Abstract

We study the dependence of the particle loading rate of a rubidium vapor cell magneto-optic trap (MOT). Using a trap depth determination of the MOT that relies on measurements of loss rates during optical excitation of colliding atoms to a repulsive molecular state, we experimentally determine the MOT escape velocity and show that the loading rate scales with escape velocity to the fourth power, or, equivalently, with the square of the trap depth. We also demonstrate that the loading rate is directly proportional to the background rubidium density. We thus experimentally confirm the loading rate model used in the literature since the invention of the MOT. In addition to confirming this long-standing conjecture, we show that the loading rate dependence can be used to reliably infer the trap depth and to tune the relative depth of a MOT (i.e., capture and escape velocities) when the background density is held fixed. The measurements have allowed an experimental determination of the relationship between capture and escape velocities in our MOTs of vc=1.29(0.12)ve.

© 2012 Optical Society of America

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  7. K. J. Matherson, R. D. Glover, D. E. Laban, and R. T. Sang, “Measurement of low-energy total absolute atomic collision cross sections with the metastable P23 state of neon using a magneto-optical trap,” Phys. Rev. A 78, 042712 (2008).
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  8. H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. D. Hoffmann, S. Bali, and T. Walker, “Trap-depth measurements using ultracold collisions,” Phys. Rev. A 54, R1030–R1033 (1996).
    [CrossRef]
  28. N. Evetts, “A study of the excited state atoms in cold atom traps and a test of the reif model to determine trap depth,” undergraduate honors thesis (University of British Columbia, 2011); available online at https://circle.ubc.ca/2429/36858 .
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    [CrossRef]
  30. K. Ladouceur, B. G. Klappauf, J. Van Dongen, N. Rauhut, B. Schuster, A. K. Mills, D. J. Jones, and K. W. Madison, “Compact laser cooling apparatus for simultaneous cooling of lithium and rubidium,” J. Opt. Soc. Am. B 26, 210–217 (2009).
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    [CrossRef]
  33. J. Van Dongen, C. Zhu, D. Clement, G. Dufour, J. L. Booth, and K. W. Madison, “Trap-depth determination from residual gas collisions,” Phys. Rev. A 84, 022708 (2011).
    [CrossRef]
  34. S. Bali, D. Hoffmann, and T. Walker, “Novel intensity dependence of ultracold collisions involving repulsive states,” Europhys. Lett. 27, 273–277 (1994).
    [CrossRef]
  35. S. H. Patil and K. T. Tang, “Multipolar polarizabilities and two- and three-body dispersion coefficients for alkali isoelectronic sequences,” J. Chem. Phys. 106, 2298–2305 (1997).
    [CrossRef]
  36. M. Marinescu, H. R. Sadeghpour, and A. Dalgarno, “Dispersion coefficients for alkali-metal dimers,” Phys. Rev. A 49, 982–988 (1994).
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2011

J. Van Dongen, C. Zhu, D. Clement, G. Dufour, J. L. Booth, and K. W. Madison, “Trap-depth determination from residual gas collisions,” Phys. Rev. A 84, 022708 (2011).
[CrossRef]

2009

D. E. Fagnan, J. Wang, C. Zhu, P. Djuricanin, B. G. Klappauf, J. L. Booth, and K. W. Madison, “Observation of quantum diffractive collisions using shallow atomic traps,” Phys. Rev. A 80, 022712 (2009).
[CrossRef]

K. Ladouceur, B. G. Klappauf, J. Van Dongen, N. Rauhut, B. Schuster, A. K. Mills, D. J. Jones, and K. W. Madison, “Compact laser cooling apparatus for simultaneous cooling of lithium and rubidium,” J. Opt. Soc. Am. B 26, 210–217 (2009).
[CrossRef]

2008

K. J. Matherson, R. D. Glover, D. E. Laban, and R. T. Sang, “Measurement of low-energy total absolute atomic collision cross sections with the metastable P23 state of neon using a magneto-optical trap,” Phys. Rev. A 78, 042712 (2008).
[CrossRef]

2007

M. H. Shah, H. A. Camp, M. L. Trachy, G. Veshapidze, M. A. Gearba, and B. D. DePaola, “Model-independent measurement of the excited fraction in a magneto-optical trap,” Phys. Rev. A 75, 053418 (2007).
[CrossRef]

J. Szczepkowski, E. Paul-Kwiek, G. Auböck, L. Holler, C. Binder, and L. Windholz, “Semiclasical model of magneto-optical trap depth,” Eur. Phys. J. Spec. Top. 144, 265–271 (2007).
[CrossRef]

J. L. Booth, J. Van Dongen, P. Lebel, B. G. Klappauf, and K. W. Madison, “Dual-channel amplification in a single-mode diode laser for multi-isotope laser cooling,” J. Opt. Soc. Am. B 24, 2914–2920 (2007).
[CrossRef]

2006

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

B. J. Claessens, J. P. Ashmore, R. T. Sang, W. R. MacGillivray, H. C. W. Beijerinck, and E. J. D. Vredenbregt, “Measurement of the photoionization cross section of the (2p)5(3p)3D3 state of neon,” Phys. Rev. A 73, 012706 (2006).
[CrossRef]

