Abstract

We report on directly measuring the atom number in a Bose- Einstein condensate by the method of optical pumping. Only the branching ratio of the spontaneous decay in the system and the absorption energy of a probe laser beam are required to determine the atom number. The measured absorption energy is not affected by the measurement condition such as the intensity, detuning, and polarization of the probe beam, the magnetic field, etc. We have shown that atom numbers as low as a few thousands can be measured. The atom number is an important parameter in the studies of Bose condensates and its accuracy is greatly improved by this sensitive and robust method.

© 2007 Optical Society of America

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  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor," Science 269, 198-201 (1995).
    [CrossRef]
  2. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Bose-Einstein Condensation in a Gas of Sodium Atoms, " Phys. Rev. Lett. 75, 3969-3973 (1995).
    [CrossRef]
  3. M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Observation of Interference between Two Bose Condensates," Science 275, 637-641 (1997).
    [CrossRef]
  4. M. Greiner, O. Mandel, T. Esslinger, T.W. H¨ansch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature (London) 415, 39-44 (2002).
    [CrossRef]
  5. S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm, "Bose-Einstein Condensation of Molecules," Science 302, 2101-2103 (2003).
    [CrossRef]
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    [CrossRef]
  7. M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, "Observation of Bose-Einstein Condensation of Molecules," Phys. Rev. Lett. 91, 250401 (2003).
    [CrossRef]
  8. L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, "Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature (London) 397, 594-598 (1999).
    [CrossRef]
  9. C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, "Observation of coherent optical information storage in an atomic medium using halted light pulses," Nature (London) 409, 490-493 (2001).
    [CrossRef]
  10. N. S. Ginsberg, S. R. Garner, and L. V. Hau, "Coherent control of optical information with matter wave dynamics," Nature (London) 445, 623-626 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. C. F. Li and G. C. Guo, "Quantum nondemolition measurement of the atom number of a Bose-Einstein condensate," Phys. Lett. A 248, 117-123 (1998).
    [CrossRef]
  14. In a two-level system, the absorption cross section of a laser field is equal to the imaginary part of [3λ 2/(2π)]ρegΓ′/Ω, where ρeg is the amplitude of the density matrix element between the excited state |e> and the ground state |g>, Γ′ is the spontaneous decay rate from |e> to |g>, and Γ is the Rabi frequency of the laser field. For the solution of ρeg, see M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997), Sec. 5.3.2 and Eq. (17.1.20).
  15. Y. C. Chen, Y. A. Liao, L. Hsu, and I. A. Yu, "Simple technique for directly and accurately measuring the number of atoms in a magneto-optical trap," Phys. Rev. A  64, 031401(R) (2001).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2007 (1)

N. S. Ginsberg, S. R. Garner, and L. V. Hau, "Coherent control of optical information with matter wave dynamics," Nature (London) 445, 623-626 (2007).
[CrossRef]

2003 (3)

S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm, "Bose-Einstein Condensation of Molecules," Science 302, 2101-2103 (2003).
[CrossRef]

M. Greiner, C. A. Regal, and D. S. Jin, "Emergence of a molecular Bose-Einstein condensate from a Fermi gas," Nature (London) 426, 537-540 (2003).
[CrossRef]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, "Observation of Bose-Einstein Condensation of Molecules," Phys. Rev. Lett. 91, 250401 (2003).
[CrossRef]

2002 (1)

M. Greiner, O. Mandel, T. Esslinger, T.W. H¨ansch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature (London) 415, 39-44 (2002).
[CrossRef]

2001 (2)

A. J. Leggett, "Bose-Einstein condensation in the alkali gases: Some fundamental concepts," Rev. Mod. Phys. 73, 307-356 (2001).
[CrossRef]

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, "Observation of coherent optical information storage in an atomic medium using halted light pulses," Nature (London) 409, 490-493 (2001).
[CrossRef]

1999 (2)

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, "Vortices in a Bose- Einstein Condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, "Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature (London) 397, 594-598 (1999).
[CrossRef]

1998 (1)

C. F. Li and G. C. Guo, "Quantum nondemolition measurement of the atom number of a Bose-Einstein condensate," Phys. Lett. A 248, 117-123 (1998).
[CrossRef]

1997 (1)

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Observation of Interference between Two Bose Condensates," Science 275, 637-641 (1997).
[CrossRef]

1995 (4)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor," Science 269, 198-201 (1995).
[CrossRef]

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Bose-Einstein Condensation in a Gas of Sodium Atoms, " Phys. Rev. Lett. 75, 3969-3973 (1995).
[CrossRef]

