Abstract

In this paper we show that the sensitivity of absorption imaging of ultracold atoms can be significantly improved by imaging in a standing-wave configuration. We present simulations of single-atom absorption imaging both for a travelling-wave and a standing-wave imaging setup, based on a scattering approach to calculate the optical density of a single atom. We find that the optical density of a single atom is determined only by the numerical aperture of the imaging system. We determine optimum imaging parameters, taking all relevant sources of noise into account. For reflective imaging we find an improvement of 1.7 in the maximum signal-to-noise ratio can be achieved. This is particularly useful for imaging in the vicinity of an atom chip, where a reflective surface is naturally present.

© 2013 OSA

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2012 (1)

E. W. Streed, A. Jechow, B. G. Norton, and D. Kielpinski, “Absorption imaging of a single atom.” Nature Commun.3, 933 (2012).
[CrossRef]

2011 (3)

J. Goldwin, M. Trupke, J. Kenner, a. Ratnapala, and E. a. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity.” Nature Commun.2, 418 (2011).
[CrossRef]

V. Y. F. Leung, A. Tauschinsky, N. J. Druten, and R. J. C. Spreeuw, “Microtrap arrays on magnetic film atom chips for quantum information science,” Quantum Inf. Proc.10, 955–974 (2011).
[CrossRef]

D. A. Smith, S. Aigner, S. Hofferberth, M. Gring, M. Andersson, S. Wildermuth, P. Krüger, S. Schneider, T. Schumm, and J. Schmiedmayer, “Absorption imaging of ultracold atoms on atom chips,” Opt. Express19, 8471 (2011).
[CrossRef] [PubMed]

2010 (5)

J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, “Lossless State Detection of Single Neutral Atoms,” Phys. Rev. Lett.104, 203601 (2010).
[CrossRef] [PubMed]

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

C. Ockeloen, A. Tauschinsky, R. Spreeuw, and S. Whitlock, “Detection of small atom numbers through image processing,” Phys. Rev. A.82, 061606 (2010).
[CrossRef]

S. Whitlock, C. F. Ockeloen, and R. J. C. Spreeuw, “Sub-Poissonian Atom-Number Fluctuations by Three-Body Loss in Mesoscopic Ensembles,” Phys. Rev. Lett.104, 120402 (2010).
[CrossRef] [PubMed]

2009 (4)

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. Spreeuw, “Two-dimensional array of microtraps with atomic shift register on a chip,” New J. Phys.11, 023021 (2009).
[CrossRef]

M. Wilzbach, D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Schmiedmayer, “Simple integrated single-atom detector,” Opt. Lett.34, 259–261 (2009).
[CrossRef] [PubMed]

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

2007 (2)

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys.3, 556–560 (2007).
[CrossRef]

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

2002 (1)

A. J. E. M. Janssen, “Extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A.19, 849 (2002).
[CrossRef]

2001 (1)

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap.” Nature411, 1024–7 (2001).
[CrossRef] [PubMed]

1987 (1)

1980 (1)

W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, “Localized visible Bâ{+} mono-ion oscillator,” Phys. Rev. A.22, 1137–1140 (1980).
[CrossRef]

Aigner, S.

Aljunid, S. A.

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Andersson, M.

Bergquist, J. C.

Betz, T.

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Bochmann, J.

J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, “Lossless State Detection of Single Neutral Atoms,” Phys. Rev. Lett.104, 203601 (2010).
[CrossRef] [PubMed]

Bücker, R.

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Chen, Z.

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Chng, B.

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Cohen-Tannoudij, C.

C. Cohen-Tannoudij, J. Dupont-Roc, and G. Grynberg, Atom—Photon Interactions (Wiley-VCH Verlag GmbH, Weinheim, Germany, 1992).

Colombe, Y.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Dehmelt, H.

W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, “Localized visible Bâ{+} mono-ion oscillator,” Phys. Rev. A.22, 1137–1140 (1980).
[CrossRef]

Druten, N. J.