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

2005

2004

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

2002

B. Ueberholz, S. Kuhr, D. Frese, V. Gomer, and D. Meschede, “Cold collisions in a high-gradient magneto-optical trap,” J. Phys. B: At. Mol. Opt. Phys. 35, 4899–4914 (2002).
[CrossRef]

2000

V. S. Bagnato, L. G. Marcassa, S. G. Miranda, S. R. Muniz, and A. L. de Oliveira, “Measuring the capture velocity of atoms in a magneto-optical trap as a function of laser intensity,” Phys. Rev. A 62, 013404 (2000).
[CrossRef]

1999

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (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. G. Miranda, S. R. Muniz, G. D. Telles, L. G. Marcassa, K. Helmerson, and V. S. Bagnato, “Dark-spot atomic-beam slowing for on-axis loading of traps,” Phys. Rev. A 59, 882–885 (1999).
[CrossRef]

1998

V. Vuletić, C. Chin, A. J. Kerman, and S. Chu, “Degenerate raman sideband cooling of trapped cesium atoms at very high atomic densities,” Phys. Rev. Lett. 81, 5768–5771 (1998).
[CrossRef]

1997

S. D. Gensemer, V. Sanchez-Villicana, K. Y. N. Tan, T. T. Grove, and P. L. Gould, “Trap-loss collisions of Rb85 and Rb87: dependence on trap parameters,” Phys. Rev. A 56, 4055–4063 (1997).
[CrossRef]

S. H. Patil and K. T. Tang, “Multipolar polarizabilities and two- and three-body dispersion coefficients for alkali isoelectronic sequences,” J. Chem. Phys. 106, 2298–2305 (1997).
[CrossRef]

1996

D. Hoffmann, S. Bali, and T. Walker, “Trap-depth measurements using ultracold collisions,” Phys. Rev. A 54, R1030–R1033 (1996).
[CrossRef]

R. S. Schappe, T. Walker, L. W. Anderson, and C. C. Lin, “Absolute electron-impact ionization cross section measurements using a magneto-optical trap,” Phys. Rev. Lett. 76, 4328–4331 (1996).
[CrossRef]

1994

B. P. Anderson and M. A. Kasevich, “Enhanced loading of a magneto-optic trap from an atomic beam,” Phys. Rev. A 50, R3581–R3584 (1994).
[CrossRef]

M. Marinescu, H. R. Sadeghpour, and A. Dalgarno, “Dispersion coefficients for alkali-metal dimers,” Phys. Rev. A 49, 982–988 (1994).
[CrossRef]

S. Bali, D. Hoffmann, and T. Walker, “Novel intensity dependence of ultracold collisions involving repulsive states,” Europhys. Lett. 27, 273–277 (1994).
[CrossRef]

1993

J. Kawanaka, K. Shimizu, H. Takuma, and F. Shimizu, “Quadratic collisional loss rate of a Li7 trap,” Phys. Rev. A 48, R883–R885 (1993).
[CrossRef]

1992

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef]

D. J. Wineland, J. Dalibard, and C. Cohen-Tannoudji, “Sisyphus cooling of a bound atom,” J. Opt. Soc. Am. B 9, 32–42(1992).
[CrossRef]

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, “Isotopic difference in trap loss collisions of laser cooled rubidium atoms,” Phys. Rev. Lett. 69, 897–900 (1992).
[CrossRef]

1990

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]

1989

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]

1988

1987

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]

Ahmed, E. M.

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

Anderson, B. P.

B. P. Anderson and M. A. Kasevich, “Enhanced loading of a magneto-optic trap from an atomic beam,” Phys. Rev. A 50, R3581–R3584 (1994).
[CrossRef]

Anderson, L. W.

R. S. Schappe, T. Walker, L. W. Anderson, and C. C. Lin, “Absolute electron-impact ionization cross section measurements using a magneto-optical trap,” Phys. Rev. Lett. 76, 4328–4331 (1996).
[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]

Ashmore, J. P.

B. J. Claessens, J. P. Ashmore, R. T. Sang, W. R. MacGillivray, H. C. W. Beijerinck, and E. J. D. Vredenbregt, “Measurement of the photoionization cross section of the (2p)5(3p)3D3 state of neon,” Phys. Rev. A 73, 012706 (2006).
[CrossRef]

Auböck, G.

J. Szczepkowski, E. Paul-Kwiek, G. Auböck, L. Holler, C. Binder, and L. Windholz, “Semiclasical model of magneto-optical trap depth,” Eur. Phys. J. Spec. Top. 144, 265–271 (2007).
[CrossRef]

Bagnato, V. S.

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

V. S. Bagnato, L. G. Marcassa, S. G. Miranda, S. R. Muniz, and A. L. de Oliveira, “Measuring the capture velocity of atoms in a magneto-optical trap as a function of laser intensity,” Phys. Rev. A 62, 013404 (2000).
[CrossRef]

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

S. G. Miranda, S. R. Muniz, G. D. Telles, L. G. Marcassa, K. Helmerson, and V. S. Bagnato, “Dark-spot atomic-beam slowing for on-axis loading of traps,” Phys. Rev. A 59, 882–885 (1999).
[CrossRef]

Bali, S.

D. Hoffmann, S. Bali, and T. Walker, “Trap-depth measurements using ultracold collisions,” Phys. Rev. A 54, R1030–R1033 (1996).
[CrossRef]

S. Bali, D. Hoffmann, and T. Walker, “Novel intensity dependence of ultracold collisions involving repulsive states,” Europhys. Lett. 27, 273–277 (1994).
[CrossRef]

Beijerinck, H. C. W.

