Abstract

Nearly two centuries ago Talbot first observed the fascinating effect whereby light propagating through a periodic structure generates a “carpet” of image revivals in the near field. Here we report the first observation of the spatial Talbot effect for light interacting with periodic Bose–Einstein condensate interference fringes. The Talbot effect can lead to dramatic loss of fringe visibility in images, degrading precision interferometry; however, we demonstrate how the effect can also be used as a tool to enhance visibility, as well as extend the useful focal range of matter-wave detection systems by orders of magnitude. We show that negative optical densities arise from matter-wave induced lensing of detuned imaging light—yielding Talbot-enhanced single-shot interference visibility of >135% compared to the ideal visibility for resonant light.

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2016 (2)

V. A. Henderson, P. F. Griffin, E. Riis, and A. S. Arnold, “Comparative simulations of Fresnel holography methods for atomic waveguides,” New J. Phys. 18, 025007 (2016).
[Crossref]

T. A. Bell, J. A. P. Glidden, L. Humbert, M. W. J. Bromley, S. A. Haine, M. J. Davis, T. W. Neely, M. A. Baker, and H. Rubinsztein-Dunlop, “Bose-Einstein condensation in large time-averaged optical ring potentials,” New J. Phys. 18, 035003 (2016).
[Crossref]

2015 (3)

T. Kovachy, J. M. Hogan, A. Sugarbaker, S. M. Dickerson, C. A. Donnelly, C. Overstreet, and M. A. Kasevich, “Matter wave lensing to picokelvin temperatures,” Phys. Rev. Lett. 114, 143004 (2015).
[Crossref]

A. McDonald, G. McConnell, D. C. Cox, E. Riis, and P. F. Griffin, “3D mapping of intensity field about the focus of a micrometer-scale parabolic mirror,” Opt. Express 23, 2375–2382 (2015).
[Crossref]

C. Ryu and M. G. Boshier, “Integrated coherent matter wave circuits,” New J. Phys. 17, 092002 (2015).
[Crossref]

2014 (6)

S. Eckel, F. Jendrzejewski, A. Kumar, C. J. Lobb, and G. K. Campbell, “Interferometric measurement of the current-phase relationship of a superfluid weak link,” Phys. Rev. X 4, 031052 (2014).
[Crossref]

L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
[Crossref]

J. Léonard, M. Lee, A. Morales, T. M. Karg, T. Esslinger, and T. Donner, “Optical transport and manipulation of an ultracold atomic cloud using focus-tunable lenses,” New J. Phys. 16, 093028 (2014).
[Crossref]

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. M. Robb, A. S. Arnold, R. Kaiser, and T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
[Crossref]

C. Ryu, K. C. Henderson, and M. G. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a Bose–Einstein condensate,” New J. Phys. 16, 013046 (2014).
[Crossref]

G. A. Sinuco-León, K. A. Burrows, A. S. Arnold, and B. M. Garraway, “Inductively guided circuits for ultracold dressed atoms,” Nat. Commun. 5, 5289 (2014).
[Crossref]

2013 (5)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref]

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[Crossref]

H. Müntinga, H. Ahlers, M. Krutzik, A. Wenzlawski, S. Arnold, D. Becker, K. Bongs, H. Dittus, H. Duncker, N. Gaaloul, C. Gherasim, E. Giese, C. Grzeschik, T. W. Hänsch, O. Hellmig, W. Herr, S. Herrmann, E. Kajari, S. Kleinert, C. Lämmerzahl, W. Lewoczko-Adamczyk, J. Malcolm, N. Meyer, R. Nolte, A. Peters, M. Popp, J. Reichel, A. Roura, J. Rudolph, M. Schiemangk, M. Schneider, S. T. Seidel, K. Sengstock, V. Tamma, T. Valenzuela, A. Vogel, R. Walser, T. Wendrich, P. Windpassinger, W. Zeller, T. van Zoest, W. Ertmer, W. P. Schleich, and E. M. Rasel, “Interferometry with Bose-Einstein condensates in microgravity,” Phys. Rev. Lett. 110, 093602 (2013).
[Crossref]

