Abstract

Absorption imaging of ultracold atoms is the foundation for quantitative extraction of information from experiments with ultracold atoms. Due to the limited exposure time available in these systems, the signal-to-noise ratio is largest for high intensity absorption imaging where the intensity of the imaging light is on the order of the saturation intensity. In this case, the absolute value of the intensity of the imaging light enters as an additional parameter making it more sensitive to systematic errors. Here, we present a novel and robust technique to determine the imaging beam intensity in units of the effective saturation intensity to better than 5%. We do this by measuring the momentum transferred to the atoms by the imaging light while varying its intensity. We further utilize the method to quantify the purity of the polarization of the imaging light and to determine the correct imaging detuning.

© 2017 Optical Society of America

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References

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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] [PubMed]
  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] [PubMed]
  3. M. R. Matthews, B. P. Anderson, P. Haljan, D. Hall, C. Wieman, and E. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498 (1999).
    [Crossref]
  4. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
    [Crossref] [PubMed]
  5. C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
    [Crossref] [PubMed]
  6. M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, “Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas,” Science 335, 563–567 (2012).
    [Crossref] [PubMed]
  7. W. Ketterle, D. Durfee, and D. Stamper-Kurn, “Making, probing and understanding Bose-Einstein condensates,” in Bose-Einstein Condensation in Atomic Gases, M. Inguscio, S. Stringari, and C. Wieman, eds. (IOS Press, Amsterdam, 1999).
  8. G. Reinaudi, T. Lahaye, Z. Wang, and D. Guéry-Odelin, “Strong saturation absorption imaging of dense clouds of ultracold atoms,” Opt. Lett. 32, 3143–3145 (2007).
    [Crossref] [PubMed]
  9. T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, and J. Dalibard, “Exploring the thermodynamics of a two-dimensional Bose gas,” Phys. Rev. Lett. 107, 130401 (2011).
    [Crossref] [PubMed]
  10. C. J. Foot, Atomic physics, vol. 7 (Oxford University Press, 2005).
  11. W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
    [Crossref] [PubMed]
  12. L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
    [Crossref]
  13. M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
    [Crossref] [PubMed]
  14. M. Horikoshi, A. Ito, T. Ikemachi, Y. Aratake, M. Kuwata-Gonokami, and M. Koashi, “Accurate in situ acquisition of column density of a dense cloud of ultracold 6Li atoms using absorption imaging,” arXiv:1608:07152 (2016).

2015 (2)

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

2012 (2)

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
[Crossref]

M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, “Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas,” Science 335, 563–567 (2012).
[Crossref] [PubMed]

2011 (2)

C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
[Crossref] [PubMed]

T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, and J. Dalibard, “Exploring the thermodynamics of a two-dimensional Bose gas,” Phys. Rev. Lett. 107, 130401 (2011).
[Crossref] [PubMed]

2007 (1)

2001 (1)

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref] [PubMed]

1999 (1)

M. R. Matthews, B. P. Anderson, P. Haljan, D. Hall, C. Wieman, and E. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498 (1999).
[Crossref]

1995 (2)

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] [PubMed]

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] [PubMed]

Abo-Shaeer, J. R.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref] [PubMed]

Anderson, B. P.

M. R. Matthews, B. P. Anderson, P. Haljan, D. Hall, C. Wieman, and E. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498 (1999).
[Crossref]

Anderson, M. H.

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] [PubMed]

Andrews, M. R.

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] [PubMed]

Aratake, Y.

M. Horikoshi, A. Ito, T. Ikemachi, Y. Aratake, M. Kuwata-Gonokami, and M. Koashi, “Accurate in situ acquisition of column density of a dense cloud of ultracold 6Li atoms using absorption imaging,” arXiv:1608:07152 (2016).

Bayha, L.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Boettcher, I.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Cheuk, L. W.

M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, “Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas,” Science 335, 563–567 (2012).
[Crossref] [PubMed]

Chin, C.

C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
[Crossref] [PubMed]

Chomaz, L.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
[Crossref]

T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, and J. Dalibard, “Exploring the thermodynamics of a two-dimensional Bose gas,” Phys. Rev. Lett. 107, 130401 (2011).
[Crossref] [PubMed]

Corman, L.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
[Crossref]

Cornell, E.

M. R. Matthews, B. P. Anderson, P. Haljan, D. Hall, C. Wieman, and E. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498 (1999).
[Crossref]

Cornell, E. A.

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] [PubMed]

Dalibard, J.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
[Crossref]

T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, and J. Dalibard, “Exploring the thermodynamics of a two-dimensional Bose gas,” Phys. Rev. Lett. 107, 130401 (2011).
[Crossref] [PubMed]

Davis, K. B.

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] [PubMed]

Desbuquois, R.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
[Crossref]

T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, and J. Dalibard, “Exploring the thermodynamics of a two-dimensional Bose gas,” Phys. Rev. Lett. 107, 130401 (2011).
[Crossref] [PubMed]

Durfee, D.

