Ghost imaging with atoms

Journal name:
Nature
Volume:
540,
Pages:
100–103
Date published:
DOI:
doi:10.1038/nature20154
Received
Accepted
Published online

Ghost imaging is a counter-intuitive phenomenon—first realized in quantum optics1, 2—that enables the image of a two-dimensional object (mask) to be reconstructed using the spatio-temporal properties of a beam of particles with which it never interacts. Typically, two beams of correlated photons are used: one passes through the mask to a single-pixel (bucket) detector while the spatial profile of the other is measured by a high-resolution (multi-pixel) detector. The second beam never interacts with the mask. Neither detector can reconstruct the mask independently, but temporal cross-correlation between the two beams can be used to recover a ‘ghost’ image. Here we report the realization of ghost imaging using massive particles instead of photons. In our experiment, the two beams are formed by correlated pairs of ultracold, metastable helium atoms3, which originate from s-wave scattering of two colliding Bose–Einstein condensates4, 5. We use higher-order Kapitza–Dirac scattering6, 7, 8 to generate a large number of correlated atom pairs, enabling the creation of a clear ghost image with submillimetre resolution. Future extensions of our technique could lead to the realization of ghost interference9, and enable tests of Einstein–Podolsky–Rosen entanglement9 and Bell’s inequalities10 with atoms.

At a glance

Figures

  1. Schematic of atomic ghost imaging.
    Figure 1: Schematic of atomic ghost imaging.

    Correlated pairs of atoms created in a collision form two beams. One beam passes through the object to be imaged (‘O’) and the arrival times of the individual atoms are detected by a bucket detector (‘B’). The second beam never interacts with the object, but is detected with full temporal and spatial resolution by a multi-pixel detector (‘M’). A correlator (‘C’) then reconstructs the image of the object.

  2. Schematic of the experiment and resulting ghost image.
    Figure 2: Schematic of the experiment and resulting ghost image.

    a, The experiment starts by using Kapitza–Dirac diffraction laser beams (yellow arrows) to split the trapped BEC cloud (dark red sphere) into different momentum states (for simplicity, only the first diffraction order is shown as the clouds evolve in time). Binary atomic collisions populate an s-wave scattering halo (pale red sphere) with correlated pairs of opposite momenta (±k), which then expand as they fall under gravity (g). In the momentum space associated with the centre-of-mass reference frame, the BECs are situated at opposite poles of the s-wave scattering sphere. Some of the halo atoms pass through a mask placed 10 mm above the bucket port of the single-atom detector, while their diametrically opposing counterparts (separated by the dashed grey line) are registered by the multi-pixel port. b, Experimental data from 2,000 individual experimental runs showing the 11 halos produced in the collision process, where the individual atom counts are reconstructed in three-dimensional momentum space. Kapitza–Dirac diffraction produces 12 diffraction orders −6, … +5 along ez. Collisions between each pair of adjacent orders result in 11 independent scattering halos. c, Individual ghost images from each of the halos from 68,835 experimental runs are combined to form the final image (bottom; scale bar, 5 mm). Because of the difference in absolute velocities for different diffraction orders, the halos that land first cover only a fraction of the image.

  3. Cross-correlation function.
    Figure 3: Cross-correlation function.

    The main plot shows g(2)(0, 0, Δz) as a function of only the vertical coordinate Δz. The solid line is a Gaussian fit, which has an r.m.s. width of σz = 0.37 mm, corresponding to the correlation length. Error bars show the statistical error over the 54,473 experimental runs. The inset shows g(2)x, Δy, 0) for the experimental data.

  4. Resolution and visibility of the ghost image.
    Figure 4: Resolution and visibility of the ghost image.

    a, Ghost image (top) of the vertical bars of the ‘U’ (indicated by the yellow bars). The image is integrated vertically to yield an intensity (bottom, circles), which is fitted with the convolution with the PSF (bottom, solid line). This yields a width (representing the imaging resolution) of 0.40 mm. b, The visibility (V = (I − B)/(I + B)) is shown as a function of the number of halos (Nhalos) that are accumulated to form the image. I is the mean intensity within the shape to be imaged (yellow ‘N’, as shown in the inset) and B is the mean intensity outside the ‘N’. Each plotted image is the result of accumulating reconstructed images from different s-wave halos. The dashed curve is a guide to the eye; error bars show the standard error of the mean across the image pixels.