S. Machluf, Y. Japha, and R. Folman, “Coherent Stern-Gerlach momentum splitting on an atom chip,” Nat. Commun. 4, 2424 (2013).
[Crossref]

J. Wen, Y. Zhang, and M. Xiao, “The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics,” Adv. Opt. Photon. 5, 83–130 (2013).
[Crossref]

2012 (3)

K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, and F. Ferlaino, “Bose-Einstein condensation of erbium,” Phys. Rev. Lett. 108, 210401 (2012).
[Crossref]

J. D. Pritchard, A. N. Dinkelaker, A. S. Arnold, P. F. Griffin, and E. Riis, “Demonstration of an inductively coupled ring trap for cold atoms,” New J. Phys. 14, 103047 (2012).
[Crossref]

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

2011 (3)

M. J. Mark, E. Haller, J. G. Danzl, K. Lauber, M. Gustavsson, and H.-C. Nägerl, “Demonstration of the temporal matter-wave Talbot effect for trapped matter waves,” New J. Phys. 13, 085008 (2011).
[Crossref]

M. Lu, N. Q. Burdick, S. H. Youn, and B. L. Lev, “Strongly dipolar Bose-Einstein condensate of dysprosium,” Phys. Rev. Lett. 107, 190401 (2011).
[Crossref]

C. Kohstall, S. Riedl, E. R. Sánchez Guajardo, L. A. Sidorenkov, J. Hecker Denschlag, and R. Grimm, “Observation of interference between two molecular Bose-Einstein condensates,” New J. Phys. 13, 065027 (2011).
[Crossref]

2010 (4)

M. E. Zawadzki, P. F. Griffin, E. Riis, and A. S. Arnold, “Spatial interference from well-separated split condensates,” Phys. Rev. A 81, 043608 (2010).
[Crossref]

H. Müller, A. Peters, and S. Chu, “A precision measurement of the gravitational redshift by the interference of matter waves,” Nature 463, 926–929 (2010).
[Crossref]

W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, “Probing the superfluid-to-Mott insulator transition at the single-atom level,” Science 329, 547–550 (2010).
[Crossref]

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom-resolved fluorescence imaging of an atomic Mott insulator,” Nature 467, 68–72 (2010).
[Crossref]

2009 (2)

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates,” New J. Phys. 11, 043030 (2009).
[Crossref]

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

2008 (1)

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B 41, 211001 (2008).
[Crossref]

2007 (3)

G.-B. Jo, Y. Shin, S. Will, T. A. Pasquini, M. Saba, W. Ketterle, D. E. Pritchard, M. Vengalattore, and M. Prentiss, “Long phase coherence time and number squeezing of two Bose-Einstein condensates on an atom chip,” Phys. Rev. Lett. 98, 030407 (2007).
[Crossref]

S. Hofferberth, I. Lesanovsky, B. Fischer, T. Schumm, and J. Schmiedmayer, “Non-equilibrium coherence dynamics in one-dimensional Bose gases,” Nature 449, 324–327 (2007).
[Crossref]

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
[Crossref]

2006 (4)

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving peak brightness in an atom laser,” Phys. Rev. Lett. 96, 140403 (2006).
[Crossref]

Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, “Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas,” Nature 441, 1118–1121 (2006).
[Crossref]

O. Garcia, B. Deissler, K. J. Hughes, J. M. Reeves, and C. A. Sackett, “Bose-Einstein-condensate interferometer with macroscopic arm separation,” Phys. Rev. A 74, 031601 (2006).
[Crossref]

A. S. Arnold, C. S. Garvie, and E. Riis, “Large magnetic storage ring for Bose-Einstein condensates,” Phys. Rev. A 73, 041606(R) (2006).
[Crossref]

2005 (4)