W. Ketterle, D. Durfee, and D. Stamper-Kurn, “Making, probing and understanding Bose-Einstein condensates,” in Bose-Einstein Condensation in Atomic Gases, M. Inguscio, S. Stringari, and C. Wieman, eds. (IOS Press, Amsterdam, 1999).

Durfee, D. S.

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] [PubMed]

Ensher, J. R.

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] [PubMed]

Foot, C. J.

C. J. Foot, Atomic physics, vol. 7 (Oxford University Press, 2005).

Gemelke, N.

C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
[Crossref] [PubMed]

Guéry-Odelin, D.

Günter, K. J.

T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, and J. Dalibard, “Exploring the thermodynamics of a two-dimensional Bose gas,” Phys. Rev. Lett. 107, 130401 (2011).
[Crossref] [PubMed]

Haljan, P.

M. R. Matthews, B. P. Anderson, P. Haljan, D. Hall, C. Wieman, and E. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498 (1999).
[Crossref]

Hall, D.

M. R. Matthews, B. P. Anderson, P. Haljan, D. Hall, C. Wieman, and E. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498 (1999).
[Crossref]

Horikoshi, M.

M. Horikoshi, A. Ito, T. Ikemachi, Y. Aratake, M. Kuwata-Gonokami, and M. Koashi, “Accurate in situ acquisition of column density of a dense cloud of ultracold 6Li atoms using absorption imaging,” arXiv:1608:07152 (2016).

Hueck, K.

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

Hung, C.-L.

C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
[Crossref] [PubMed]

Ikemachi, T.

M. Horikoshi, A. Ito, T. Ikemachi, Y. Aratake, M. Kuwata-Gonokami, and M. Koashi, “Accurate in situ acquisition of column density of a dense cloud of ultracold 6Li atoms using absorption imaging,” arXiv:1608:07152 (2016).

Ito, A.

M. Horikoshi, A. Ito, T. Ikemachi, Y. Aratake, M. Kuwata-Gonokami, and M. Koashi, “Accurate in situ acquisition of column density of a dense cloud of ultracold 6Li atoms using absorption imaging,” arXiv:1608:07152 (2016).

Jochim, S.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Kedar, D.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Ketterle, W.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref] [PubMed]

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] [PubMed]

W. Ketterle, D. Durfee, and D. Stamper-Kurn, “Making, probing and understanding Bose-Einstein condensates,” in Bose-Einstein Condensation in Atomic Gases, M. Inguscio, S. Stringari, and C. Wieman, eds. (IOS Press, Amsterdam, 1999).

Koashi, M.

M. Horikoshi, A. Ito, T. Ikemachi, Y. Aratake, M. Kuwata-Gonokami, and M. Koashi, “Accurate in situ acquisition of column density of a dense cloud of ultracold 6Li atoms using absorption imaging,” arXiv:1608:07152 (2016).

Ku, M. J. H.

M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, “Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas,” Science 335, 563–567 (2012).
[Crossref] [PubMed]

Kurn, D. M.

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] [PubMed]

Kuwata-Gonokami, M.

M. Horikoshi, A. Ito, T. Ikemachi, Y. Aratake, M. Kuwata-Gonokami, and M. Koashi, “Accurate in situ acquisition of column density of a dense cloud of ultracold 6Li atoms using absorption imaging,” arXiv:1608:07152 (2016).

Lahaye, T.

Lompe, T.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Luick, N.

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

Mathey, L.

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

Matthews, M. R.

M. R. Matthews, B. P. Anderson, P. Haljan, D. Hall, C. Wieman, and E. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498 (1999).
[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] [PubMed]

Mewes, M. O.

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] [PubMed]

Morgener, K.

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

Moritz, H.

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

Murthy, P. A.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Neidig, M.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Raman, C.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref] [PubMed]

Reinaudi, G.

Ries, M. G.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Siegl, J.

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

Singh, V. P.

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

Sommer, A. T.

M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, “Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas,” Science 335, 563–567 (2012).
[Crossref] [PubMed]

Stamper-Kurn, D.

W. Ketterle, D. Durfee, and D. Stamper-Kurn, “Making, probing and understanding Bose-Einstein condensates,” in Bose-Einstein Condensation in Atomic Gases, M. Inguscio, S. Stringari, and C. Wieman, eds. (IOS Press, Amsterdam, 1999).

van Druten, N. J.

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] [PubMed]

Vogels, J. M.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of vortex lattices in Bose-Einstein condensates,” Science 292, 476–479 (2001).
[Crossref] [PubMed]

Wang, Z.

Weimer, W.

W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, “Critical velocity in the BEC-BCS crossover,” Phys. Rev. Lett. 114, 095301 (2015).
[Crossref] [PubMed]

Wenz, A. N.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Wieman, C.

M. R. Matthews, B. P. Anderson, P. Haljan, D. Hall, C. Wieman, and E. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498 (1999).
[Crossref]

Wieman, C. E.

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] [PubMed]

Yefsah, T.

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
[Crossref]

T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Günter, and J. Dalibard, “Exploring the thermodynamics of a two-dimensional Bose gas,” Phys. Rev. Lett. 107, 130401 (2011).
[Crossref] [PubMed]

Zhang, X.