  5. The object.
    Extended Data Fig. 1: The object.

    Microscope image of the mask used to create the ghost image. The region indicated by the dashed line forms the vertical bars shown in Fig. 4a, which was used to determine the ghost imaging resolution.

  6. Ghost image visibility.
    Extended Data Fig. 2: Ghost image visibility.

    Visibilities (dots) for images (insets) reconstructed from each individual halo with different average numbers of atoms . Diffraction orders producing the halos are labelled as (  + 1, ). The dashed curve is a guide to the eye. Error bars represent the standard error of the mean associated with the variances of the pixel values contributing to I and B.

References

  1. Erkmen, B. I. & Shapiro, J. H. Ghost imaging: from quantum to classical to computational. Adv. Opt. Photonics 2, 405450 (2010)
  2. Shapiro, J. H. & Boyd, R. W. The physics of ghost imaging. Quantum Inf. Process. 11, 949993 (2012)
  3. Vassen, W. et al. Cold and trapped metastable noble gases. Rev. Mod. Phys. 84, 175210 (2012)
  4. Perrin, A. et al. Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose–Einstein condensates. Phys. Rev. Lett. 99, 150405 (2007)
  5. Jaskula, J.-C. et al. Sub-Poissonian number differences in four-wave mixing of matter waves. Phys. Rev. Lett. 105, 190402 (2010)
  6. Kapitza, P. L. & Dirac, P. A. M. The reflection of electrons from standing light waves. Math. Proc. Camb. Philos. Soc. 29, 297300 (1933)
  7. Gould, P. L., Ruff, G. A. & Pritchard, D. E. Diffraction of atoms by light: the near-resonant Kapitza–Dirac effect. Phys. Rev. Lett. 56, 827830 (1986)
  8. Ovchinnikov, Yu. B. et al. Diffraction of a released Bose–Einstein condensate by a pulsed standing light wave. Phys. Rev. Lett. 83, 284287 (1999)
  9. Kofler, J. et al. Einstein–Podolsky–Rosen correlations from colliding Bose–Einstein condensates. Phys. Rev. A 86, 032115 (2012)
  10. Jack, B. et al. Holographic ghost imaging and the violation of a Bell inequality. Phys. Rev. Lett. 103, 083602 (2009)
  11. Pittman, T. B., Shih, Y. H., Strekalov, D. V. & Sergienko, A. V. Optical imaging by means of two-photon quantum entanglement. Phys. Rev. A 52, R3429R3432 (1995)
  12. Strekalov, D. V., Sergienko, A. V., Klyshko, D. N. & Shih, Y. H. Observation of two-photon “ghost” interference and diffraction. Phys. Rev. Lett. 74, 36003603 (1995)
  13. Klyshko, D. N. Effect of focusing on photon correlation in parametric light scattering. Sov. Phys. JETP 67, 11311135 (1988)
  14. Belinskii, A. V. & Klyshko, D. N. Two-photon optics: diffraction, holography, and transformation of two-dimensional signals. Sov. Phys. JETP 78, 259262 (1994)
  15. Hardy, N. D. & Shapiro, J. H. Computational ghost imaging versus imaging laser radar for three-dimensional imaging. Phys. Rev. A 87, 023820 (2013)
  16. Yuan, S., Yao, J., Liu, X., Zhou, X. & Li, Z. Cryptanalysis and security enhancement of optical cryptography based on computational ghost imaging. Opt. Commun. 365, 180185 (2016)
  17. Yu, H. et al. Fourier-transform ghost imaging with hard X rays. Phys. Rev. Lett. 117, 113901 (2016)
  18. Pelliccia, D., Rack, A., Scheel, M., Cantelli, V. & Paganin, D. M. Experimental X-ray ghost imaging. Phys. Rev. Lett. 117, 113902 (2016)
  19. Sun, B. et al. 3D computational imaging with single-pixel detectors. Science 340, 844847 (2013)
  20. Ryczkowski, P., Barbier, M., Friberg, A. T., Dudley, J. M. & Genty, G. Ghost imaging in the time domain. Nat. Photon. 10, 167170 (2016)