S. Gupta, K. W. Murch, K. L. Moore, T. P. Purdy, and D. M. Stamper-Kurn, “Bose-Einstein condensation in a circular waveguide,” Phys. Rev. Lett. 95, 143201 (2005).
[Crossref]

Y.-J. Wang, D. Z. Anderson, V. M. Bright, E. A. Cornell, Q. Diot, T. Kishimoto, M. Prentiss, R. A. Saravanan, S. R. Segal, and S. Wu, “Atom Michelson interferometer on a chip using a Bose-Einstein condensate,” Phys. Rev. Lett. 94, 090405 (2005).
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Y. Shin, C. Sanner, G.-B. Jo, T. A. Pasquini, M. Saba, W. Ketterle, D. E. Pritchard, M. Vengalattore, and M. Prentiss, “Interference of Bose-Einstein condensates split with an atom chip,” Phys. Rev. A 72, 021604(R) (2005).
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T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Krüger, “Matter-wave interferometry in a double well on an atom chip,” Nat. Phys. 1, 57–62 (2005).
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2004 (1)

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard, and A. E. Leanhardt, “Atom interferometry with Bose-Einstein condensates in a double-well potential,” Phys. Rev. Lett. 92, 050405 (2004).
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2003 (1)

T. Weber, M. Herbig, M. Mark, H.-C. Nägerl, and R. Grimm, “Bose-Einstein condensation of cesium,” Science 299, 232–235 (2003).
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2002 (2)

A. S. Arnold, C. MacCormick, and M. G. Boshier, “Adaptive inelastic magnetic mirror for Bose-Einstein condensates,” Phys. Rev. A 65, 031601 (2002).
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S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, “Contrast interferometry using Bose-Einstein condensates to measure h/m and α,” Phys. Rev. Lett. 89, 140401 (2002).
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2001 (4)

S. Inouye, S. Gupta, T. Rosenband, A. P. Chikkatur, A. Görlitz, T. L. Gustavson, A. E. Leanhardt, D. E. Pritchard, and W. Ketterle, “Observation of vortex phase singularities in Bose-Einstein condensates,” Phys. Rev. Lett. 87, 080402 (2001).
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A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25–61 (2001).
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K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “Waveguide for Bose-Einstein condensates,” Phys. Rev. A 63, 031602 (2001).
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D. J. Han, M. T. DePue, and D. S. Weiss, “Loading and compressing Cs atoms in a very far-off-resonant light trap,” Phys. Rev. A 63, 023405 (2001).
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2000 (2)

J. M. McGuirk, M. J. Snadden, and M. A. Kasevich, “Large area light-pulse atom interferometry,” Phys. Rev. Lett. 85, 4498–4501 (2000).
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T. L. Gustavson, A. Landragin, and M. A. Kasevich, “Rotation sensing with a dual atom-interferometer Sagnac gyroscope,” Classical Quantum Gravity 17, 2385–2398 (2000).
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1999 (1)

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
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1997 (3)

T. L. Gustavson, P. Bouyer, and M. A. Kasevich, “Precision rotation measurements with an atom interferometer gyroscope,” Phys. Rev. Lett. 78, 2046–2049 (1997).
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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).
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S. Nowak, Ch. Kurtsiefer, T. Pfau, and C. David, “High-order Talbot fringes for atomic matter waves,” Opt. Lett. 22, 1430–1432 (1997).
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1996 (2)

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996).
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M. O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Collective excitations of a Bose-Einstein condensate in a magnetic trap,” Phys. Rev. Lett. 77, 988–991 (1996).
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1995 (3)

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14–R17 (1995).
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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).
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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).
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1989 (1)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–108 (1989).
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1881 (1)

Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196–205 (1881).
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1836 (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9(56), 401–407 (1836).
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Ackemann, T.

