Stark shifts observed as the intensity of the central TEM00 beams was varied. The dashed line shows the value of the shift expected from Eq. (12). The gradient of the results agrees well with theory, but there is an additional offset that is due to the slight asymmetry of the signal used to stabilize the mode-locked laser.

Fig. 9
Fig. 9

Spectra taken with different probe powers, both with the cooling lasers off. For the upper trace, 550 mW of mode-locked light was used; 80 mW of light was used for the lower trace. It can be seen that the mode-locked laser produces no significant ac-Stark shift of the two-photon transition.

Equations (15)

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u00(r, z)=1ω(z)2π1/2×exp-iΨ(z)-r21ω2(z)+ik2R(z),
ω2(z)=ω021+z2zr2,
R(z)=z1+zr2z2,
Ψ(z)=tan-1 zzr,
zr=πω02nλ.
unmHG(x, y, z)=1ω2πn!m!1/22-N/2×exp-i(n+m+1)×Ψ-(x2+y2)1ω2+ik2R×Hnx2ωHmy2ω,
unmLG(r, ϕ, z)=1ω2πn!m!1/2 min(n, m)!×exp-i(n+m+1)Ψ-i(n-m)ϕ-r2×1ω2+ik2R(-1)min(n,m)×r2ω|n-m|Lmin(n,m)|n-m|2r2ω2,
N=n+m.
unmHGx+y2, x-y2, z
=k=0N b(n, m, k)uN-k,kHG(x, y, z),
unmLG(x, y, z)=k=0N ikb(n, m, k)uN-k,kHG(x, y, z),
b(n, m, k)=1k!(N-k)!k!2Nn!m!1/2×dkdtk[(1-t)n(1+t)m]|t=0.
ΔacΓ=14ΔΓ+Δ2Γ2+I2Is1/2,
μ2=37μ2MF=34,
Is=73IsMF=34,

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