Quantum superposition at the half-metre scale

Journal name:
Nature
Volume:
528,
Pages:
530–533
Date published:
DOI:
doi:10.1038/nature16155
Received
Accepted
Published online

The quantum superposition principle allows massive particles to be delocalized over distant positions. Though quantum mechanics has proved adept at describing the microscopic world, quantum superposition runs counter to intuitive conceptions of reality and locality when extended to the macroscopic scale1, as exemplified by the thought experiment of Schrödinger’s cat2. Matter-wave interferometers3, which split and recombine wave packets in order to observe interference, provide a way to probe the superposition principle on macroscopic scales4 and explore the transition to classical physics5. In such experiments, large wave-packet separation is impeded by the need for long interaction times and large momentum beam splitters, which cause susceptibility to dephasing and decoherence1. Here we use light-pulse atom interferometry6, 7 to realize quantum interference with wave packets separated by up to 54 centimetres on a timescale of 1 second. These results push quantum superposition into a new macroscopic regime, demonstrating that quantum superposition remains possible at the distances and timescales of everyday life. The sub-nanokelvin temperatures of the atoms and a compensation of transverse optical forces enable a large separation while maintaining an interference contrast of 28 per cent. In addition to testing the superposition principle in a new regime, large quantum superposition states are vital to exploring gravity with atom interferometers in greater detail. We anticipate that these states could be used to increase sensitivity in tests of the equivalence principle8, 9, 10, 11, 12, measure the gravitational Aharonov–Bohm effect13, and eventually detect gravitational waves14 and phase shifts associated with general relativity12.

At a glance

Figures

  1. Fountain interferometer.
    Figure 1: Fountain interferometer.

    a, After evaporative cooling and a magnetic lensing sequence (see Methods), the ultra-cold atom cloud is launched vertically from below the cylindrical magnetic shield using an optical lattice. At t = 0, the first beam splitter sequence splits the cloud into a superposition of momentum states separated by nħk. At t = T, the wave packet is fully separated, and a mirror sequence reverses the momentum states of the two halves of the cloud. At t = 2T, the clouds spatially overlap, and a final beam splitter sequence is applied. After a short drift time, the output ports spatially separate by 6 mm owing to their differing momenta, and the two complementary ports are imaged. This diagram is not to scale, and the upward- and downward-going clouds are shown horizontally displaced for clarity. The red, cylindrical arrows illustrate the counter-propagating laser beams that drive the Bragg transitions. The blue spheres represent the atomic wave packets. The solid and dashed lines show the trajectories of the atomic wave packets (solid lines correspond to nħk greater momentum in the upward direction than the dashed lines), and the yellow arrowheads indicate the direction of motion. b, Pulse sequence of a 16ħk interferometer, see Methods for details. The main plot depicts the spacetime trajectories of the wave packets, and the pulse train underneath shows the temporal profile of the laser pulse sequences. c, A moving standing wave (red wave, direction of motion indicated by red arrow) induces a Bragg transition of one specific velocity class and changes its momentum by 2ħk, for example, from 2ħk to 4ħk. The black lines show a zoomed-in view of the spacetime trajectories, labelled by momentum. The black dot indicates the point at which the transition from momentum 2ħk to 4ħk occurs.

  2. Wave packets separated by 54 cm.
    Figure 2: Wave packets separated by 54 cm.

    We adjust the launch height of the millimetre-sized atom cloud so that it passes the detector when the wave packets (corresponding to the two peaks in the image) are maximally separated. In order to visualize the full extent of the wave function, we take 36 snapshots of different slices of the distribution. The images are taken at slightly different times between the atom launch and the fluorescence imaging and are stitched together according to the velocity of the atoms. The vertical height in the plot corresponds to atom density (red indicates higher density).

  3. Fluorescence images of output ports.
    Figure 3: Fluorescence images of output ports.

    The two atom clouds resulting from the final beam splitter constitute the output ports of the interferometer. A single fluorescence image allows us to extract the atom number in each port. a, The 2ħk interferometer shows high contrast with nearly full population oscillation between the upper port (front image) and the lower port (back image). b, For the 90ħk interferometer, the population oscillates by more than 40%. Owing to spontaneous emission and velocity selectivity, the detected atom number is more than ten times smaller than for 2ħk. All displayed images are normalized to have the same peak height and are labelled with δϕ corresponding to the interferometer phase modulo 2π. Each image is 13.8 × 9.7 mm, and the data are smoothed with a Gaussian filter with radius 0.5 mm.