G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. M. Robb, A. S. Arnold, R. Kaiser, and T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
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H. Müntinga, H. Ahlers, M. Krutzik, A. Wenzlawski, S. Arnold, D. Becker, K. Bongs, H. Dittus, H. Duncker, N. Gaaloul, C. Gherasim, E. Giese, C. Grzeschik, T. W. Hänsch, O. Hellmig, W. Herr, S. Herrmann, E. Kajari, S. Kleinert, C. Lämmerzahl, W. Lewoczko-Adamczyk, J. Malcolm, N. Meyer, R. Nolte, A. Peters, M. Popp, J. Reichel, A. Roura, J. Rudolph, M. Schiemangk, M. Schneider, S. T. Seidel, K. Sengstock, V. Tamma, T. Valenzuela, A. Vogel, R. Walser, T. Wendrich, P. Windpassinger, W. Zeller, T. van Zoest, W. Ertmer, W. P. Schleich, and E. M. Rasel, “Interferometry with Bose-Einstein condensates in microgravity,” Phys. Rev. Lett. 110, 093602 (2013).
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K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, and F. Ferlaino, “Bose-Einstein condensation of erbium,” Phys. Rev. Lett. 108, 210401 (2012).
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Andersen, M. F.

C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
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Anderson, D. Z.

Y.-J. Wang, D. Z. Anderson, V. M. Bright, E. A. Cornell, Q. Diot, T. Kishimoto, M. Prentiss, R. A. Saravanan, S. R. Segal, and S. Wu, “Atom Michelson interferometer on a chip using a Bose-Einstein condensate,” Phys. Rev. Lett. 94, 090405 (2005).
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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).
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Andersson, L. M.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Krüger, “Matter-wave interferometry in a double well on an atom chip,” Nat. Phys. 1, 57–62 (2005).
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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).
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M. O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Collective excitations of a Bose-Einstein condensate in a magnetic trap,” Phys. Rev. Lett. 77, 988–991 (1996).
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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).
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Arlt, J.

K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “Waveguide for Bose-Einstein condensates,” Phys. Rev. A 63, 031602 (2001).
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V. A. Henderson, P. F. Griffin, E. Riis, and A. S. Arnold, “Comparative simulations of Fresnel holography methods for atomic waveguides,” New J. Phys. 18, 025007 (2016).
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G. Labeyrie, E. Tesio, P. M. Gomes, G.-L. Oppo, W. J. Firth, G. R. M. Robb, A. S. Arnold, R. Kaiser, and T. Ackemann, “Optomechanical self-structuring in a cold atomic gas,” Nat. Photonics 8, 321–325 (2014).
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G. A. Sinuco-León, K. A. Burrows, A. S. Arnold, and B. M. Garraway, “Inductively guided circuits for ultracold dressed atoms,” Nat. Commun. 5, 5289 (2014).
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J. D. Pritchard, A. N. Dinkelaker, A. S. Arnold, P. F. Griffin, and E. Riis, “Demonstration of an inductively coupled ring trap for cold atoms,” New J. Phys. 14, 103047 (2012).
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M. E. Zawadzki, P. F. Griffin, E. Riis, and A. S. Arnold, “Spatial interference from well-separated split condensates,” Phys. Rev. A 81, 043608 (2010).
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N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B 41, 211001 (2008).
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A. S. Arnold, C. S. Garvie, and E. Riis, “Large magnetic storage ring for Bose-Einstein condensates,” Phys. Rev. A 73, 041606(R) (2006).
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A. S. Arnold, C. MacCormick, and M. G. Boshier, “Adaptive inelastic magnetic mirror for Bose-Einstein condensates,” Phys. Rev. A 65, 031601 (2002).
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H. Müntinga, H. Ahlers, M. Krutzik, A. Wenzlawski, S. Arnold, D. Becker, K. Bongs, H. Dittus, H. Duncker, N. Gaaloul, C. Gherasim, E. Giese, C. Grzeschik, T. W. Hänsch, O. Hellmig, W. Herr, S. Herrmann, E. Kajari, S. Kleinert, C. Lämmerzahl, W. Lewoczko-Adamczyk, J. Malcolm, N. Meyer, R. Nolte, A. Peters, M. Popp, J. Reichel, A. Roura, J. Rudolph, M. Schiemangk, M. Schneider, S. T. Seidel, K. Sengstock, V. Tamma, T. Valenzuela, A. Vogel, R. Walser, T. Wendrich, P. Windpassinger, W. Zeller, T. van Zoest, W. Ertmer, W. P. Schleich, and E. M. Rasel, “Interferometry with Bose-Einstein condensates in microgravity,” Phys. Rev. Lett. 110, 093602 (2013).
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Baier, S.