C.-L. Hung, X. Zhang, N. Gemelke, and C. Chin, “Observation of scale invariance and universality in two-dimensional Bose gases,” Nature 470, 236–239 (2011).
[Crossref] [PubMed]

Zürn, G.

M. G. Ries, A. N. Wenz, G. Zürn, L. Bayha, I. Boettcher, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, and S. Jochim, “Observation of pair condensation in the quasi-2D BEC-BCS crossover,” Phys. Rev. Lett. 114, 230401 (2015).
[Crossref] [PubMed]

Zwierlein, M. W.

M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, “Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas,” Science 335, 563–567 (2012).
[Crossref] [PubMed]

Nature (1)

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Figures (5)

Fig. 1
Fig. 1

Sketch of the experimental setup: a) Absorption imaging of a cloud of ultracold atoms trapped inside a vacuum chamber. Imaging of the cloud is possible along two axes, the main axis (z-axis) and an auxiliary imaging axis (x-axis). By flashing on the main imaging beam, the atoms accelerate in z-direction. After some time of flight their position is recorded with the auxiliary imaging. b) Density distributions after 80 μs time of flight imaged along the auxiliary imaging direction. The flight distances shown in c) are extracted from the images and plotted as a function of the intensity of the imaging pulse, which is measured on the main imaging camera. From the saturation of the flight distance we can determine the count rate on the main imaging camera which corresponds to the effective saturation intensity.

Fig. 2
Fig. 2

Flight distance vs. laser detuning: The resonance frequency of the imaging laser is found by varying the detuning and thereby maximizing the flight distance of the atoms after illumination with a 1 μs long imaging pulse. A Lorentzian fit (solid lines) to the data gives the center frequency as well as the width of the imaging transition, which shows power broadening for high intensities. The saturation parameter s 0 = I / I s a t e f f for the different curves is extracted from the fits. The red dashed line indicates the theoretically expected position of the maxima which are affected by the accumulated Doppler shift during the imaging pulse. The x-axis is offset by the fitted resonance frequency.

Fig. 3
Fig. 3

Chirp efficiency: Velocity of the atom cloud after accelerating it with the z-imaging beam with different illumination times at I i n = 3.75 I s a t e f f. The effect of chirping the imaging beam frequency to compensate for the Doppler shift is clearly visible. In the unchirped case (red triangles), the scattering rate decreases with illumination time and therefore the increase in cloud velocity becomes nonlinear. In the chirped case (blue open circles) acceleration is constant. The lines indicate the theoretically expected cloud velocity for the unchirped (red solid) and chirped case (blue dashed). The error bars indicate the systematic error estimated for the magnification of the auxiliary imaging.

Fig. 4
Fig. 4

Determination of the effective saturation count rate C s a t e f f: a) The difference in position for two times of flight (Δt = 10 μs) is shown as a function of imaging beam intensity and hence Cin. The velocity of the cloud saturates for higher imaging beam intensities and the saturation counts are determined by fitting Eq. (5) to the data. The resulting effective saturation count rate is C s a t , k e f f = ( 32.7 ± 0.6 ) ( px μ s ) 1. b) The saturation parameter s0 extracted from a Lorentzian fit to the power broadened spectra presented in Fig. 2 is plotted as a function of the count rate Cin on the main camera. The error bars represent the Lorentzian fit error. A linear fit to the data yields C s a t , s e f f = ( 31.5 ± 1.3 ) ( px μ s ) 1.

Fig. 5
Fig. 5

Proof of validity and optimization of signal-to-noise ratio: a) Extracted atom number as a function of imaging beam intensity using the modified (blue circles) and unmodified (red squares) Beer-Lambert law. Each data-point is an average of about ≈70 measurements. The error-bars are smaller than the size of the symbols. When evaluating the data with the modified Beer-Lambert law the atom number does not depend on the imaging intensity. This validates our method to determine the value of the effective saturation intensity I s a t e f f. For low imaging intensities the result from the unmodified Beer-Lambert law approaches the correct atom number. b) The signal-to-noise ratio evaluated on a single pixel basis is maximized for intensities of I = 1.5 I s a t e f f. The blue line is a guide to the eye.

Equations (6)

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d I ( x , y , z ) d z = n ( x , y , z ) σ e f f 1 1 + I ( x , y , z ) / I s a t e f f I ( x , y , z ) ,
o d ( x , y ) = σ e f f n 2 D ( x , y ) = σ e f f n ( x , y , z ) d z = ln ( I o u t ( x , y ) I i n ( x , y ) ) Long-Term + I i n ( x , y ) I o u t ( x , y ) I s a t e f f Lin-Term ,
C = I A p i x / M 2 h c / λ × T × Q E × G ,
σ e f f n 2 D ( i , j ) = ln ( C o u t ( i , j ) C i n ( i , j ) ) + C i n ( i , j ) C o u t ( i , j ) C s a t e f f .
γ ( s ) = Γ 2 s 0 1 + s 0 .
z ( ν L , s ) = z 0 + η Γ 2 s 0 1 + s 0 + ( 2 Δ Γ ) 2

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