Abstract

We measure the number of atoms N trapped in a conventional vapor-cell magneto-optic trap (MOT) using beams that have a diameter d in the range 1–5 mm. We show that the Nd3.6 scaling law observed for larger MOTs is a robust approximation for optimized MOTs with beam diameters as small as 3 mm. For smaller beams, the description of the scaling depends on how d is defined. The most consistent picture of the scaling is obtained when d is defined as the diameter where the intensity profile of the trapping beams decreases to the saturation intensity. Using this definition, N scales as d6 for d<2.3mm but, at larger d, N still scales as d3.6.

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  1. J. Kitching, S. Knappe, and E. A. Donley, IEEE Sens. J. 11, 1749 (2011).
    [CrossRef]
  2. G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
    [CrossRef]
  3. C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
    [CrossRef]
  4. K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
    [CrossRef]
  5. K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526(1992).
    [CrossRef]
  6. S. Pollock, J. P. Cotter, A. Laliotis, F. Ramirez-Martinez, and E. A. Hinds, New J. Phys. 13, 043029 (2011).
    [CrossRef]
  7. C. J. Myatt, N. R. Newbury, and C. E. Wieman, Opt. Lett. 18, 649 (1993).
    [CrossRef]
  8. P. Kohns, P. Buch, W. Süptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
    [CrossRef]
  9. R. Lutwak, D. Emmons, R. M. Garvey, and P. Vlitas, in Proceedings of the 33rd Annual Precise Time and Time Interval (PTTI) Meeting (2001).
  10. H. J. McGuinness, A. V. Rakholia, and G. W. Biedermann, Appl. Phys. Lett. 100, 011106 (2012).
    [CrossRef]

2012 (1)

H. J. McGuinness, A. V. Rakholia, and G. W. Biedermann, Appl. Phys. Lett. 100, 011106 (2012).
[CrossRef]

2011 (2)

S. Pollock, J. P. Cotter, A. Laliotis, F. Ramirez-Martinez, and E. A. Hinds, New J. Phys. 13, 043029 (2011).
[CrossRef]

J. Kitching, S. Knappe, and E. A. Donley, IEEE Sens. J. 11, 1749 (2011).
[CrossRef]

1999 (1)

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

1993 (2)

C. J. Myatt, N. R. Newbury, and C. E. Wieman, Opt. Lett. 18, 649 (1993).
[CrossRef]

P. Kohns, P. Buch, W. Süptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

1992 (2)

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef]

K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526(1992).
[CrossRef]

1990 (1)

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef]

Biedermann, G. W.

H. J. McGuinness, A. V. Rakholia, and G. W. Biedermann, Appl. Phys. Lett. 100, 011106 (2012).
[CrossRef]

Buch, P.

P. Kohns, P. Buch, W. Süptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Chang, S.

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

Chu, S.

Clairon, A.

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

Cotter, J. P.

S. Pollock, J. P. Cotter, A. Laliotis, F. Ramirez-Martinez, and E. A. Hinds, New J. Phys. 13, 043029 (2011).
[CrossRef]

Csambal, C.

P. Kohns, P. Buch, W. Süptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Donley, E. A.

J. Kitching, S. Knappe, and E. A. Donley, IEEE Sens. J. 11, 1749 (2011).
[CrossRef]

Emmons, D.

R. Lutwak, D. Emmons, R. M. Garvey, and P. Vlitas, in Proceedings of the 33rd Annual Precise Time and Time Interval (PTTI) Meeting (2001).

Ertmer, W.

P. Kohns, P. Buch, W. Süptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Garvey, R. M.

R. Lutwak, D. Emmons, R. M. Garvey, and P. Vlitas, in Proceedings of the 33rd Annual Precise Time and Time Interval (PTTI) Meeting (2001).

Gibble, K. E.

Hinds, E. A.

S. Pollock, J. P. Cotter, A. Laliotis, F. Ramirez-Martinez, and E. A. Hinds, New J. Phys. 13, 043029 (2011).
[CrossRef]

Kasapi, S.

Kitching, J.

J. Kitching, S. Knappe, and E. A. Donley, IEEE Sens. J. 11, 1749 (2011).
[CrossRef]

Knappe, S.

J. Kitching, S. Knappe, and E. A. Donley, IEEE Sens. J. 11, 1749 (2011).
[CrossRef]

Kohns, P.

P. Kohns, P. Buch, W. Süptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Laliotis, A.

S. Pollock, J. P. Cotter, A. Laliotis, F. Ramirez-Martinez, and E. A. Hinds, New J. Phys. 13, 043029 (2011).
[CrossRef]

Laurent, Ph.

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

Lemonde, P.

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

Lindquist, K.