  21. Brida, G., Genovese, M. & Ruo Berchera, I. Experimental realization of sub-shot-noise quantum imaging. Nat. Photon. 4, 227230 (2010)
  22. Morris, P. A., Aspden, R., Bell, J. E. C., Boyd, R. W. & Padgett, M. J. Imaging with a small number of photons. Nat. Commun. 6, 5913 (2015)
  23. Bennink, R. S., Bentley, S. J. & Boyd, R. W. “Two-photon” coincidence imaging with a classical source. Phys. Rev. Lett. 89, 113601 (2002)
  24. Bennink, R. S., Bentley, S. J., Boyd, R. W. & Howell, J. C. Quantum and classical coincidence imaging. Phys. Rev. Lett. 92, 033601 (2004)
  25. Ferri, F. et al. High-resolution ghost image and ghost diffraction experiments with thermal light. Phys. Rev. Lett. 94, 183602 (2005)
  26. Yasuda, M. & Shimizu, F. Observation of two-atom correlation of an ultracold neon atomic beam. Phys. Rev. Lett. 77, 30903093 (1996)
  27. Jeltes, T. et al. Comparison of the Hanbury Brown–Twiss effect for bosons and fermions. Nature 445, 402405 (2007)
  28. Hodgman, S. S., Dall, R. G., Manning, A. G., Baldwin, K. G. H. & Truscott, A. G. Direct measurement of long-range third-order coherence in Bose–Einstein condensates. Science 331, 10461049 (2011)
  29. Lewis-Swan, R. J. & Kheruntsyan, K. V. Proposal for demonstrating the Hong–Ou–Mandel effect with matter waves. Nat. Commun. 5, 3752 (2014)
  30. Lewis-Swan, R. J. & Kheruntsyan, K. V. Proposal for a motional-state Bell inequality test with ultracold atoms. Phys. Rev. A 91, 052114 (2015)
  31. Dall, R. G. & Truscott, A. G. Bose–Einstein condensation of metastable helium in a bi-planar quadrupole Ioffe configuration trap. Opt. Commun. 270, 255261 (2007)
  32. Manning, A. G., Khakimov, R. I., Dall, R. G. & Truscott, A. G. Wheeler’s delayed-choice gedanken experiment with a single atom. Nat. Phys. 11, 539542 (2015)
  33. Dall, R. G. et al. Ideal n-body correlations with massive particles. Nat. Phys. 9, 341344 (2013)

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Author information

Affiliations

  1. Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 2601, Australia

    • R. I. Khakimov,
    • B. M. Henson,
    • D. K. Shin,
    • S. S. Hodgman,
    • R. G. Dall,
    • K. G. H. Baldwin &
    • A. G. Truscott

Contributions

R.I.K., R.G.D. and A.G.T. conceived the experiment. R.I.K. performed the experiment and collected the data. All authors contributed to the conceptual formulation of the physics, the interpretation of the data and the writing of the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Reviewer Information Nature thanks M. A. Kasevich and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author details

Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: The object. (260 KB)

    Microscope image of the mask used to create the ghost image. The region indicated by the dashed line forms the vertical bars shown in Fig. 4a, which was used to determine the ghost imaging resolution.

  2. Extended Data Figure 2: Ghost image visibility. (215 KB)

    Visibilities (dots) for images (insets) reconstructed from each individual halo with different average numbers of atoms . Diffraction orders producing the halos are labelled as (  + 1, ). The dashed curve is a guide to the eye. Error bars represent the standard error of the mean associated with the variances of the pixel values contributing to I and B.

Additional data