Abstract

We have studied the locomotion track of 87Rb Bose-Einstein condensate during decompressing the trap into the center of the glass cell in a quadrupole-Ioffe configuration trap. In order to change the position of the BEC, the current in the quadrupole coils is reduced while the current in the Ioffe coil keeps constant. Because of the strongly reduced trap frequencies of the moved trap, the BEC considerably sags down due to the gravity. Thus an inflexion point exists in the process of moving BEC. When rubidium atoms go over the inflexion point, they cannot keep in balance under the gravity and the force provided by a magnetic field, and flow downward and towards Ioffe coil. By utilizing this effect, the trapped atoms with the spin state |F = 2, mF = 1⋩, which are left over in the BEC, can be separated from the BEC of |F = 2, mF = 2⋩ state.

© 2010 Optical Society of America

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  1. Y. Miroshnychenko, D. Schrader, S. Kuhr,W. Alt, I. Dotsenko, M. Khudaverdyan, A. Rauschenbeutel, and D. Meschede, "Continued imaging of the transport of a single neutral atom," Opt. Express 11, 3498-3502 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
    [CrossRef] [PubMed]
  4. J. Arlt, O . Marago, S .Webster, S . Hopkins, and C. J . Foot, "A pyramidal magneto-optical trap as a source of slow atoms," Opt. Commun. 157, 303-309 (1998).
    [CrossRef]
  5. A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
    [CrossRef] [PubMed]
  6. L. Fallani, C. Fort, J. E. Lye, and M. Inguscio, "Bose-Einstein condensate in an optical lattice with tunable spacing: transport and static properties," Opt. Express 13, 4303-4313 (2005).
    [CrossRef] [PubMed]
  7. T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
    [CrossRef]
  8. T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
    [CrossRef] [PubMed]
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    [CrossRef]
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  11. H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230401 (2001)
    [CrossRef] [PubMed]
  12. C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  17. X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
    [CrossRef]
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    [CrossRef]
  19. D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).
  20. T. Bergeman, G. Erez, and H. J. Metcalf, "Magnetostatic trapping fields for neutral atoms," Phys. Rev. A 35, 1535-1546 (1987).
    [CrossRef] [PubMed]
  21. D. Xiong, P. Wang, Z. Fu, and J. Zhang, "Evaporative cooling rubidium atoms with microwave radiation," Chin. Opt. Lett.in press.
  22. M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
    [CrossRef]
  23. C. Silber, S. Gunther, C. Marzok, B. Deh, Ph. W. ourteille, and C. Zimmermann, "Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases," Phys. Rev. Lett. 95, 170408 (2005).
    [CrossRef] [PubMed]

2008 (2)

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).

2007 (2)

D. Wei, D. Xiong, H. Chen, P. Wang, L. Guo, and J. Zhang, "Simultaneous Magneto-optical Trpping of Fermionic 40K and Bosonic 87Rb atoms," Chin. Phys. Lett. 24, 1541-1544 (2007).
[CrossRef]

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

2006 (1)

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 159 (2006)
[CrossRef]

2005 (4)

L. Fallani, C. Fort, J. E. Lye, and M. Inguscio, "Bose-Einstein condensate in an optical lattice with tunable spacing: transport and static properties," Opt. Express 13, 4303-4313 (2005).
[CrossRef] [PubMed]

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[CrossRef]

C. Silber, S. Gunther, C. Marzok, B. Deh, Ph. W. ourteille, and C. Zimmermann, "Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases," Phys. Rev. Lett. 95, 170408 (2005).
[CrossRef] [PubMed]

2004 (1)

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

2003 (1)

2002 (3)

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
[CrossRef] [PubMed]

R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002)

2001 (2)

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230401 (2001)
[CrossRef] [PubMed]

W. Wohlleben, F. Chevy, K. Madison, and J. Dalibard, "An atom faucet," Eur. Phys. J. D 15, 237-244 (2001).
[CrossRef]

1999 (1)

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]

1998 (2)

T. Esslinger, I. Bloch, and T. W. Hansch, "Magnetostatic trapping fields for natural atoms," Phys. Rev. A 58, R2664-R2267 (1998).
[CrossRef]

J. Arlt, O . Marago, S .Webster, S . Hopkins, and C. J . Foot, "A pyramidal magneto-optical trap as a source of slow atoms," Opt. Commun. 157, 303-309 (1998).
[CrossRef]

1996 (1)

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
[CrossRef] [PubMed]

1987 (1)

T. Bergeman, G. Erez, and H. J. Metcalf, "Magnetostatic trapping fields for neutral atoms," Phys. Rev. A 35, 1535-1546 (1987).
[CrossRef] [PubMed]

Alt, W.

