Abstract

We propose a scheme to engage phase shifting interferometry on cold atomic samples and present the simulation results under several experimentally achievable conditions nowadays. This method allows far-detuning, low power probing, and is intrinsically nondestructive. This novel detection means yields image quality superior to the conventional phase contrast imaging at certain conditions and could be experimentally realized. Furthermore, the longitudinal resolution of imaging by this manner is mainly set by optical interference and can be better than the diffraction limit. This scheme also provides special advantages to diagnose the surface-trapped clouds, with which phase imaging on the fabricated wires and atoms altogether is possible as well.

© 2011 Optical Society of America

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2010 (1)

B.-W. Shianu, T.-P. Ku, and D.-J. Han, "Real-Time Phase Difference Control of Optical Beams Using a MachVZehnder Interferometer," J. Phys. Soc. Jpn. 79, 034302 (2010).
[CrossRef]

2009 (3)

W. S. Bakr, J. I. Gillen, A. Peng, S. Folling, and M. Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice," Nature 462, 74 (2009).
[CrossRef] [PubMed]

M. Karski, L. Forster, J. M. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging," Phys. Rev. Lett. 102, 053001 (2009).
[CrossRef] [PubMed]

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Folling, and M. Greiner, "Two-dimensional quantum gas in a hybrid surface trap," Phys. Rev. A 80, 021602 (2009).
[CrossRef]

2008 (2)

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

2007 (3)

K. Nelson, X. Li, and D. Weiss, "Imaging single atoms in a three-dimensional array," Nat. Phys. 3, 556 (2007).
[CrossRef]

M. Vannoni, M. Trivi, and G. Molesini, "Phase-shift interferometry with a digital photo camera," Eur. J. Phys. 28, 117 (2007).
[CrossRef]

J. Fortagh, and C. Zimmermann, "Magnetic microtraps for ultracold atoms," Rev. Mod. Phys. 79, 235 (2007).
[CrossRef]

2006 (1)

2005 (2)

2004 (2)

2001 (1)

2000 (2)

R. Folman, P. Kruger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, "Controlling Cold Atoms using Nanofabricated Surfaces: Atom Chips," Phys. Rev. Lett. 84, 4749 (2000).
[CrossRef] [PubMed]

M. T. DePue, S. L. Winoto, D. J. Han, and D. S. Weiss, "Transient compression of a MOT and high density fluorescent imaging of optically thick clouds of atoms," Opt. Commun. 180, 73 (2000).
[CrossRef]

1997 (1)

C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number," Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

1996 (2)

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Nondestructive Observation of a Bose Condensate," Science 273, 84 (1996).
[CrossRef] [PubMed]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

1990 (1)

M. Takeda, "Spatial-carrier fringes-pattern analysis and its applications to precision interferometry and profilometry: An overview," Ind. Metrol. 1, 79 (1990).
[CrossRef]

Alt, W.

M. Karski, L. Forster, J. M. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging," Phys. Rev. Lett. 102, 053001 (2009).
[CrossRef] [PubMed]

Anderson, R.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Andrews, M. R.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Nondestructive Observation of a Bose Condensate," Science 273, 84 (1996).
[CrossRef] [PubMed]

Badizadegan, K.

Bakr, W. S.

W. S. Bakr, J. I. Gillen, A. Peng, S. Folling, and M. Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice," Nature 462, 74 (2009).
[CrossRef] [PubMed]

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Folling, and M. Greiner, "Two-dimensional quantum gas in a hybrid surface trap," Phys. Rev. A 80, 021602 (2009).
[CrossRef]

Bell, S. C.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Bitou, Y.

Bradley, C. C.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number," Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

Cai, L. Z.

Cassettari, D.

R. Folman, P. Kruger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, "Controlling Cold Atoms using Nanofabricated Surfaces: Atom Chips," Phys. Rev. Lett. 84, 4749 (2000).
[CrossRef] [PubMed]

Choi, J. M.

M. Karski, L. Forster, J. M. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging," Phys. Rev. Lett. 102, 053001 (2009).
[CrossRef] [PubMed]

Dasari, R. R.

DePue, M. T.