K. B. Davis, M. O. Mewes, M. A. Joffe, M. R. Andrews, and W. Ketterle, "Evaporative Cooling of Sodium Atoms," Phys. Rev. Lett. 74, 5202-5205 (1995).
[CrossRef]

W. Petrich, M. H. Anderson, J. R. Ensher, and E. A. Cornell, "Stable, Tightly Confining Magnetic Trap for Evaporative Cooling of Neutral Atoms," Phys. Rev. Lett. 74, 3352-3355 (1995).
[CrossRef]

1989 (1)

1986 (1)

H. F. Hess, "Evaporative cooling of magnetically trapped and compressed spin-polarized hydrogen," Phys. Rev. B 34, 3476-3479 (1986).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (London) (5)

M. Greiner, C. A. Regal, and D. S. Jin, "Emergence of a molecular Bose-Einstein condensate from a Fermi gas," Nature (London) 426, 537-540 (2003).
[CrossRef]

M. Greiner, O. Mandel, T. Esslinger, T.W. H¨ansch, and I. Bloch, "Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms," Nature (London) 415, 39-44 (2002).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, C. H. Behroozi, "Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature (London) 397, 594-598 (1999).
[CrossRef]

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, "Observation of coherent optical information storage in an atomic medium using halted light pulses," Nature (London) 409, 490-493 (2001).
[CrossRef]

N. S. Ginsberg, S. R. Garner, and L. V. Hau, "Coherent control of optical information with matter wave dynamics," Nature (London) 445, 623-626 (2007).
[CrossRef]

Phys. Lett. A (1)

C. F. Li and G. C. Guo, "Quantum nondemolition measurement of the atom number of a Bose-Einstein condensate," Phys. Lett. A 248, 117-123 (1998).
[CrossRef]

Phys. Rev. B (1)

H. F. Hess, "Evaporative cooling of magnetically trapped and compressed spin-polarized hydrogen," Phys. Rev. B 34, 3476-3479 (1986).
[CrossRef]

Phys. Rev. Lett. (5)

K. B. Davis, M. O. Mewes, M. A. Joffe, M. R. Andrews, and W. Ketterle, "Evaporative Cooling of Sodium Atoms," Phys. Rev. Lett. 74, 5202-5205 (1995).
[CrossRef]

W. Petrich, M. H. Anderson, J. R. Ensher, and E. A. Cornell, "Stable, Tightly Confining Magnetic Trap for Evaporative Cooling of Neutral Atoms," Phys. Rev. Lett. 74, 3352-3355 (1995).
[CrossRef]

M. W. Zwierlein, C. A. Stan, C. H. Schunck, S. M. F. Raupach, S. Gupta, Z. Hadzibabic, and W. Ketterle, "Observation of Bose-Einstein Condensation of Molecules," Phys. Rev. Lett. 91, 250401 (2003).
[CrossRef]

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, "Vortices in a Bose- Einstein Condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
[CrossRef]

K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Bose-Einstein Condensation in a Gas of Sodium Atoms, " Phys. Rev. Lett. 75, 3969-3973 (1995).
[CrossRef]

Rev. Mod. Phys. (1)

A. J. Leggett, "Bose-Einstein condensation in the alkali gases: Some fundamental concepts," Rev. Mod. Phys. 73, 307-356 (2001).
[CrossRef]

Science (3)

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Observation of Interference between Two Bose Condensates," Science 275, 637-641 (1997).
[CrossRef]

S. Jochim, M. Bartenstein, A. Altmeyer, G. Hendl, S. Riedl, C. Chin, J. Hecker Denschlag, and R. Grimm, "Bose-Einstein Condensation of Molecules," Science 302, 2101-2103 (2003).
[CrossRef]

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, "Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor," Science 269, 198-201 (1995).
[CrossRef]

Other (2)

In a two-level system, the absorption cross section of a laser field is equal to the imaginary part of [3λ 2/(2π)]ρegΓ′/Ω, where ρeg is the amplitude of the density matrix element between the excited state |e> and the ground state |g>, Γ′ is the spontaneous decay rate from |e> to |g>, and Γ is the Rabi frequency of the laser field. For the solution of ρeg, see M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997), Sec. 5.3.2 and Eq. (17.1.20).

Y. C. Chen, Y. A. Liao, L. Hsu, and I. A. Yu, "Simple technique for directly and accurately measuring the number of atoms in a magneto-optical trap," Phys. Rev. A  64, 031401(R) (2001).

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