B. J. Claessens, J. P. Ashmore, R. T. Sang, W. R. MacGillivray, H. C. W. Beijerinck, and E. J. D. Vredenbregt, “Measurement of the photoionization cross section of the (2p)5(3p)3D3 state of neon,” Phys. Rev. A 73, 012706 (2006).
[CrossRef]

Binder, C.

J. Szczepkowski, E. Paul-Kwiek, G. Auböck, L. Holler, C. Binder, and L. Windholz, “Semiclasical model of magneto-optical trap depth,” Eur. Phys. J. Spec. Top. 144, 265–271 (2007).
[CrossRef]

Bjorkholm, J. E.

Booth, J. L.

J. Van Dongen, C. Zhu, D. Clement, G. Dufour, J. L. Booth, and K. W. Madison, “Trap-depth determination from residual gas collisions,” Phys. Rev. A 84, 022708 (2011).
[CrossRef]

D. E. Fagnan, J. Wang, C. Zhu, P. Djuricanin, B. G. Klappauf, J. L. Booth, and K. W. Madison, “Observation of quantum diffractive collisions using shallow atomic traps,” Phys. Rev. A 80, 022712 (2009).
[CrossRef]

J. L. Booth, J. Van Dongen, P. Lebel, B. G. Klappauf, and K. W. Madison, “Dual-channel amplification in a single-mode diode laser for multi-isotope laser cooling,” J. Opt. Soc. Am. B 24, 2914–2920 (2007).
[CrossRef]

Busch, H. C.

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

Cable, A.

M. Prentiss, A. Cable, J. E. Bjorkholm, S. Chu, E. L. Raab, and D. E. Pritchard, “Atomic-density-dependent losses in an optical trap,” Opt. Lett. 13, 452–454 (1988).
[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]

Caires, A. R. L.

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

Camp, H. A.

M. H. Shah, H. A. Camp, M. L. Trachy, G. Veshapidze, M. A. Gearba, and B. D. DePaola, “Model-independent measurement of the excited fraction in a magneto-optical trap,” Phys. Rev. A 75, 053418 (2007).
[CrossRef]

Chin, C.

V. Vuletić, C. Chin, A. J. Kerman, and S. Chu, “Degenerate raman sideband cooling of trapped cesium atoms at very high atomic densities,” Phys. Rev. Lett. 81, 5768–5771 (1998).
[CrossRef]

Chu, S.

V. Vuletić, C. Chin, A. J. Kerman, and S. Chu, “Degenerate raman sideband cooling of trapped cesium atoms at very high atomic densities,” Phys. Rev. Lett. 81, 5768–5771 (1998).
[CrossRef]

M. Prentiss, A. Cable, J. E. Bjorkholm, S. Chu, E. L. Raab, and D. E. Pritchard, “Atomic-density-dependent losses in an optical trap,” Opt. Lett. 13, 452–454 (1988).
[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]

Claessens, B. J.

B. J. Claessens, J. P. Ashmore, R. T. Sang, W. R. MacGillivray, H. C. W. Beijerinck, and E. J. D. Vredenbregt, “Measurement of the photoionization cross section of the (2p)5(3p)3D3 state of neon,” Phys. Rev. A 73, 012706 (2006).
[CrossRef]

Clement, D.

J. Van Dongen, C. Zhu, D. Clement, G. Dufour, J. L. Booth, and K. W. Madison, “Trap-depth determination from residual gas collisions,” Phys. Rev. A 84, 022708 (2011).
[CrossRef]

Cohen-Tannoudji, C.

Dalgarno, A.

M. Marinescu, H. R. Sadeghpour, and A. Dalgarno, “Dispersion coefficients for alkali-metal dimers,” Phys. Rev. A 49, 982–988 (1994).
[CrossRef]

Dalibard, J.

de Oliveira, A. L.

V. S. Bagnato, L. G. Marcassa, S. G. Miranda, S. R. Muniz, and A. L. de Oliveira, “Measuring the capture velocity of atoms in a magneto-optical trap as a function of laser intensity,” Phys. Rev. A 62, 013404 (2000).
[CrossRef]

DePaola, B. D.

M. H. Shah, H. A. Camp, M. L. Trachy, G. Veshapidze, M. A. Gearba, and B. D. DePaola, “Model-independent measurement of the excited fraction in a magneto-optical trap,” Phys. Rev. A 75, 053418 (2007).
[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]

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, “Isotopic difference in trap loss collisions of laser cooled rubidium atoms,” Phys. Rev. Lett. 69, 897–900 (1992).
[CrossRef]

Djuricanin, P.

D. E. Fagnan, J. Wang, C. Zhu, P. Djuricanin, B. G. Klappauf, J. L. Booth, and K. W. Madison, “Observation of quantum diffractive collisions using shallow atomic traps,” Phys. Rev. A 80, 022712 (2009).
[CrossRef]

Dufour, G.

J. Van Dongen, C. Zhu, D. Clement, G. Dufour, J. L. Booth, and K. W. Madison, “Trap-depth determination from residual gas collisions,” Phys. Rev. A 84, 022708 (2011).
[CrossRef]

Evetts, N.