Anderson, M. H.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
[CrossRef] [PubMed]

Andersson, L. M.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Arlt, J.

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

J. Arlt, O . Marago, S .Webster, S . Hopkins, and C. J . Foot, "A pyramidal magneto-optical trap as a source of slow atoms," Opt. Commun. 157, 303-309 (1998).
[CrossRef]

Bagnato, V. 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]

Bar-Joseph, I.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Barrett, M. D.

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

Becher, C.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

Bergeman, T.

T. Bergeman, G. Erez, and H. J. Metcalf, "Magnetostatic trapping fields for neutral atoms," Phys. Rev. A 35, 1535-1546 (1987).
[CrossRef] [PubMed]

Blatt, R.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

Bloch, I.

T. Esslinger, I. Bloch, and T. W. Hansch, "Magnetostatic trapping fields for natural atoms," Phys. Rev. A 58, R2664-R2267 (1998).
[CrossRef]

Chang, M.-S.

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

Chapman, M. S.

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

Chen, H.

D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).

D. Wei, D. Xiong, H. Chen, P. Wang, L. Guo, and J. Zhang, "Simultaneous Magneto-optical Trpping of Fermionic 40K and Bosonic 87Rb atoms," Chin. Phys. Lett. 24, 1541-1544 (2007).
[CrossRef]

Chen, S.

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[CrossRef]

Chen, X.

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[CrossRef]

Chevy, F.

W. Wohlleben, F. Chevy, K. Madison, and J. Dalibard, "An atom faucet," Eur. Phys. J. D 15, 237-244 (2001).
[CrossRef]

Chikkatur, A. P.

T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
[CrossRef] [PubMed]

Cornell, E. A.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
[CrossRef] [PubMed]

Corwin, K. L.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
[CrossRef] [PubMed]

Dalibard, J.

W. Wohlleben, F. Chevy, K. Madison, and J. Dalibard, "An atom faucet," Eur. Phys. J. D 15, 237-244 (2001).
[CrossRef]

Deh, B.

C. Silber, S. Gunther, C. Marzok, B. Deh, Ph. W. ourteille, and C. Zimmermann, "Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases," Phys. Rev. Lett. 95, 170408 (2005).
[CrossRef] [PubMed]

Denschlag, J.

R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002)

Denschlag, J. H.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 159 (2006)
[CrossRef]

Dotsenko, I.

Erez, G.

T. Bergeman, G. Erez, and H. J. Metcalf, "Magnetostatic trapping fields for neutral atoms," Phys. Rev. A 35, 1535-1546 (1987).
[CrossRef] [PubMed]

Ertmer, W.

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

Eschner, J.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

Esslinger, T.

T. Esslinger, I. Bloch, and T. W. Hansch, "Magnetostatic trapping fields for natural atoms," Phys. Rev. A 58, R2664-R2267 (1998).
[CrossRef]

Falke, St.

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

Fallani, L.

Folman, R.

R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002)

Foot, C. J

J. Arlt, O . Marago, S .Webster, S . Hopkins, and C. J . Foot, "A pyramidal magneto-optical trap as a source of slow atoms," Opt. Commun. 157, 303-309 (1998).
[CrossRef]

Fort, C.

Fortagh, J.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230401 (2001)
[CrossRef] [PubMed]

Fortier, K. M.

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

Frese, D.

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

Fu, Z.

D. Xiong, P. Wang, Z. Fu, and J. Zhang, "Evaporative cooling rubidium atoms with microwave radiation," Chin. Opt. Lett.in press.

G¨orlitz, A.

T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
[CrossRef] [PubMed]

Gao, F.

D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).

Grossmann, A.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230401 (2001)
[CrossRef] [PubMed]

Groth, S.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Gunther, S.

C. Silber, S. Gunther, C. Marzok, B. Deh, Ph. W. ourteille, and C. Zimmermann, "Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases," Phys. Rev. Lett. 95, 170408 (2005).
[CrossRef] [PubMed]

Guo, L.