M. T. DePue, S. L. Winoto, D. J. Han, and D. S. Weiss, "Transient compression of a MOT and high density fluorescent imaging of optically thick clouds of atoms," Opt. Commun. 180, 73 (2000).
[CrossRef]

Domen, K. F. E. M.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

Dong, G. Y.

Durfee, D. S.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Nondestructive Observation of a Bose Condensate," Science 273, 84 (1996).
[CrossRef] [PubMed]

Fang, S.

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

Fang-Yen, C.

Feld, M. S.

Folling, S.

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Folling, and M. Greiner, "Two-dimensional quantum gas in a hybrid surface trap," Phys. Rev. A 80, 021602 (2009).
[CrossRef]

W. S. Bakr, J. I. Gillen, A. Peng, S. Folling, and M. Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice," Nature 462, 74 (2009).
[CrossRef] [PubMed]

Folman, R.

R. Folman, P. Kruger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, "Controlling Cold Atoms using Nanofabricated Surfaces: Atom Chips," Phys. Rev. Lett. 84, 4749 (2000).
[CrossRef] [PubMed]

Forster, L.

M. Karski, L. Forster, J. M. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging," Phys. Rev. Lett. 102, 053001 (2009).
[CrossRef] [PubMed]

Fortagh, J.

J. Fortagh, and C. Zimmermann, "Magnetic microtraps for ultracold atoms," Rev. Mod. Phys. 79, 235 (2007).
[CrossRef]

Gillen, J. I.

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Folling, and M. Greiner, "Two-dimensional quantum gas in a hybrid surface trap," Phys. Rev. A 80, 021602 (2009).
[CrossRef]

W. S. Bakr, J. I. Gillen, A. Peng, S. Folling, and M. Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice," Nature 462, 74 (2009).
[CrossRef] [PubMed]

Greiner, M.

W. S. Bakr, J. I. Gillen, A. Peng, S. Folling, and M. Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice," Nature 462, 74 (2009).
[CrossRef] [PubMed]

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Folling, and M. Greiner, "Two-dimensional quantum gas in a hybrid surface trap," Phys. Rev. A 80, 021602 (2009).
[CrossRef]

Han, D. J.

M. T. DePue, S. L. Winoto, D. J. Han, and D. S. Weiss, "Transient compression of a MOT and high density fluorescent imaging of optically thick clouds of atoms," Opt. Commun. 180, 73 (2000).
[CrossRef]

Han, D.-J.

B.-W. Shianu, T.-P. Ku, and D.-J. Han, "Real-Time Phase Difference Control of Optical Beams Using a MachVZehnder Interferometer," J. Phys. Soc. Jpn. 79, 034302 (2010).
[CrossRef]

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

Hessmo, B.

R. Folman, P. Kruger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, "Controlling Cold Atoms using Nanofabricated Surfaces: Atom Chips," Phys. Rev. Lett. 84, 4749 (2000).
[CrossRef] [PubMed]

Hofmann, C. S.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Hollberg, L.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Hong, D.-S.

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

Hong, F.-L.

Huang, S.-J.

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

Hulet, R. G.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number," Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

Inaba, H.

Iwai, H.

Kadlecek, S.

Karski, M.

M. Karski, L. Forster, J. M. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging," Phys. Rev. Lett. 102, 053001 (2009).
[CrossRef] [PubMed]

Ketterle, W.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Nondestructive Observation of a Bose Condensate," Science 273, 84 (1996).
[CrossRef] [PubMed]

Kruger, P.

R. Folman, P. Kruger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, "Controlling Cold Atoms using Nanofabricated Surfaces: Atom Chips," Phys. Rev. Lett. 84, 4749 (2000).
[CrossRef] [PubMed]

Ku, T.-P.

B.-W. Shianu, T.-P. Ku, and D.-J. Han, "Real-Time Phase Difference Control of Optical Beams Using a MachVZehnder Interferometer," J. Phys. Soc. Jpn. 79, 034302 (2010).
[CrossRef]

Kurn, D. M.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Nondestructive Observation of a Bose Condensate," Science 273, 84 (1996).
[CrossRef] [PubMed]

Li, G.-W.

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

Li, X.