N. Evetts, “A study of the excited state atoms in cold atom traps and a test of the reif model to determine trap depth,” undergraduate honors thesis (University of British Columbia, 2011); available online at https://circle.ubc.ca/2429/36858 .

Fagnan, D. E.

D. E. Fagnan, J. Wang, C. Zhu, P. Djuricanin, B. G. Klappauf, J. L. Booth, and K. W. Madison, “Observation of quantum diffractive collisions using shallow atomic traps,” Phys. Rev. A 80, 022712 (2009).
[CrossRef]

Frese, D.

B. Ueberholz, S. Kuhr, D. Frese, V. Gomer, and D. Meschede, “Cold collisions in a high-gradient magneto-optical trap,” J. Phys. B: At. Mol. Opt. Phys. 35, 4899–4914 (2002).
[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]

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]

Gearba, M. A.

M. H. Shah, H. A. Camp, M. L. Trachy, G. Veshapidze, M. A. Gearba, and B. D. DePaola, “Model-independent measurement of the excited fraction in a magneto-optical trap,” Phys. Rev. A 75, 053418 (2007).
[CrossRef]

Gensemer, S. D.

S. D. Gensemer, V. Sanchez-Villicana, K. Y. N. Tan, T. T. Grove, and P. L. Gould, “Trap-loss collisions of Rb85 and Rb87: dependence on trap parameters,” Phys. Rev. A 56, 4055–4063 (1997).
[CrossRef]

Glover, R. D.

K. J. Matherson, R. D. Glover, D. E. Laban, and R. T. Sang, “Measurement of low-energy total absolute atomic collision cross sections with the metastable P23 state of neon using a magneto-optical trap,” Phys. Rev. A 78, 042712 (2008).
[CrossRef]

Gomer, V.

B. Ueberholz, S. Kuhr, D. Frese, V. Gomer, and D. Meschede, “Cold collisions in a high-gradient magneto-optical trap,” J. Phys. B: At. Mol. Opt. Phys. 35, 4899–4914 (2002).
[CrossRef]

Gould, P. L.

S. D. Gensemer, V. Sanchez-Villicana, K. Y. N. Tan, T. T. Grove, and P. L. Gould, “Trap-loss collisions of Rb85 and Rb87: dependence on trap parameters,” Phys. Rev. A 56, 4055–4063 (1997).
[CrossRef]

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, “Isotopic difference in trap loss collisions of laser cooled rubidium atoms,” Phys. Rev. Lett. 69, 897–900 (1992).
[CrossRef]

Grove, T. T.

S. D. Gensemer, V. Sanchez-Villicana, K. Y. N. Tan, T. T. Grove, and P. L. Gould, “Trap-loss collisions of Rb85 and Rb87: dependence on trap parameters,” Phys. Rev. A 56, 4055–4063 (1997).
[CrossRef]

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, “Isotopic difference in trap loss collisions of laser cooled rubidium atoms,” Phys. Rev. Lett. 69, 897–900 (1992).
[CrossRef]

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]

Helmerson, K.

S. G. Miranda, S. R. Muniz, G. D. Telles, L. G. Marcassa, K. Helmerson, and V. S. Bagnato, “Dark-spot atomic-beam slowing for on-axis loading of traps,” Phys. Rev. A 59, 882–885 (1999).
[CrossRef]

Hoffmann, D.

D. Hoffmann, S. Bali, and T. Walker, “Trap-depth measurements using ultracold collisions,” Phys. Rev. A 54, R1030–R1033 (1996).
[CrossRef]

S. Bali, D. Hoffmann, and T. Walker, “Novel intensity dependence of ultracold collisions involving repulsive states,” Europhys. Lett. 27, 273–277 (1994).
[CrossRef]

Holler, L.

J. Szczepkowski, E. Paul-Kwiek, G. Auböck, L. Holler, C. Binder, and L. Windholz, “Semiclasical model of magneto-optical trap depth,” Eur. Phys. J. Spec. Top. 144, 265–271 (2007).
[CrossRef]

Jones, D. J.

Julienne, P. S.

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

Kaiser, R.

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

Kasevich, M. A.

B. P. Anderson and M. A. Kasevich, “Enhanced loading of a magneto-optic trap from an atomic beam,” Phys. Rev. A 50, R3581–R3584 (1994).
[CrossRef]

Kawanaka, J.

J. Kawanaka, K. Shimizu, H. Takuma, and F. Shimizu, “Quadratic collisional loss rate of a Li7 trap,” Phys. Rev. A 48, R883–R885 (1993).
[CrossRef]

Kerman, A. J.

V. Vuletić, C. Chin, A. J. Kerman, and S. Chu, “Degenerate raman sideband cooling of trapped cesium atoms at very high atomic densities,” Phys. Rev. Lett. 81, 5768–5771 (1998).
[CrossRef]

Klappauf, B. G.

Kuhr, S.

B. Ueberholz, S. Kuhr, D. Frese, V. Gomer, and D. Meschede, “Cold collisions in a high-gradient magneto-optical trap,” J. Phys. B: At. Mol. Opt. Phys. 35, 4899–4914 (2002).
[CrossRef]

Laban, D. E.