D. Wei, D. Xiong, H. Chen, P. Wang, L. Guo, and J. Zhang, "Simultaneous Magneto-optical Trpping of Fermionic 40K and Bosonic 87Rb atoms," Chin. Phys. Lett. 24, 1541-1544 (2007).
[CrossRef]

Gupta, S.

T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
[CrossRef] [PubMed]

Gustavson, T. L.

T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
[CrossRef] [PubMed]

Hamley, C. D.

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

Hansch, T. W.

T. Esslinger, I. Bloch, and T. W. Hansch, "Magnetostatic trapping fields for natural atoms," Phys. Rev. A 58, R2664-R2267 (1998).
[CrossRef]

Hass, M.

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

Haubrich, D.

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

Henkel, C.

R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002)

Henninger, T.

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

Hofferberth, S.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Hopkins, S

J. Arlt, O . Marago, S .Webster, S . Hopkins, and C. J . Foot, "A pyramidal magneto-optical trap as a source of slow atoms," Opt. Commun. 157, 303-309 (1998).
[CrossRef]

Inguscio, M.

John, S.

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

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]

Khudaverdyan, M.

Klempt, C.

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

Kreuter, A.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

Kruger, P.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002)

Kuhr, S.

Lang, F.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 159 (2006)
[CrossRef]

Leanhardt, A. E.

T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
[CrossRef] [PubMed]

Leibfried, D.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

Leung, V.

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

Lu, Z. T.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
[CrossRef] [PubMed]

Lye, J. E.

Ma, X.

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[CrossRef]

Madison, K.

W. Wohlleben, F. Chevy, K. Madison, and J. Dalibard, "An atom faucet," Eur. Phys. J. D 15, 237-244 (2001).
[CrossRef]

Marago, O

J. Arlt, O . Marago, S .Webster, S . Hopkins, and C. J . Foot, "A pyramidal magneto-optical trap as a source of slow atoms," Opt. Commun. 157, 303-309 (1998).
[CrossRef]

Marzok, C.

C. Silber, S. Gunther, C. Marzok, B. Deh, Ph. W. ourteille, and C. Zimmermann, "Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases," Phys. Rev. Lett. 95, 170408 (2005).
[CrossRef] [PubMed]

Meschede, A.

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

Meschede, D.

Metcalf, H. J.

T. Bergeman, G. Erez, and H. J. Metcalf, "Magnetostatic trapping fields for neutral atoms," Phys. Rev. A 35, 1535-1546 (1987).
[CrossRef] [PubMed]

Miroshnychenko, Y.

Mundt, A. B.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

Ott, H.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230401 (2001)
[CrossRef] [PubMed]

Pritchard, D. E.

T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
[CrossRef] [PubMed]

Rauschenbeutel, A.

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

Y. Miroshnychenko, D. Schrader, S. Kuhr,W. Alt, I. Dotsenko, M. Khudaverdyan, A. Rauschenbeutel, and D. Meschede, "Continued imaging of the transport of a single neutral atom," Opt. Express 11, 3498-3502 (2003).
[CrossRef] [PubMed]

Renn, M. J.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
[CrossRef] [PubMed]

Sauer, J. A.

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

Schlotterbeck, G.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230401 (2001)
[CrossRef] [PubMed]

Schmid, S.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 159 (2006)
[CrossRef]

Schmidt-Kaler, F.

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

Schmiedmayer, J.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002)

Schrader, D.

Schumm, T.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Silber, C.

C. Silber, S. Gunther, C. Marzok, B. Deh, Ph. W. ourteille, and C. Zimmermann, "Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases," Phys. Rev. Lett. 95, 170408 (2005).
[CrossRef] [PubMed]

Thalhammer, G.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 159 (2006)
[CrossRef]

Topic, O.

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

Wang, P.

D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).

D. Wei, D. Xiong, H. Chen, P. Wang, L. Guo, and J. Zhang, "Simultaneous Magneto-optical Trpping of Fermionic 40K and Bosonic 87Rb atoms," Chin. Phys. Lett. 24, 1541-1544 (2007).
[CrossRef]

D. Xiong, P. Wang, Z. Fu, and J. Zhang, "Evaporative cooling rubidium atoms with microwave radiation," Chin. Opt. Lett.in press.

Wang, Y.

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[CrossRef]

Weber, C.

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

Webster, S

J. Arlt, O . Marago, S .Webster, S . Hopkins, and C. J . Foot, "A pyramidal magneto-optical trap as a source of slow atoms," Opt. Commun. 157, 303-309 (1998).
[CrossRef]

Wei, D.