K. Nelson, X. Li, and D. Weiss, "Imaging single atoms in a three-dimensional array," Nat. Phys. 3, 556 (2007).
[CrossRef]

Lukin, M. D.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Maier, T.

R. Folman, P. Kruger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, "Controlling Cold Atoms using Nanofabricated Surfaces: Atom Chips," Phys. Rev. Lett. 84, 4749 (2000).
[CrossRef] [PubMed]

Meng, X. F.

Meschede, D.

M. Karski, L. Forster, J. M. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging," Phys. Rev. Lett. 102, 053001 (2009).
[CrossRef] [PubMed]

Mewes, M.-O.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Nondestructive Observation of a Bose Condensate," Science 273, 84 (1996).
[CrossRef] [PubMed]

Mohamed, T.

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

Molesini, G.

M. Vannoni, M. Trivi, and G. Molesini, "Phase-shift interferometry with a digital photo camera," Eur. J. Phys. 28, 117 (2007).
[CrossRef]

Nelson, K.

K. Nelson, X. Li, and D. Weiss, "Imaging single atoms in a three-dimensional array," Nat. Phys. 3, 556 (2007).
[CrossRef]

Newell, R.

Nikonov, D. E.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Onae, A.

Paganin, D.

Peng, A.

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Folling, and M. Greiner, "Two-dimensional quantum gas in a hybrid surface trap," Phys. Rev. A 80, 021602 (2009).
[CrossRef]

W. S. Bakr, J. I. Gillen, A. Peng, S. Folling, and M. Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice," Nature 462, 74 (2009).
[CrossRef] [PubMed]

Popescu, G.

Robinson, H. G.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Sackett, C. A.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number," Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

Schmiedmayer, J.

R. Folman, P. Kruger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, "Controlling Cold Atoms using Nanofabricated Surfaces: Atom Chips," Phys. Rev. Lett. 84, 4749 (2000).
[CrossRef] [PubMed]

Scholten, R. E.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, "Off-resonant defocus-contrast imaging of cold atoms," Opt. Lett. 29, 232 (2004).
[CrossRef] [PubMed]

Scully, M. O.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Sebby, J.

Sheludko, D. V.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Shen, X. X.

Shianu, B.-W.

B.-W. Shianu, T.-P. Ku, and D.-J. Han, "Real-Time Phase Difference Control of Optical Beams Using a MachVZehnder Interferometer," J. Phys. Soc. Jpn. 79, 034302 (2010).
[CrossRef]

Takatsuji, T.

Takeda, M.

M. Takeda, "Spatial-carrier fringes-pattern analysis and its applications to precision interferometry and profilometry: An overview," Ind. Metrol. 1, 79 (1990).
[CrossRef]

Trivi, M.

M. Vannoni, M. Trivi, and G. Molesini, "Phase-shift interferometry with a digital photo camera," Eur. J. Phys. 28, 117 (2007).
[CrossRef]

Turner, L. D.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, "Off-resonant defocus-contrast imaging of cold atoms," Opt. Lett. 29, 232 (2004).
[CrossRef] [PubMed]

Unterwaditzer, P.

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Folling, and M. Greiner, "Two-dimensional quantum gas in a hybrid surface trap," Phys. Rev. A 80, 021602 (2009).
[CrossRef]

van Druten, N. J.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Nondestructive Observation of a Bose Condensate," Science 273, 84 (1996).
[CrossRef] [PubMed]

Vannoni, M.

M. Vannoni, M. Trivi, and G. Molesini, "Phase-shift interferometry with a digital photo camera," Eur. J. Phys. 28, 117 (2007).
[CrossRef]

Velichansky, V. L.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Vredenbregt, E. J. D.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Walker, T. G.

Wang, Y. R.

Wax, A.

Weber, K. P.

Weiss, D.

K. Nelson, X. Li, and D. Weiss, "Imaging single atoms in a three-dimensional array," Nat. Phys. 3, 556 (2007).
[CrossRef]

Weiss, D. S.

M. T. DePue, S. L. Winoto, D. J. Han, and D. S. Weiss, "Transient compression of a MOT and high density fluorescent imaging of optically thick clouds of atoms," Opt. Commun. 180, 73 (2000).
[CrossRef]

Widera, A.