V. Y. F. Leung, A. Tauschinsky, N. J. Druten, and R. J. C. Spreeuw, “Microtrap arrays on magnetic film atom chips for quantum information science,” Quantum Inf. Proc.10, 955–974 (2011).
[CrossRef]

Dubois, G.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Dupont-Roc, J.

C. Cohen-Tannoudij, J. Dupont-Roc, and G. Grynberg, Atom—Photon Interactions (Wiley-VCH Verlag GmbH, Weinheim, Germany, 1992).

Estève, J.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Fernholz, T.

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. Spreeuw, “Two-dimensional array of microtraps with atomic shift register on a chip,” New J. Phys.11, 023021 (2009).
[CrossRef]

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

Fischer, D.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

Gehr, R.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Gerritsma, R.

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. Spreeuw, “Two-dimensional array of microtraps with atomic shift register on a chip,” New J. Phys.11, 023021 (2009).
[CrossRef]

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

Goedkoop, J. B.

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

Goldwin, J.

J. Goldwin, M. Trupke, J. Kenner, a. Ratnapala, and E. a. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity.” Nature Commun.2, 418 (2011).
[CrossRef]

Grangier, P.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap.” Nature411, 1024–7 (2001).
[CrossRef] [PubMed]

Gring, M.

Groth, S.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

M. Wilzbach, D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Schmiedmayer, “Simple integrated single-atom detector,” Opt. Lett.34, 259–261 (2009).
[CrossRef] [PubMed]

Grynberg, G.

C. Cohen-Tannoudij, J. Dupont-Roc, and G. Grynberg, Atom—Photon Interactions (Wiley-VCH Verlag GmbH, Weinheim, Germany, 1992).

Guhl, C.

J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, “Lossless State Detection of Single Neutral Atoms,” Phys. Rev. Lett.104, 203601 (2010).
[CrossRef] [PubMed]

Heine, D.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

M. Wilzbach, D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Schmiedmayer, “Simple integrated single-atom detector,” Opt. Lett.34, 259–261 (2009).
[CrossRef] [PubMed]

Hessmo, B.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

M. Wilzbach, D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Schmiedmayer, “Simple integrated single-atom detector,” Opt. Lett.34, 259–261 (2009).
[CrossRef] [PubMed]

Hinds, E. a.

J. Goldwin, M. Trupke, J. Kenner, a. Ratnapala, and E. a. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity.” Nature Commun.2, 418 (2011).
[CrossRef]

Hofferberth, S.

Hohenstatt, M.

W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, “Localized visible Bâ{+} mono-ion oscillator,” Phys. Rev. A.22, 1137–1140 (1980).
[CrossRef]

Huber, F.

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Itano, W. M.

Janssen, A. J. E. M.

A. J. E. M. Janssen, “Extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A.19, 849 (2002).
[CrossRef]

Jechow, A.

E. W. Streed, A. Jechow, B. G. Norton, and D. Kielpinski, “Absorption imaging of a single atom.” Nature Commun.3, 933 (2012).
[CrossRef]

Kenner, J.

J. Goldwin, M. Trupke, J. Kenner, a. Ratnapala, and E. a. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity.” Nature Commun.2, 418 (2011).
[CrossRef]

Kielpinski, D.

E. W. Streed, A. Jechow, B. G. Norton, and D. Kielpinski, “Absorption imaging of a single atom.” Nature Commun.3, 933 (2012).
[CrossRef]

Koller, C.

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Krüger, P.

Kurtsiefer, C.

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Leung, V. Y. F.

V. Y. F. Leung, A. Tauschinsky, N. J. Druten, and R. J. C. Spreeuw, “Microtrap arrays on magnetic film atom chips for quantum information science,” Quantum Inf. Proc.10, 955–974 (2011).
[CrossRef]

Lev, B. L.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Li, X.