D. Wei, D. Xiong, H. Chen, P. Wang, L. Guo, and J. Zhang, "Simultaneous Magneto-optical Trpping of Fermionic 40K and Bosonic 87Rb atoms," Chin. Phys. Lett. 24, 1541-1544 (2007).
[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. E.

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
[CrossRef] [PubMed]

Wildermuth, S.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Will, J.

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

Winkler, K.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 159 (2006)
[CrossRef]

Wohlleben, W.

W. Wohlleben, F. Chevy, K. Madison, and J. Dalibard, "An atom faucet," Eur. Phys. J. D 15, 237-244 (2001).
[CrossRef]

Xia, L.

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[CrossRef]

Xiong, D.

D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).

D. Wei, D. Xiong, H. Chen, P. Wang, L. Guo, and J. Zhang, "Simultaneous Magneto-optical Trpping of Fermionic 40K and Bosonic 87Rb atoms," Chin. Phys. Lett. 24, 1541-1544 (2007).
[CrossRef]

D. Xiong, P. Wang, Z. Fu, and J. Zhang, "Evaporative cooling rubidium atoms with microwave radiation," Chin. Opt. Lett.in press.

Yang, F.

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[CrossRef]

You, L.

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

Yu, X.

D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).

Zhang, J.

D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).

D. Wei, D. Xiong, H. Chen, P. Wang, L. Guo, and J. Zhang, "Simultaneous Magneto-optical Trpping of Fermionic 40K and Bosonic 87Rb atoms," Chin. Phys. Lett. 24, 1541-1544 (2007).
[CrossRef]

D. Xiong, P. Wang, Z. Fu, and J. Zhang, "Evaporative cooling rubidium atoms with microwave radiation," Chin. Opt. Lett.in press.

Zhang, W.

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

Zhou, X.

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[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]

Zimmermann, C.

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230401 (2001)
[CrossRef] [PubMed]

Adv. At. Mol. Opt. Phys. (1)

R. Folman, P. Kruger, J. Schmiedmayer, J. Denschlag, and C. Henkel, "Microscopic atom optics: from wires to an atom chip," Adv. At. Mol. Opt. Phys. 48, 263-356 (2002)

Chin. Opt. Lett. (1)

D. Xiong, P. Wang, Z. Fu, and J. Zhang, "Evaporative cooling rubidium atoms with microwave radiation," Chin. Opt. Lett.in press.

Chin. Phys. Lett. (3)

X. Ma, S. Chen, F. Yang, L. Xia, X. Zhou, Y. Wang, and X. Chen, "Observation of F = 2 spinor Bose-Einstein condensation in a magnetic field," Chin. Phys. Lett. 22, 1106-1109 (2005)
[CrossRef]

D. Wei, D. Xiong, H. Chen, P. Wang, L. Guo, and J. Zhang, "Simultaneous Magneto-optical Trpping of Fermionic 40K and Bosonic 87Rb atoms," Chin. Phys. Lett. 24, 1541-1544 (2007).
[CrossRef]

D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, "Quantum Degenerate FermiCBose mixtures of 40K and 87Rb atoms in a Quadrupole-Ioffe configuration trap," Chin. Phys. Lett. 23, 843-846 (2008).

Eur. Phys. J. D (2)

C. Klempt, T. Henninger, O. Topic, J. Will, St. Falke, W. Ertmer, and J. Arlt, "Transport of a quantum degenerate heteronuclear Bose-Fermi mixture in a harmonic trap," Eur. Phys. J. D 48,121-126 (2008).
[CrossRef]

W. Wohlleben, F. Chevy, K. Madison, and J. Dalibard, "An atom faucet," Eur. Phys. J. D 15, 237-244 (2001).
[CrossRef]

Nat. Phys. (1)

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

New J. Phys. (2)

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 159 (2006)
[CrossRef]

M. Hass, V. Leung, D. Frese, D. Haubrich, S. John, C. Weber, A. Rauschenbeutel, and A. Meschede, "Speciesselective microwave cooling of a mixture of rubidium and caesium atoms," New J. Phys. 9, 147 (2007).
[CrossRef]

Opt. Commun. (1)

J. Arlt, O . Marago, S .Webster, S . Hopkins, and C. J . Foot, "A pyramidal magneto-optical trap as a source of slow atoms," Opt. Commun. 157, 303-309 (1998).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (2)