M. Karski, L. Forster, J. M. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging," Phys. Rev. Lett. 102, 053001 (2009).
[CrossRef] [PubMed]

Winoto, S. L.

M. T. DePue, S. L. Winoto, D. J. Han, and D. S. Weiss, "Transient compression of a MOT and high density fluorescent imaging of optically thick clouds of atoms," Opt. Commun. 180, 73 (2000).
[CrossRef]

Wu, H.-S.

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

Xu, X. F.

Yang, X. L.

Zibrov, A. S.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

Zimmermann, C.

J. Fortagh, and C. Zimmermann, "Magnetic microtraps for ultracold atoms," Rev. Mod. Phys. 79, 235 (2007).
[CrossRef]

Appl. Opt. (1)

Eur. J. Phys. (1)

M. Vannoni, M. Trivi, and G. Molesini, "Phase-shift interferometry with a digital photo camera," Eur. J. Phys. 28, 117 (2007).
[CrossRef]

Ind. Metrol. (1)

M. Takeda, "Spatial-carrier fringes-pattern analysis and its applications to precision interferometry and profilometry: An overview," Ind. Metrol. 1, 79 (1990).
[CrossRef]

J. Phys. Soc. Jpn. (2)

B.-W. Shianu, T.-P. Ku, and D.-J. Han, "Real-Time Phase Difference Control of Optical Beams Using a MachVZehnder Interferometer," J. Phys. Soc. Jpn. 79, 034302 (2010).
[CrossRef]

G.-W. Li, S.-J. Huang, H.-S. Wu, S. Fang, D.-S. Hong, T. Mohamed, and D.-J. Han, "A Michelson Interferometer for Relative Phase Locking of Optical Beams," J. Phys. Soc. Jpn. 77, 024301 (2008).
[CrossRef]

Nat. Phys. (1)

K. Nelson, X. Li, and D. Weiss, "Imaging single atoms in a three-dimensional array," Nat. Phys. 3, 556 (2007).
[CrossRef]

Nature (1)

W. S. Bakr, J. I. Gillen, A. Peng, S. Folling, and M. Greiner, "A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice," Nature 462, 74 (2009).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. T. DePue, S. L. Winoto, D. J. Han, and D. S. Weiss, "Transient compression of a MOT and high density fluorescent imaging of optically thick clouds of atoms," Opt. Commun. 180, 73 (2000).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (3)

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

J. I. Gillen, W. S. Bakr, A. Peng, P. Unterwaditzer, S. Folling, and M. Greiner, "Two-dimensional quantum gas in a hybrid surface trap," Phys. Rev. A 80, 021602 (2009).
[CrossRef]

Phys. Rev. Lett. (4)

R. Folman, P. Kruger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, "Controlling Cold Atoms using Nanofabricated Surfaces: Atom Chips," Phys. Rev. Lett. 84, 4749 (2000).
[CrossRef] [PubMed]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, "Experimental Demonstration of Enhanced Index of Refraction via Quantum Coherence in Rb," Phys. Rev. Lett. 76, 3935 (1996).
[CrossRef] [PubMed]

C. C. Bradley, C. A. Sackett, and R. G. Hulet, "Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number," Phys. Rev. Lett. 78, 985 (1997).
[CrossRef]

M. Karski, L. Forster, J. M. Choi, W. Alt, A. Widera, and D. Meschede, "Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging," Phys. Rev. Lett. 102, 053001 (2009).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

J. Fortagh, and C. Zimmermann, "Magnetic microtraps for ultracold atoms," Rev. Mod. Phys. 79, 235 (2007).
[CrossRef]

Science (1)

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, Nondestructive Observation of a Bose Condensate," Science 273, 84 (1996).
[CrossRef] [PubMed]

Other (8)

L. D. Turner, "Holographic Imaging of Cold Atoms," Ph.D. dissertation, University of Melbourne, Australia, 2004.

J. E. Greivenkamp, and J. H. Bruning, "Phase Shifting Interferometry," in Optical Shop Testing, ed. D. Malacara, (J. Wiley, 1992) pp. 501-598.

EEV 512 × 1024 CCD (Princeton Instruments) allows full-frame transfer and readout in 273 ms.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., (McGraw-Hill, 1996).