K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, and F. Ferlaino, “Bose-Einstein condensation of erbium,” Phys. Rev. Lett. 108, 210401 (2012).
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T. A. Bell, J. A. P. Glidden, L. Humbert, M. W. J. Bromley, S. A. Haine, M. J. Davis, T. W. Neely, M. A. Baker, and H. Rubinsztein-Dunlop, “Bose-Einstein condensation in large time-averaged optical ring potentials,” New J. Phys. 18, 035003 (2016).
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W. S. Bakr, A. Peng, M. E. Tai, R. Ma, J. Simon, J. I. Gillen, S. Fölling, L. Pollet, and M. Greiner, “Probing the superfluid-to-Mott insulator transition at the single-atom level,” Science 329, 547–550 (2010).
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T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Krüger, “Matter-wave interferometry in a double well on an atom chip,” Nat. Phys. 1, 57–62 (2005).
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Battelier, B.

Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, “Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas,” Nature 441, 1118–1121 (2006).
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H. Müntinga, H. Ahlers, M. Krutzik, A. Wenzlawski, S. Arnold, D. Becker, K. Bongs, H. Dittus, H. Duncker, N. Gaaloul, C. Gherasim, E. Giese, C. Grzeschik, T. W. Hänsch, O. Hellmig, W. Herr, S. Herrmann, E. Kajari, S. Kleinert, C. Lämmerzahl, W. Lewoczko-Adamczyk, J. Malcolm, N. Meyer, R. Nolte, A. Peters, M. Popp, J. Reichel, A. Roura, J. Rudolph, M. Schiemangk, M. Schneider, S. T. Seidel, K. Sengstock, V. Tamma, T. Valenzuela, A. Vogel, R. Walser, T. Wendrich, P. Windpassinger, W. Zeller, T. van Zoest, W. Ertmer, W. P. Schleich, and E. M. Rasel, “Interferometry with Bose-Einstein condensates in microgravity,” Phys. Rev. Lett. 110, 093602 (2013).
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T. A. Bell, J. A. P. Glidden, L. Humbert, M. W. J. Bromley, S. A. Haine, M. J. Davis, T. W. Neely, M. A. Baker, and H. Rubinsztein-Dunlop, “Bose-Einstein condensation in large time-averaged optical ring potentials,” New J. Phys. 18, 035003 (2016).
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Berry, M. V.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996).
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Beugnon, J.

L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
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L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
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J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom-resolved fluorescence imaging of an atomic Mott insulator,” Nature 467, 68–72 (2010).
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H. Müntinga, H. Ahlers, M. Krutzik, A. Wenzlawski, S. Arnold, D. Becker, K. Bongs, H. Dittus, H. Duncker, N. Gaaloul, C. Gherasim, E. Giese, C. Grzeschik, T. W. Hänsch, O. Hellmig, W. Herr, S. Herrmann, E. Kajari, S. Kleinert, C. Lämmerzahl, W. Lewoczko-Adamczyk, J. Malcolm, N. Meyer, R. Nolte, A. Peters, M. Popp, J. Reichel, A. Roura, J. Rudolph, M. Schiemangk, M. Schneider, S. T. Seidel, K. Sengstock, V. Tamma, T. Valenzuela, A. Vogel, R. Walser, T. Wendrich, P. Windpassinger, W. Zeller, T. van Zoest, W. Ertmer, W. P. Schleich, and E. M. Rasel, “Interferometry with Bose-Einstein condensates in microgravity,” Phys. Rev. Lett. 110, 093602 (2013).
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K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “Waveguide for Bose-Einstein condensates,” Phys. Rev. A 63, 031602 (2001).
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Boshier, M. G.