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys.3, 556–560 (2007).
[CrossRef]

Liew, T. C H

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Liu, X.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

M. Wilzbach, D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Schmiedmayer, “Simple integrated single-atom detector,” Opt. Lett.34, 259–261 (2009).
[CrossRef] [PubMed]

Long, R.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Loziczky, S.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

Luigjes, J. A.

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

Manz, S.

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Maslennikov, G.

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Moehring, D. L.

J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, “Lossless State Detection of Single Neutral Atoms,” Phys. Rev. Lett.104, 203601 (2010).
[CrossRef] [PubMed]

Mücke, M.

J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, “Lossless State Detection of Single Neutral Atoms,” Phys. Rev. Lett.104, 203601 (2010).
[CrossRef] [PubMed]

Nelson, K. D.

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys.3, 556–560 (2007).
[CrossRef]

Neuhauser, W.

W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, “Localized visible Bâ{+} mono-ion oscillator,” Phys. Rev. A.22, 1137–1140 (1980).
[CrossRef]

Norton, B. G.

E. W. Streed, A. Jechow, B. G. Norton, and D. Kielpinski, “Absorption imaging of a single atom.” Nature Commun.3, 933 (2012).
[CrossRef]

Ockeloen, C.

C. Ockeloen, A. Tauschinsky, R. Spreeuw, and S. Whitlock, “Detection of small atom numbers through image processing,” Phys. Rev. A.82, 061606 (2010).
[CrossRef]

Ockeloen, C. F.

S. Whitlock, C. F. Ockeloen, and R. J. C. Spreeuw, “Sub-Poissonian Atom-Number Fluctuations by Three-Body Loss in Mesoscopic Ensembles,” Phys. Rev. Lett.104, 120402 (2010).
[CrossRef] [PubMed]

Perrin, A.

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Plisson, T.

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Protsenko, I.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap.” Nature411, 1024–7 (2001).
[CrossRef] [PubMed]

Ratnapala, a.

J. Goldwin, M. Trupke, J. Kenner, a. Ratnapala, and E. a. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity.” Nature Commun.2, 418 (2011).
[CrossRef]

Raub, T.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

M. Wilzbach, D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Schmiedmayer, “Simple integrated single-atom detector,” Opt. Lett.34, 259–261 (2009).
[CrossRef] [PubMed]

Reichel, J.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Rempe, G.

J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, “Lossless State Detection of Single Neutral Atoms,” Phys. Rev. Lett.104, 203601 (2010).
[CrossRef] [PubMed]

Reymond, G.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap.” Nature411, 1024–7 (2001).
[CrossRef] [PubMed]

Ritter, S.

J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, “Lossless State Detection of Single Neutral Atoms,” Phys. Rev. Lett.104, 203601 (2010).
[CrossRef] [PubMed]

Rohringer, W.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

Rottmann, J.

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Scarani, V.

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Schlatter, H.

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

Schlosser, N.

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap.” Nature411, 1024–7 (2001).
[CrossRef] [PubMed]

Schmiedmayer, J.

D. A. Smith, S. Aigner, S. Hofferberth, M. Gring, M. Andersson, S. Wildermuth, P. Krüger, S. Schneider, T. Schumm, and J. Schmiedmayer, “Absorption imaging of ultracold atoms on atom chips,” Opt. Express19, 8471 (2011).
[CrossRef] [PubMed]

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

M. Wilzbach, D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Schmiedmayer, “Simple integrated single-atom detector,” Opt. Lett.34, 259–261 (2009).
[CrossRef] [PubMed]

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Schneider, S.

Schumm, T.

D. A. Smith, S. Aigner, S. Hofferberth, M. Gring, M. Andersson, S. Wildermuth, P. Krüger, S. Schneider, T. Schumm, and J. Schmiedmayer, “Absorption imaging of ultracold atoms on atom chips,” Opt. Express19, 8471 (2011).
[CrossRef] [PubMed]

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

Smith, D. A.

Spreeuw, R.