K. J. Matherson, R. D. Glover, D. E. Laban, and R. T. Sang, “Measurement of low-energy total absolute atomic collision cross sections with the metastable P23 state of neon using a magneto-optical trap,” Phys. Rev. A 78, 042712 (2008).
[CrossRef]

Ladouceur, K.

Lebel, P.

Lin, C. C.

R. S. Schappe, T. Walker, L. W. Anderson, and C. C. Lin, “Absolute electron-impact ionization cross section measurements using a magneto-optical trap,” Phys. Rev. Lett. 76, 4328–4331 (1996).
[CrossRef]

Lindquist, K.

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef]

MacGillivray, W. R.

B. J. Claessens, J. P. Ashmore, R. T. Sang, W. R. MacGillivray, H. C. W. Beijerinck, and E. J. D. Vredenbregt, “Measurement of the photoionization cross section of the (2p)5(3p)3D3 state of neon,” Phys. Rev. A 73, 012706 (2006).
[CrossRef]

Madison, K. W.

J. Van Dongen, C. Zhu, D. Clement, G. Dufour, J. L. Booth, and K. W. Madison, “Trap-depth determination from residual gas collisions,” Phys. Rev. A 84, 022708 (2011).
[CrossRef]

D. E. Fagnan, J. Wang, C. Zhu, P. Djuricanin, B. G. Klappauf, J. L. Booth, and K. W. Madison, “Observation of quantum diffractive collisions using shallow atomic traps,” Phys. Rev. A 80, 022712 (2009).
[CrossRef]

K. Ladouceur, B. G. Klappauf, J. Van Dongen, N. Rauhut, B. Schuster, A. K. Mills, D. J. Jones, and K. W. Madison, “Compact laser cooling apparatus for simultaneous cooling of lithium and rubidium,” J. Opt. Soc. Am. B 26, 210–217 (2009).
[CrossRef]

J. L. Booth, J. Van Dongen, P. Lebel, B. G. Klappauf, and K. W. Madison, “Dual-channel amplification in a single-mode diode laser for multi-isotope laser cooling,” J. Opt. Soc. Am. B 24, 2914–2920 (2007).
[CrossRef]

Mancini, M. W.

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

Marcassa, L. G.

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

V. S. Bagnato, L. G. Marcassa, S. G. Miranda, S. R. Muniz, and A. L. de Oliveira, “Measuring the capture velocity of atoms in a magneto-optical trap as a function of laser intensity,” Phys. Rev. A 62, 013404 (2000).
[CrossRef]

S. G. Miranda, S. R. Muniz, G. D. Telles, L. G. Marcassa, K. Helmerson, and V. S. Bagnato, “Dark-spot atomic-beam slowing for on-axis loading of traps,” Phys. Rev. A 59, 882–885 (1999).
[CrossRef]

Marinescu, M.

M. Marinescu, H. R. Sadeghpour, and A. Dalgarno, “Dispersion coefficients for alkali-metal dimers,” Phys. Rev. A 49, 982–988 (1994).
[CrossRef]

Matherson, K. J.

K. J. Matherson, R. D. Glover, D. E. Laban, and R. T. Sang, “Measurement of low-energy total absolute atomic collision cross sections with the metastable P23 state of neon using a magneto-optical trap,” Phys. Rev. A 78, 042712 (2008).
[CrossRef]

Meschede, D.

B. Ueberholz, S. Kuhr, D. Frese, V. Gomer, and D. Meschede, “Cold collisions in a high-gradient magneto-optical trap,” J. Phys. B: At. Mol. Opt. Phys. 35, 4899–4914 (2002).
[CrossRef]

Metcalf, H. J.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, 1999).

Mills, A. K.

Miranda, S. G.

V. S. Bagnato, L. G. Marcassa, S. G. Miranda, S. R. Muniz, and A. L. de Oliveira, “Measuring the capture velocity of atoms in a magneto-optical trap as a function of laser intensity,” Phys. Rev. A 62, 013404 (2000).
[CrossRef]

S. G. Miranda, S. R. Muniz, G. D. Telles, L. G. Marcassa, K. Helmerson, and V. S. Bagnato, “Dark-spot atomic-beam slowing for on-axis loading of traps,” Phys. Rev. A 59, 882–885 (1999).
[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]

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]

Muniz, S. R.

V. S. Bagnato, L. G. Marcassa, S. G. Miranda, S. R. Muniz, and A. L. de Oliveira, “Measuring the capture velocity of atoms in a magneto-optical trap as a function of laser intensity,” Phys. Rev. A 62, 013404 (2000).
[CrossRef]

S. G. Miranda, S. R. Muniz, G. D. Telles, L. G. Marcassa, K. Helmerson, and V. S. Bagnato, “Dark-spot atomic-beam slowing for on-axis loading of traps,” Phys. Rev. A 59, 882–885 (1999).
[CrossRef]

Overstreet, K. R.

Patil, S. H.

S. H. Patil and K. T. Tang, “Multipolar polarizabilities and two- and three-body dispersion coefficients for alkali isoelectronic sequences,” J. Chem. Phys. 106, 2298–2305 (1997).
[CrossRef]

Paul-Kwiek, E.

J. Szczepkowski, E. Paul-Kwiek, G. Auböck, L. Holler, C. Binder, and L. Windholz, “Semiclasical model of magneto-optical trap depth,” Eur. Phys. J. Spec. Top. 144, 265–271 (2007).
[CrossRef]

Prentiss, M.