C. Ryu and M. G. Boshier, “Integrated coherent matter wave circuits,” New J. Phys. 17, 092002 (2015).
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C. Ryu, K. C. Henderson, and M. G. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a Bose–Einstein condensate,” New J. Phys. 16, 013046 (2014).
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K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates,” New J. Phys. 11, 043030 (2009).
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A. S. Arnold, C. MacCormick, and M. G. Boshier, “Adaptive inelastic magnetic mirror for Bose-Einstein condensates,” Phys. Rev. A 65, 031601 (2002).
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T. L. Gustavson, P. Bouyer, and M. A. Kasevich, “Precision rotation measurements with an atom interferometer gyroscope,” Phys. Rev. Lett. 78, 2046–2049 (1997).
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Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
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B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
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Y.-J. Wang, D. Z. Anderson, V. M. Bright, E. A. Cornell, Q. Diot, T. Kishimoto, M. Prentiss, R. A. Saravanan, S. R. Segal, and S. Wu, “Atom Michelson interferometer on a chip using a Bose-Einstein condensate,” Phys. Rev. Lett. 94, 090405 (2005).
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T. A. Bell, J. A. P. Glidden, L. Humbert, M. W. J. Bromley, S. A. Haine, M. J. Davis, T. W. Neely, M. A. Baker, and H. Rubinsztein-Dunlop, “Bose-Einstein condensation in large time-averaged optical ring potentials,” New J. Phys. 18, 035003 (2016).
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M. Lu, N. Q. Burdick, S. H. Youn, and B. L. Lev, “Strongly dipolar Bose-Einstein condensate of dysprosium,” Phys. Rev. Lett. 107, 190401 (2011).
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K. Bongs, S. Burger, S. Dettmer, D. Hellweg, J. Arlt, W. Ertmer, and K. Sengstock, “Waveguide for Bose-Einstein condensates,” Phys. Rev. A 63, 031602 (2001).
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G. A. Sinuco-León, K. A. Burrows, A. S. Arnold, and B. M. Garraway, “Inductively guided circuits for ultracold dressed atoms,” Nat. Commun. 5, 5289 (2014).
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J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, “Single-atom-resolved fluorescence imaging of an atomic Mott insulator,” Nature 467, 68–72 (2010).
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S. Inouye, S. Gupta, T. Rosenband, A. P. Chikkatur, A. Görlitz, T. L. Gustavson, A. E. Leanhardt, D. E. Pritchard, and W. Ketterle, “Observation of vortex phase singularities in Bose-Einstein condensates,” Phys. Rev. Lett. 87, 080402 (2001).
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L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
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H. Müller, A. Peters, and S. Chu, “A precision measurement of the gravitational redshift by the interference of matter waves,” Nature 463, 926–929 (2010).
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A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25–61 (2001).
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C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, “Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap,” Phys. Rev. Lett. 99, 260401 (2007).
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L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407–5411 (1999).
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Y.-J. Wang, D. Z. Anderson, V. M. Bright, E. A. Cornell, Q. Diot, T. Kishimoto, M. Prentiss, R. A. Saravanan, S. R. Segal, and S. Wu, “Atom Michelson interferometer on a chip using a Bose-Einstein condensate,” Phys. Rev. Lett. 94, 090405 (2005).
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L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbène, J. Dalibard, and J. Beugnon, “Quench-induced supercurrents in an annular Bose gas,” Phys. Rev. Lett. 113, 135302 (2014).
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T. A. Bell, J. A. P. Glidden, L. Humbert, M. W. J. Bromley, S. A. Haine, M. J. Davis, T. W. Neely, M. A. Baker, and H. Rubinsztein-Dunlop, “Bose-Einstein condensation in large time-averaged optical ring potentials,” New J. Phys. 18, 035003 (2016).
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Supplementary Material (1)

NameDescription
» Dataset 1       Experimental and theoretical results corresponding to the figures in the main article.