C. Ockeloen, A. Tauschinsky, R. Spreeuw, and S. Whitlock, “Detection of small atom numbers through image processing,” Phys. Rev. A.82, 061606 (2010).
[CrossRef]

Spreeuw, R. J.

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. Spreeuw, “Two-dimensional array of microtraps with atomic shift register on a chip,” New J. Phys.11, 023021 (2009).
[CrossRef]

Spreeuw, R. J. C.

V. Y. F. Leung, A. Tauschinsky, N. J. Druten, and R. J. C. Spreeuw, “Microtrap arrays on magnetic film atom chips for quantum information science,” Quantum Inf. Proc.10, 955–974 (2011).
[CrossRef]

S. Whitlock, C. F. Ockeloen, and R. J. C. Spreeuw, “Sub-Poissonian Atom-Number Fluctuations by Three-Body Loss in Mesoscopic Ensembles,” Phys. Rev. Lett.104, 120402 (2010).
[CrossRef] [PubMed]

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

Steinmetz, T.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Streed, E. W.

E. W. Streed, A. Jechow, B. G. Norton, and D. Kielpinski, “Absorption imaging of a single atom.” Nature Commun.3, 933 (2012).
[CrossRef]

Tauschinsky, A.

V. Y. F. Leung, A. Tauschinsky, N. J. Druten, and R. J. C. Spreeuw, “Microtrap arrays on magnetic film atom chips for quantum information science,” Quantum Inf. Proc.10, 955–974 (2011).
[CrossRef]

C. Ockeloen, A. Tauschinsky, R. Spreeuw, and S. Whitlock, “Detection of small atom numbers through image processing,” Phys. Rev. A.82, 061606 (2010).
[CrossRef]

Tey, M. K.

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

Thiele, J.-U.

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

Toschek, P.

W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, “Localized visible Bâ{+} mono-ion oscillator,” Phys. Rev. A.22, 1137–1140 (1980).
[CrossRef]

Trupke, M.

J. Goldwin, M. Trupke, J. Kenner, a. Ratnapala, and E. a. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity.” Nature Commun.2, 418 (2011).
[CrossRef]

Volz, J.

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

Weiss, D. S.

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys.3, 556–560 (2007).
[CrossRef]

Whitlock, S.

C. Ockeloen, A. Tauschinsky, R. Spreeuw, and S. Whitlock, “Detection of small atom numbers through image processing,” Phys. Rev. A.82, 061606 (2010).
[CrossRef]

S. Whitlock, C. F. Ockeloen, and R. J. C. Spreeuw, “Sub-Poissonian Atom-Number Fluctuations by Three-Body Loss in Mesoscopic Ensembles,” Phys. Rev. Lett.104, 120402 (2010).
[CrossRef] [PubMed]

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. Spreeuw, “Two-dimensional array of microtraps with atomic shift register on a chip,” New J. Phys.11, 023021 (2009).
[CrossRef]

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

Wildermuth, S.

Wilzbach, M.

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

M. Wilzbach, D. Heine, S. Groth, X. Liu, T. Raub, B. Hessmo, and J. Schmiedmayer, “Simple integrated single-atom detector,” Opt. Lett.34, 259–261 (2009).
[CrossRef] [PubMed]

Wineland, D. J.

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

A. J. E. M. Janssen, “Extended Nijboer–Zernike approach for the computation of optical point-spread functions,” J. Opt. Soc. Am. A.19, 849 (2002).
[CrossRef]

Nat. Phys. (1)

K. D. Nelson, X. Li, and D. S. Weiss, “Imaging single atoms in a three-dimensional array,” Nat. Phys.3, 556–560 (2007).
[CrossRef]

Nature (1)

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-poissonian loading of single atoms in a microscopic dipole trap.” Nature411, 1024–7 (2001).
[CrossRef] [PubMed]

Nature Commun. (2)

J. Goldwin, M. Trupke, J. Kenner, a. Ratnapala, and E. a. Hinds, “Fast cavity-enhanced atom detection with low noise and high fidelity.” Nature Commun.2, 418 (2011).
[CrossRef]