M. Prentiss, A. Cable, J. E. Bjorkholm, S. Chu, E. L. Raab, and D. E. Pritchard, “Atomic-density-dependent losses in an optical trap,” Opt. Lett. 13, 452–454 (1988).
[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]

Pritchard, D. E.

M. Prentiss, A. Cable, J. E. Bjorkholm, S. Chu, E. L. Raab, and D. E. Pritchard, “Atomic-density-dependent losses in an optical trap,” Opt. Lett. 13, 452–454 (1988).
[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]

Raab, E. L.

M. Prentiss, A. Cable, J. E. Bjorkholm, S. Chu, E. L. Raab, and D. E. Pritchard, “Atomic-density-dependent losses in an optical trap,” Opt. Lett. 13, 452–454 (1988).
[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]

Rauhut, N.

Reif, F.

F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, 1998).

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]

Sadeghpour, H. R.

M. Marinescu, H. R. Sadeghpour, and A. Dalgarno, “Dispersion coefficients for alkali-metal dimers,” Phys. Rev. A 49, 982–988 (1994).
[CrossRef]

Sanchez-Villicana, V.

S. D. Gensemer, V. Sanchez-Villicana, K. Y. N. Tan, T. T. Grove, and P. L. Gould, “Trap-loss collisions of Rb85 and Rb87: dependence on trap parameters,” Phys. Rev. A 56, 4055–4063 (1997).
[CrossRef]

Sang, R. T.

K. J. Matherson, R. D. Glover, D. E. Laban, and R. T. Sang, “Measurement of low-energy total absolute atomic collision cross sections with the metastable P23 state of neon using a magneto-optical trap,” Phys. Rev. A 78, 042712 (2008).
[CrossRef]

B. J. Claessens, J. P. Ashmore, R. T. Sang, W. R. MacGillivray, H. C. W. Beijerinck, and E. J. D. Vredenbregt, “Measurement of the photoionization cross section of the (2p)5(3p)3D3 state of neon,” Phys. Rev. A 73, 012706 (2006).
[CrossRef]

Schappe, R. S.

R. S. Schappe, T. Walker, L. W. Anderson, and C. C. Lin, “Absolute electron-impact ionization cross section measurements using a magneto-optical trap,” Phys. Rev. Lett. 76, 4328–4331 (1996).
[CrossRef]

Schuster, B.

Schwettmann, A.

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]

Shaffer, J. P.

Shaffer, M. K.

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

Shah, M. H.

M. H. Shah, H. A. Camp, M. L. Trachy, G. Veshapidze, M. A. Gearba, and B. D. DePaola, “Model-independent measurement of the excited fraction in a magneto-optical trap,” Phys. Rev. A 75, 053418 (2007).
[CrossRef]

Shimizu, F.

J. Kawanaka, K. Shimizu, H. Takuma, and F. Shimizu, “Quadratic collisional loss rate of a Li7 trap,” Phys. Rev. A 48, R883–R885 (1993).
[CrossRef]

Shimizu, K.

J. Kawanaka, K. Shimizu, H. Takuma, and F. Shimizu, “Quadratic collisional loss rate of a Li7 trap,” Phys. Rev. A 48, R883–R885 (1993).
[CrossRef]

Stephens, M.

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef]

Sukenik, C. I.

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, “Trap loss in a dual-species Rb-Ar* magneto-optical trap,” Phys. Rev. A 73, 023406 (2006).
[CrossRef]

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]

Szczepkowski, J.

J. Szczepkowski, E. Paul-Kwiek, G. Auböck, L. Holler, C. Binder, and L. Windholz, “Semiclasical model of magneto-optical trap depth,” Eur. Phys. J. Spec. Top. 144, 265–271 (2007).
[CrossRef]

Takuma, H.

J. Kawanaka, K. Shimizu, H. Takuma, and F. Shimizu, “Quadratic collisional loss rate of a Li7 trap,” Phys. Rev. A 48, R883–R885 (1993).
[CrossRef]

Tallant, J.

Tan, K. Y. N.

S. D. Gensemer, V. Sanchez-Villicana, K. Y. N. Tan, T. T. Grove, and P. L. Gould, “Trap-loss collisions of Rb85 and Rb87: dependence on trap parameters,” Phys. Rev. A 56, 4055–4063 (1997).
[CrossRef]

Tan, K.-Y. N.

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, “Isotopic difference in trap loss collisions of laser cooled rubidium atoms,” Phys. Rev. Lett. 69, 897–900 (1992).
[CrossRef]

Tang, K. T.

S. H. Patil and K. T. Tang, “Multipolar polarizabilities and two- and three-body dispersion coefficients for alkali isoelectronic sequences,” J. Chem. Phys. 106, 2298–2305 (1997).
[CrossRef]

Telles, G. D.

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

S. G. Miranda, S. R. Muniz, G. D. Telles, L. G. Marcassa, K. Helmerson, and V. S. Bagnato, “Dark-spot atomic-beam slowing for on-axis loading of traps,” Phys. Rev. A 59, 882–885 (1999).
[CrossRef]

Trachy, M. L.

M. H. Shah, H. A. Camp, M. L. Trachy, G. Veshapidze, M. A. Gearba, and B. D. DePaola, “Model-independent measurement of the excited fraction in a magneto-optical trap,” Phys. Rev. A 75, 053418 (2007).
[CrossRef]

Ueberholz, B.