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Figures (5)

Fig. 1.
Fig. 1. Matter-wave interference. (a) Experimental absorption image (1.4  mm×1.4  mm) of a condensate axially split by a blue-detuned optical dipole beam at 160 ms levitation time; scalebar indicates optical density (OD). (b) Background-subtracted, angle-corrected, row-averaged OD profile (red points) of the red rectangular region in (a). The fitted sine wave has a parabolic spatial envelope and offset (gray curve) for fringe visibility and period extraction. (c) Fringe period as a function of levitation time: experimental data (black dots); inferred fringe period evolution [blue curve, Eq. (2) with ωz=13.8±1.4  rad/s and d=45  μm]; ballistic expansion theory [red line, Eq. (1)].
Fig. 2.
Fig. 2. Theoretical light propagation through BEC fringes. (a)–(c) Ten BEC fringes along x=0 of peak optical density OD0=0.4 and visibility 80% interact with resonant light leading, on propagation (x>0), to periodic phase [(a) in radians] and OD (b) profile revivals. Antinodes of OD (red points) correspond to nodes of the phase, and vice versa. The central fringe at z=0 is displayed (c) for red, resonant (black), and blue laser detunings of Γ/2, 0, and Γ/2, illustrating how detuning not only phase-shifts the fringes in x, but can also enhance visibility relative to the initial optical density. After the light in images (a), (b), and (c) propagates through a 300-mm-long ×2 magnification imaging system, the corresponding phase, OD, and visibility are shown in (d), (e), and (f), respectively. Note the chirp in the spatial period about the image plane [white dashed line in (d) and (e)].
Fig. 3.
Fig. 3. (a) Single-shot 1D BEC OD profile (21 row average, Δ=+4  MHz), with visibility C=1.5 from fitting data points (black) with Eq. (4) (green curve). (b) Experimental (dots) and theoretical [curves from Fig. 2(e)] visibility as a function of camera position for detunings 4, 0, and +4  MHz (red, black, and blue, respectively). All error bars in this paper represent the standard deviation of results from three separate images. The central Talbot period was fit to be 6.1(0.1) mm, which agrees well with the theoretical Talbot period of 6.4(0.3) mm predicted from the fringe period and Eq. (5).
Fig. 4.
Fig. 4. Talbot period variation with fringe period. Visibility is observed as a function of camera position for Δ=+0.5  MHz imaging light after 140, 160, and 170 ms levitation. From fits to these data Talbot periods were measured to be 3.0(0.1) mm, 6.1(0.2) mm, and 7.6(0.2) mm, respectively, which agree with the theoretical Talbot periods of 3.4(0.1) mm, 6.3(0.2) mm, and 8.1(0.8) mm determined from the experimental fringe periods associated with the 140, 160, and 170 ms levitation times. Inset optical density plots (320  μm×280  μm) show the observed visibility changing through the Talbot period.
Fig. 5.
Fig. 5. Interference visibility as a function of levitation time and imaging detuning. Red triangles, black circles and blue squares denote detunings Δ=4  MHz, 0 MHz, and +4  MHz, respectively. For comparison theory curves are provided of optimal visibility using Eq. (6) with pixelation-free final visibility values of C=0.8, 1.0, and 1.3, shown by the black, green, and cyan curves, respectively. The C values 0.8 and 1.3 are chosen to approximately match the theoretical and experimental values from Figs. 2 and 3, where OD0=0.4.

Equations (6)

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

λf=htmd,
λf=λfsinh(ωzt)ωzt.
OD=ln(IiIbIeIb),
(A0+A2(zz0)2)(Csin(kz+ϕ)+1).
Λ=(Mλf)2λ,
FCCD=1+sinc(πl/λf)Csin(2πjl/λf);

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