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef]

Luiten, A. N.

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

Lutwak, R.

R. Lutwak, D. Emmons, R. M. Garvey, and P. Vlitas, in Proceedings of the 33rd Annual Precise Time and Time Interval (PTTI) Meeting (2001).

Mann, A. G.

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

McGuinness, H. J.

H. J. McGuinness, A. V. Rakholia, and G. W. Biedermann, Appl. Phys. Lett. 100, 011106 (2012).
[CrossRef]

Monroe, C.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef]

Myatt, C. J.

Newbury, N. R.

Pollock, S.

S. Pollock, J. P. Cotter, A. Laliotis, F. Ramirez-Martinez, and E. A. Hinds, New J. Phys. 13, 043029 (2011).
[CrossRef]

Rakholia, A. V.

H. J. McGuinness, A. V. Rakholia, and G. W. Biedermann, Appl. Phys. Lett. 100, 011106 (2012).
[CrossRef]

Ramirez-Martinez, F.

S. Pollock, J. P. Cotter, A. Laliotis, F. Ramirez-Martinez, and E. A. Hinds, New J. Phys. 13, 043029 (2011).
[CrossRef]

Robinson, H.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef]

Salomon, C.

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

Santarelli, G.

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

Stephens, M.

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef]

Süptitz, W.

P. Kohns, P. Buch, W. Süptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

Swann, W.

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef]

Vlitas, P.

R. Lutwak, D. Emmons, R. M. Garvey, and P. Vlitas, in Proceedings of the 33rd Annual Precise Time and Time Interval (PTTI) Meeting (2001).

Wieman, C.

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef]

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef]

Wieman, C. E.

Appl. Phys. Lett. (1)

H. J. McGuinness, A. V. Rakholia, and G. W. Biedermann, Appl. Phys. Lett. 100, 011106 (2012).
[CrossRef]

Europhys. Lett. (1)

P. Kohns, P. Buch, W. Süptitz, C. Csambal, and W. Ertmer, Europhys. Lett. 22, 517 (1993).
[CrossRef]

IEEE Sens. J. (1)

J. Kitching, S. Knappe, and E. A. Donley, IEEE Sens. J. 11, 1749 (2011).
[CrossRef]

New J. Phys. (1)

S. Pollock, J. P. Cotter, A. Laliotis, F. Ramirez-Martinez, and E. A. Hinds, New J. Phys. 13, 043029 (2011).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

K. Lindquist, M. Stephens, and C. Wieman, Phys. Rev. A 46, 4082 (1992).
[CrossRef]

Phys. Rev. Lett. (2)

G. Santarelli, Ph. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619 (1999).
[CrossRef]

C. Monroe, W. Swann, H. Robinson, and C. Wieman, Phys. Rev. Lett. 65, 1571 (1990).
[CrossRef]

Other (1)

R. Lutwak, D. Emmons, R. M. Garvey, and P. Vlitas, in Proceedings of the 33rd Annual Precise Time and Time Interval (PTTI) Meeting (2001).

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Figures (3)

Fig. 1.
Fig. 1.

Trapped atom number as a function of beam power compared to predictions of the two-level model for two definitions of d. For the dashed curve, d=dB=2.25mm. In this case, the atom number decreases at high P because power broadening reduces the maximum slowing force. For the solid curve, d=dP for a Gaussian beam with 2w0=2.25mm. In this case, the atom number rises with P because the size of the stopping region increases. For the simulations, δ=2γ (γ is the natural linewidth) and s=P/(πd2)/Isat (the results are not sensitive to this choice for s). The simulations have been normalized to agree with the data at P=2mW. The data were taken with δ=2γ and dB/dz34G/cm.

Fig. 2.
Fig. 2.

Atom number as a function of effective beam diameter dP (see text for definition) for (a) δ=2γ and (b) δ=3γ. For all these measurements, dB/dz34G/cm. The magnetic gradient was optimized for MOTs with dp3mm and δ=2γ, but, in practice, we found that N was not very sensitive to dB/dz. The maximum intensity and the intensity profile of the trapping beams vary significantly, but these changes are mostly accounted for by dP. The scatter in the data is due to day to day variations in the alignment of the MOT and some intensity dependence that is not accounted for by dP. The lines are fits to the data with the scaling exponents fixed.

Fig. 3.
Fig. 3.

Scaling of atom number with trap size illustrated with results from [4,5,10] and a subset of our δ=2γ data corresponding to the highest intensities we studied. For the MOTs of [4,5,10], we define the beam size the same way as the original authors. In our data, one can see the ratio dP/dB is larger for the smaller beams. This is because the smaller beams are more intense.

Equations (1)

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N0.1Aσ(vcvt)4,

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