B. Ueberholz, S. Kuhr, D. Frese, V. Gomer, and D. Meschede, “Cold collisions in a high-gradient magneto-optical trap,” J. Phys. B: At. Mol. Opt. Phys. 35, 4899–4914 (2002).
[CrossRef]

van der Straten, P.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, 1999).

Van Dongen, J.

Veshapidze, G.

M. H. Shah, H. A. Camp, M. L. Trachy, G. Veshapidze, M. A. Gearba, and B. D. DePaola, “Model-independent measurement of the excited fraction in a magneto-optical trap,” Phys. Rev. A 75, 053418 (2007).
[CrossRef]

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]

Vredenbregt, E. J. D.

B. J. Claessens, J. P. Ashmore, R. T. Sang, W. R. MacGillivray, H. C. W. Beijerinck, and E. J. D. Vredenbregt, “Measurement of the photoionization cross section of the (2p)5(3p)3D3 state of neon,” Phys. Rev. A 73, 012706 (2006).
[CrossRef]

Vuletic, V.

V. Vuletić, C. Chin, A. J. Kerman, and S. Chu, “Degenerate raman sideband cooling of trapped cesium atoms at very high atomic densities,” Phys. Rev. Lett. 81, 5768–5771 (1998).
[CrossRef]

Walker, T.

R. S. Schappe, T. Walker, L. W. Anderson, and C. C. Lin, “Absolute electron-impact ionization cross section measurements using a magneto-optical trap,” Phys. Rev. Lett. 76, 4328–4331 (1996).
[CrossRef]

D. Hoffmann, S. Bali, and T. Walker, “Trap-depth measurements using ultracold collisions,” Phys. Rev. A 54, R1030–R1033 (1996).
[CrossRef]

S. Bali, D. Hoffmann, and T. Walker, “Novel intensity dependence of ultracold collisions involving repulsive states,” Europhys. Lett. 27, 273–277 (1994).
[CrossRef]

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]

Wallace, C. D.

C. D. Wallace, T. P. Dinneen, K.-Y. N. Tan, T. T. Grove, and P. L. Gould, “Isotopic difference in trap loss collisions of laser cooled rubidium atoms,” Phys. Rev. Lett. 69, 897–900 (1992).
[CrossRef]

Wang, J.

D. E. Fagnan, J. Wang, C. Zhu, P. Djuricanin, B. G. Klappauf, J. L. Booth, and K. W. Madison, “Observation of quantum diffractive collisions using shallow atomic traps,” Phys. Rev. A 80, 022712 (2009).
[CrossRef]

Weiner, J.

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

Wieman, C.

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef]

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]

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]

Wilkowski, D.

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

Windholz, L.

J. Szczepkowski, E. Paul-Kwiek, G. Auböck, L. Holler, C. Binder, and L. Windholz, “Semiclasical model of magneto-optical trap depth,” Eur. Phys. J. Spec. Top. 144, 265–271 (2007).
[CrossRef]

Wineland, D. J.

Zabawa, P.

Zhu, C.

J. Van Dongen, C. Zhu, D. Clement, G. Dufour, J. L. Booth, and K. W. Madison, “Trap-depth determination from residual gas collisions,” Phys. Rev. A 84, 022708 (2011).
[CrossRef]

D. E. Fagnan, J. Wang, C. Zhu, P. Djuricanin, B. G. Klappauf, J. L. Booth, and K. W. Madison, “Observation of quantum diffractive collisions using shallow atomic traps,” Phys. Rev. A 80, 022712 (2009).
[CrossRef]

Zilio, S.

J. Weiner, V. S. Bagnato, S. Zilio, and P. S. Julienne, “Experiments and theory in cold and ultracold collisions,” Rev. Mod. Phys. 71, 1–85 (1999).
[CrossRef]

Braz. J. Phys.

A. R. L. Caires, G. D. Telles, M. W. Mancini, L. G. Marcassa, V. S. Bagnato, D. Wilkowski, and R. Kaiser, “Intensity dependence for trap loss rate in a magneto-optical trap of strontium,” Braz. J. Phys. 34, 1504–1509 (2004).
[CrossRef]

Eur. Phys. J. Spec. Top.

J. Szczepkowski, E. Paul-Kwiek, G. Auböck, L. Holler, C. Binder, and L. Windholz, “Semiclasical model of magneto-optical trap depth,” Eur. Phys. J. Spec. Top. 144, 265–271 (2007).
[CrossRef]

Europhys. Lett.

S. Bali, D. Hoffmann, and T. Walker, “Novel intensity dependence of ultracold collisions involving repulsive states,” Europhys. Lett. 27, 273–277 (1994).
[CrossRef]

J. Chem. Phys.

S. H. Patil and K. T. Tang, “Multipolar polarizabilities and two- and three-body dispersion coefficients for alkali isoelectronic sequences,” J. Chem. Phys. 106, 2298–2305 (1997).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B: At. Mol. Opt. Phys.

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Opt. Express

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Phys. Rev. A

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of the vapor MOT cell used in these experiments. The glass cell measured 1cm×1cm×6cm, and the MOT was configured as a retroreflection MOT. In addition to the cooling and repump beams (the six laser beams shown intersecting in the center of the magnetic field coils), a photoassociation laser (drawn as the narrow laser entering the end face of the cell) was used to determine the depth of each MOT. See text for details.