T. Esslinger, I. Bloch, and T. W. Hansch, "Magnetostatic trapping fields for natural atoms," Phys. Rev. A 58, R2664-R2267 (1998).
[CrossRef]

T. Bergeman, G. Erez, and H. J. Metcalf, "Magnetostatic trapping fields for neutral atoms," Phys. Rev. A 35, 1535-1546 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (6)

C. Silber, S. Gunther, C. Marzok, B. Deh, Ph. W. ourteille, and C. Zimmermann, "Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases," Phys. Rev. Lett. 95, 170408 (2005).
[CrossRef] [PubMed]

M.-S. Chang, C. D. Hamley, M. D. Barrett, J. A. Sauer, K. M. Fortier, W. Zhang, L. You, and M. S. Chapman, "Observation of Spinor Dynamics in optically trapped 87Rb Bose-Einstein condensates," Phys. Rev. Lett. 92, 140403 (2004)
[CrossRef] [PubMed]

H. Ott, J. Fortagh, G. Schlotterbeck, A. Grossmann, and C. Zimmermann, "Bose-Einstein condensation in a surface microtrap," Phys. Rev. Lett. 87, 230401 (2001)
[CrossRef] [PubMed]

T. L. Gustavson, A. P. Chikkatur, A. E. Leanhardt, A. Gorlitz, S. Gupta, D. E. Pritchard, and W. Ketterle, "Transport of Bose-Einstein condensates with optical tweezers," Phys. Rev. Lett. 88, 020401 (2002)
[CrossRef] [PubMed]

A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Coupling a single atomic quantum bit to a high finesse optical cavity," Phys. Rev. Lett. 89, 103001 (2002).
[CrossRef] [PubMed]

Z. T. Lu, K. L. Corwin, M. J. Renn, M. H. Anderson, E. A. Cornell, and C. E. Wieman, "Low-velocity intense source of stoms from a magneto-optical trap," Phys. Rev. Lett. 77, 3331-3334 (1996).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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]

Other (1)

T. P. Meyrath, "Experiments with Bose-Einstein Condensation in an Optical Box" PhD Thesis (USA:The University of Texas) (2005)

Cited By

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the experimental apparatus showing the QUIC trap setup and a levita-tion coil.

Fig. 2.
Fig. 2.

The locomotion track of 87Rb atoms in spin |F = 2,mF = 2⋩ state during decompressing the trap into the center of the glass cell without the levitating field. The curves with square and trigonal dots are the initial current with 32 and 16 A through the QUIC coils respectively.

Fig. 3.
Fig. 3.

The contour and vector plots of the gradient field in yz-plane during ramping down the current though quadrupole coils. (A), (B), (C), and (D) show the gradient field without considering the effect of gravity and with constant Ioffe current 32 A and the quadrupole current of 32, 24, 16, 13.5 A respectively. (a) to (d) are the case considering the gravity sag for 87 Rb in the state |F = 2, mF = 2⋩.

Fig. 4.
Fig. 4.

Absorption images of 87Rb atoms in F=2 spin state with 1 ms expansion time using MW radiative evaporative cooling. Due to the gravity sag and the character of quadrupole-Ioffe configuration trap, 87Rb atoms in the |F = 2,mF = 1⋩ state is separated from them in the |F = 2,mF = 2 > state during decompressing the Ioffe trap without a levitating field.

Fig. 5.
Fig. 5.

The comparison of 87Rb atomic sample loss in the |F = 2, mF = 1⋩ state before and after its inflexion point. These absorption pictures are taken with 1 ms expansion time.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

B z = μI 2 π 1 [ ( R + ρ ) 2 + ( z A ) 2 ] 1 / 2 [ K ( k 2 ) + R 2 ρ 2 ( z A ) 2 ( R ρ ) 2 + ( z A ) 2 E ( k ) 2 ]
B ρ = μI 2 πρ z A [ ( R + ρ ) 2 + ( z A ) 2 ] 1 / 2 [ K ( k 2 ) + R 2 ρ 2 ( z A ) 2 ( R ρ ) 2 + ( z A ) 2 E ( k ) 2 ]
k 2 = 4 ( R + ρ ) 2 + ( z A ) 2
ρ = x 2 + y 2
F ( r ) = U ( r ) = g F m F μ B B ( r )

Metrics