E. W. Streed, A. Jechow, B. G. Norton, and D. Kielpinski, “Absorption imaging of a single atom.” Nature Commun.3, 933 (2012).
[CrossRef]

New J. Phys. (4)

M. K. Tey, G. Maslennikov, T. C H Liew, S. A. Aljunid, F. Huber, B. Chng, Z. Chen, V. Scarani, and C. Kurtsiefer, “Interfacing light and single atoms with a lens,” New J. Phys.11, 043011 (2009).
[CrossRef]

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. Spreeuw, “Two-dimensional array of microtraps with atomic shift register on a chip,” New J. Phys.11, 023021 (2009).
[CrossRef]

R. Bücker, A. Perrin, S. Manz, T. Betz, C. Koller, T. Plisson, J. Rottmann, T. Schumm, and J. Schmiedmayer, “Single-particle-sensitive imaging of freely propagating ultracold atoms,” New J. Phys.11, 103039 (2009).
[CrossRef]

D. Heine, W. Rohringer, D. Fischer, M. Wilzbach, T. Raub, S. Loziczky, X. Liu, S. Groth, B. Hessmo, and J. Schmiedmayer, “A single-atom detector integrated on an atom chip: fabrication, characterization and application,” New J. Phys.12, 095005 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A. (3)

R. Gerritsma, S. Whitlock, T. Fernholz, H. Schlatter, J. A. Luigjes, J.-U. Thiele, J. B. Goedkoop, and R. J. C. Spreeuw, “Lattice of microtraps for ultracold atoms based on patterned magnetic films,” Phys. Rev. A.76, 033408 (2007).
[CrossRef]

C. Ockeloen, A. Tauschinsky, R. Spreeuw, and S. Whitlock, “Detection of small atom numbers through image processing,” Phys. Rev. A.82, 061606 (2010).
[CrossRef]

W. Neuhauser, M. Hohenstatt, P. Toschek, and H. Dehmelt, “Localized visible Bâ{+} mono-ion oscillator,” Phys. Rev. A.22, 1137–1140 (1980).
[CrossRef]

Phys. Rev. Lett. (3)

J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, “Lossless State Detection of Single Neutral Atoms,” Phys. Rev. Lett.104, 203601 (2010).
[CrossRef] [PubMed]

R. Gehr, J. Volz, G. Dubois, T. Steinmetz, Y. Colombe, B. L. Lev, R. Long, J. Estève, and J. Reichel, “Cavity-Based Single Atom Preparation and High-Fidelity Hyperfine State Readout,” Phys. Rev. Lett.104, 203602 (2010).
[CrossRef] [PubMed]

S. Whitlock, C. F. Ockeloen, and R. J. C. Spreeuw, “Sub-Poissonian Atom-Number Fluctuations by Three-Body Loss in Mesoscopic Ensembles,” Phys. Rev. Lett.104, 120402 (2010).
[CrossRef] [PubMed]

Quantum Inf. Proc. (1)

V. Y. F. Leung, A. Tauschinsky, N. J. Druten, and R. J. C. Spreeuw, “Microtrap arrays on magnetic film atom chips for quantum information science,” Quantum Inf. Proc.10, 955–974 (2011).
[CrossRef]

Other (2)

D. A. Steck, “Rubidium 87 D Line Data,” http://steck.us/alkalidata 2 (2010).

C. Cohen-Tannoudij, J. Dupont-Roc, and G. Grynberg, Atom—Photon Interactions (Wiley-VCH Verlag GmbH, Weinheim, Germany, 1992).

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Figures (3)

Fig. 1
Fig. 1

Sketch of the imaging system considered for this paper. On the left the situation of a travelling wave without reflection is depicted. On the right the situation of reflective imaging (with the atom chip on top) is shown.

Fig. 2
Fig. 2

Simulated SNR as function of intensity of the incoming beam (in units of saturation intensity) and exposure time. The four subplots correspond to the four cases described in the text as indicated near the top and right axes, the color scale is normalized to the maximum SNR of case d). The black dot marks the position of the optimum.