Fig. 2.
Fig. 2.

As a verification of the Reif model, the background rubidium density was held fixed, and the scaled loading rate parameter, Mi=αγscstdRi, as a function of the MOT trap depth squared, Utrap2, is shown. The linear dependence agrees with the prediction of the Reif model.

Fig. 3.
Fig. 3.

Trap depths predicted from the loading rate parameters, Upred, plotted as a function of the trap depths measured using the modified Hoffmann technique (see text), Umeas. The predicted values were calculated using Eq. (8) scaled to the 1.34 (0.12) K trap. A trap from the center of the measured range was selected to reduce the error due to extrapolation at either end of the measurement range. The solid line (slope equal to 1 and intercept equal to 0) indicates ideal agreement between the predicted and measured trap depths.

Fig. 4.
Fig. 4.

Plot of the loss rate from a magnetic trap, ΓMT, as a function of the initial loading rate (MR) of a standard MOT. The linear relationship between these two parameters indicates that the MOT loading rate is linearly proportional to the background Rb85 density, nRb.

Fig. 5.
Fig. 5.

Loss of atoms from a magnetic trap over time. These data, collected as described in the text, were then fit to an exponential decay to extract ΓMT.

Fig. 6.
Fig. 6.

Plot of the initial MOT loading rate parameter, M, as a function of the background rubidium density, nRb, for MOTs of different depths (diamonds, 0.52  K; filled circles, 0.74  K; squares, 0.86  K; open circles, 1.34  K; stars, 1.44  K; triangles, 1.77  K). The slopes of these plots, Ei, should scale with the MOT trap depth squared [see Eq. (22)]. Removing this trap depth dependence allows an estimation of the relationship between the capture velocity, vc, and the escape velocity, ve, in a MOT.

Fig. 7.
Fig. 7.

The proportionality constants from Eq. (16) can be determined from a plot of E as a function of Utrap2. The slope of this plot is 11.93(0.25)×109Vcm3s1K2. The intercept was held fixed at 0.0 in accordance with the Reif model.

Fig. 8.
Fig. 8.

The photoassociation-related MOT loss parameter, J, as a function of the catalysis laser duty factor, d (MOT pump laser detuning was 12MHz at an intensity of 7.5mWcm2), is shown for three different catalysis laser detunings: 19.8 GHz (triangles), 42.8 GHz (squares), and 52.7 GHz (circles). The slopes of these plots are proportional to βcl, with an increase in slope indicating more photoassociation-induced losses from the MOT. Care was taken to insure that the measurements were made at low duty factors to avoid any strong perturbation of the MOT density.

Fig. 9.
Fig. 9.

Measured values of (βcln¯ssΓ+βn¯ss) as a function of the catalysis laser detuning, Δ, for a MOT having a cooling laser detuning of 12MHz and intensity of 7.5mWcm2. The onset of the observed maximum in the catalysis laser-induced photoassociation loss was at (56±5)GHz, corresponding to a trap depth of (1.34±0.12)K. The solid vertical line indicates the estimated onset of the maximum of the catalysis laser-induced losses with the dashed lines indicating the uncertainty range. (Note: the error bars on the data are the same size as or smaller than the symbols.)

Tables (3)

Tables Icon

Table 1. Measured Effective Trap Depth for a Rb85 MOT Based on Catalysis Laser Photo-Association Losses (Utrap)a

Tables Icon

Table 2. Loading Rate Parameters, M, Measured Trap Depths, and Predicted Trap Depths for Various Rb85 MOTsa

Tables Icon

Table 3. Estimates for the Reif Prefactors, α, γsc, and the Trap Area, A

Equations (26)

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dNdt=RΓNβnMOT2(r,t)dV.
Neq=Rτ=0.1Aσ(vcvp)4.
dN=nf(v)d3v·vcos(θ)dAdt.
f(v)=(m2πkBT)3/2emv2/(2kBT).
R=dNcdt=2Avc4nπ2vth3,
vc2=2b2Utrapm.
R=(8b4Aπ2m2vth3)Utrap2n.
U2=U1R2R1
V(t)=αγscN(t),
N(t)=Nss(1eγt1+ξeγt),
Nss=RΓ+βn¯ss,
N(t)=Nss(1eγt).
V.=αγscN.=αγsc(RΓNβnMOT2(r,t)dV).
V.0=αγscN.0=αγscR.
γsci=ViVstdγscstd.
Mi=(VstdVi)V0i.=αγscstdRi=αγscstd(8b4Aπ2m2vth3)Ui2n.
Γ=iniσvRb,i,
ΓMT=nRbσvRb,Rb+Γb.
Mi=αγscstdRi=kinRb.
ΓMT=(σvRb,Rbki)·Mi+Γb.
f=f0eΓMTt,
Ei=MinRb=αγscstdRinRb=αγscstd(8b4Aπ2m2vth3)Utrap2.
vc=1.29(0.12)ve.
dNdt=RΓN(β+d·βcl)nMOT2(r,t)dV.
Nss=RΓ+(β+d·βcl)n¯ss.
J=Vss0Vss1=Nss0Nss1=(βcln¯ssΓ+βn¯ss)·d,

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