E. Hecht, Optics, 4th ed., (Addison Wesley, 2002).

D. A. Steck, "Rubidium 87 D Line Data," available online at http://steck.us/alkalidata (revision 2.0.1, 2 May 2008).

M. R. Matthews, "Two-component Bose-Einstein Condensation," Ph.D. dissertation, University of Colorado, 1999.

F. L. Pedrotti, and L. S. Pedrotti, Introduction to Optics, 2nd ed., (Prentice-Hall, 1993).

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Figures (5)

Fig. 1
Fig. 1

Schematic of phase shifting interferometry on cold atomic cloud. The optical paths shown in red are the diffracted beams by the atomic cloud. Positions (a) and (b) are the two object planes, in the probe and reference arms, for the imaging lens which is sitting behind the beam splitter BS2.

Fig. 2
Fig. 2

Heating rate and peak phase shifts for four simulated atomic clouds as a function of probe beam detuning. The black solid curve shows the heating rate. The four peak phase shift curves (A) (red dashed line), (B) (black dotted line), (C) (green dashed dotted line), and (D) (blue long dashed line) correspond to the cloud parameters in Fig. 3, Fig. 4(a), Fig. 4(b) and Fig. 5, respectively. Ip = Is/100 is used in this calculation.

Fig. 3
Fig. 3

Simulated interferograms and retrieved phase image of a cigar-shape atomic cloud with ρ0 = 1.0 × 1012 atoms/cm3, N = 8×106 atoms, and aspect ratio σy/σx = 3. The probe beam detuning used in the simulation is 100 MHz. (a) The four gray-level images show the simulated interference distributions at CCD plane while PSI is engaged by four sequential phase shifts of π/2. (b) The retrieved 3D false-color phase image with a peak phase shift of about 23°.

Fig. 4
Fig. 4

Simulated false-color phase images for (a) spherically symmetric atom cloud with N = 1 × 109 atoms, ρ0 = 2.0 × 1011 atoms/cm3, σx,y,z ∼ 680 μm, under probe beam detuning of 200 MHz; (b) near pancake atom cloud with N = 6 × 106 atoms, ρ0 = 1 × 1014 atoms/cm3, and σx = (4/5) · σy ∼ 30.8 μm, σy/σz = 12, under probe beam detuning of 500 MHz.

Fig. 5
Fig. 5

Simulated false-color phase and effective thickness images on a 2D pancake cloud with N = 1 × 106 atoms. The rms radius σx,y in transverse direction is 35 μm and longitudinal radius σz is 0.25 μm. The probe beam detuning is 100 MHz. (a) The simulated 3D phase image. (b) The effective thickness image obtained by transferring from the phase image (a) using Eq. (8). The peak effective thickness in this data is 0.63 μm which is smaller than the optical diffraction limit of the simulated imaging system.

Equations (8)

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n ( r ) = 1 + ρ ( r ) σ 0 λ 4 π i 2 Δ 1 + 4 Δ 2 n R + i n I ,
I ( x , y ) = I P ( x , y ) + I R ( x , y ) + 2 I R ( x , y ) I P ( x , y ) cos [ ϕ ( x , y ) + Φ ] ,
ϕ ( x , y ) = tan 1 { [ I π ( x , y ) I 0 ( x , y ) ] sin ( π ζ / 2 ) [ I π / 2 ( x , y ) I 3 π / 2 ( x , y ) ] [ I π ( x , y ) I 0 ( x , y ) ] cos ( π ζ / 2 ) } π ζ 2 ,
γ s = Γ 2 S 1 + S ,
E P ( x , y ) = e i k ( p + q ) e i k 2 q ( x 2 + y 2 ) e i k 2 p M 2 ( x 2 + y 2 ) E P 1 ( x M , y M ) / M ,
E R ( x , y ) = e i k ( p + q ) e i k 2 q ( x 2 + y 2 ) e i k 2 p M 2 ( x 2 + y 2 ) E R 1 ( x M , y M ) / M .
ϕ ( x , y ) = ( 2 π / λ ) Δ n R 0 Z e ( x , y ) ,
Z e ( x , y ) = ( 1 + 4 Δ 2 ) ρ 0 σ 0 Δ ϕ ( x , y ) .

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