Fig. 3
Fig. 3

Simulated single-shot absorption images for optimum exposure parameters, including fringe removal. The four subplots correspond to the four cases described in section 3. Bright colors correspond to high optical density. Each subplot shows 5 × 5 pixels, with the atom initially located at the center. At larger distances from the initial position the PSF becomes negligibly small. Using Eq. 9 we extract N=(1.32, 1.39, 0.56, 1.26) atoms for subplots a)–d) respectively. These atom numbers are normalized by Napp for each imaging setup.

Tables (1)

Tables Icon

Table 1 Optimum exposure parameters, and resulting SNR for the four cases described in the text. SNRpx is the SNR obtainable from evaluating a single pixel, while SNRCRB is the SNR for an estimator achieving the Cramér-Rao bound (without taking fringe-removal into account). The normalization factor Napp for case a) and b) is as expected from the analytic treatment of section 2.1. The normalization factor in cases c) and d) can only be obtained from the simulations. Finally we give the probability of true positive measurements p1,1 and false positive measurements due to the presence of zero atoms p1,0 (see 3.2).

Equations (23)

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

I abs ( ρ ) I in ( ρ ) = σ 1 + s [ Re ( p ( ρ ) ) a χ | p ( ρ ) | 2 ]
N det ( x ) = A d ρ 0 τ d t ( I in I abs ) N ref ( x ) = A d ρ 0 τ d t I in
n ( x ) = 1 + s 0 σ 0 N det ( x ) N ref ( x )
p ( ρ , f ; t ) = 2 π ρ 0 2 0 1 r exp ( if r 2 ) × J 0 ( 2 π ρ r ρ 0 ) d r
I abs ( 0 ) I in ( 0 ) = 1 1 + s 0 ( 3 2 NA 2 9 16 NA 4 )
N app = a 1 + s 0 σ 0 I abs ( 0 ) I in ( 0 ) = 1 3 8 NA 2
N OD = a 1 + s 0 σ 0 ln ( 1 I abs ( 0 ) I in ( 0 ) )
σ n ( x ) 2 = ( 1 + s 0 σ 0 ) 2 ( σ det 2 N ref 2 + N det 2 σ ref 2 N ref 4 )
N = n ( x ) q ( x ) q ( x ) 2
SNR ( x ) = n ( x ) σ n ( x )
I det ( ρ ) = 1 2 Z 0 | in ( ρ ) + sc ( coh ) ( ρ ) | 2 + I sc ( incoh ) ( ρ )
= I in ( ρ ) + I sc ( ρ ) + I if ( ρ )
I if ( ρ ) = in ( ρ ) Z 0 Re ( sc ( coh ) ( ρ ) )
I abs ( ρ ) = I in ( ρ ) I det ( ρ ) = I if ( ρ ) I sc ( ρ )
χ P sc = I sc ( ρ ) d 2 ρ
( 1 χ ) P sc = [ I in ( ρ ) I det ( ρ ) ] d 2 ρ
P sc = I if ( ρ ) d 2 ρ
sc ( coh ) ( ρ ) = 𝒜 p ( ρ )
I abs ( ρ ) = in ( ρ ) 2 Z 0 [ 𝒜 p ( ρ ) + c . c . ] 1 + s 2 Z 0 | 𝒜 | 2 | p ( ρ ) | 2
I if ( ρ ) d 2 ρ = in ( 0 ) Re ( 𝒜 ) Z 0 = P sc
I if ( ρ ) P sc [ Re ( p ( ρ ) ) Im ( 𝒜 ) Re ( 𝒜 ) Im ( p ( ρ ) ) ]
I abs ( ρ ) P sc [ Re ( p ( ρ ) ) a χ | p ( ρ ) | 2 ]
I abs ( ρ ) I in ( 0 ) = σ 1 + s [ Re ( p ( ρ ) ) a χ | p ( ρ ) | 2 ]

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