  4. Contrast metrics.
    Figure 4: Contrast metrics.

    a, The contrast envelopes establish the interference effect. We plot versus the timing delay δT, where σ(P1) is the standard deviation of the set of observed P1 values after a sequence of 20 shots at the specified δT (P1 is the normalized population in output port 1). The data points corresponding to the blue squares, black circles and red triangles are for 30ħk, 60ħk and 90ħk. The solid curves show the theory A + BΓT − δT0), with coherence time δTc, offset A, centre δT0, and amplitude B as fitting parameters. Examples of the traces that lead to the points in the contrast envelopes are shown in Extended Data Fig. 2. Inset, comparison of fitted coherence times (points, 1 s.d. error bars from fit uncertainty) to theory (grey curve). The grey, shaded region indicates 1 s.d. theoretical uncertainty arising from uncertainty in the measured velocity spread Δvz. b, Trends in maximum observed contrast (blue data points, main panel) and normalized atom number Na in the output ports (red data points, inset) with nħk. The data points are for n = 2, 16, 30, 60 and 90. The atom number is normalized to the average number of atoms after a 2ħk interferometer. The thin, red curve in the inset shows the predicted atom number based on the measured spontaneous emission loss rate and π-pulse velocity selectivity. Error bars, 1 s.d. uncertainties computed with the analysis discussed in Methods.

  5. Spatial interference fringes.
    Figure 5: Spatial interference fringes.

    a, Horizontally integrated fluorescence images of the two 30ħk output ports (upper and lower panel) for a single run with δT = −50 μs (red). The images are fitted to a sinusoidally modulated Gaussian profile. For comparison, the output ports for δT = 100 μs have a Gaussian profile without interference fringes (blue). y axis in arbitrary units. b, Cosine (left panel) and sine (right panel) principal components of a set of 30ħk interferometer runs with δT = −50 μs, which show the effects of a vertical phase gradient across the cloud. All observed fringes are linear combinations of these basis images. Red and blue regions are anti-correlated.

  6. Dependence of contrast on absolute light shift compensation.
    Extended Data Fig. 1: Dependence of contrast on absolute light shift compensation.

    For 30ħk, the contrast as a fraction of its maximum value is plotted as a function of the asymmetry between the red and blue sidebands for one of the atom optics laser beams. To change the sideband asymmetry, we adjust the temperature of one of the frequency doubling crystals while keeping the sidebands of the second atom optics laser beam symmetric. Where Pred and Pblue are the respective optical powers in the red and blue sidebands, we define an asymmetry parameter 1 − (Pred/Pblue). Since the blue sideband is used to drive the Bragg transitions, we keep Pblue fixed in order to maintain constant Rabi frequency. This prevents us from reaching large negative values of the asymmetry parameter, because there is only enough total optical power available to increase Pred slightly without suppressing Pblue. In order to achieve a more negative effective value of the asymmetry parameter, we suppress the power in the carrier to half its usual amount for the one negative point in the plot. The carrier is blue detuned, so decreasing its power pulls the absolute light shift in the same direction as decreasing Pblue. To account for this, we plot the fractional contrast versus the effective asymmetry parameter that would yield the same light shift as the one that we implement, but at a fixed carrier power. The observed dependence of contrast on the sideband asymmetry indicates the importance of absolute light shift compensation for LMT interferometry. Error bars, 1σ.

  7. Examples of data showing interference contrast.
    Extended Data Fig. 2: Examples of data showing interference contrast.

    Plots of P1 versus experimental trial for 2ħk, 30ħk, 60ħk and 90ħk. The red traces have small values of δT and therefore display interference contrast. As discussed in the main text, we do not observe a stable fringe because of the vibration of the retroreflection mirror. For comparison, the grey traces have large values of δT so that contrast is eliminated, and they therefore show the amount of background amplitude noise in P1. Panels from left to right as follows. 2ħk: red trace, δT = 0 μs; grey trace, δT = 2 ms. 30ħk: red trace, δT = −15 μs; grey trace, δT = 100 μs. 60ħk: red trace, δT = 0 μs; grey trace, δT = 100 μs. 90ħk: red trace, δT = 1 μs; grey trace, δT = −50 μs.

  8. Bounds on macroscopic extensions of quantum mechanics.
    Extended Data Fig. 3: Bounds on macroscopic extensions of quantum mechanics.

    Exclusion curves for the minimal modification to quantum mechanics proposed in ref. 4. Points in this parameter space below a given curve in the plot have been ruled out by the corresponding experiment. The green curves show the bounds placed by the 2ħk and 90ħk atom interferometry results presented in this work. The grey, shaded area illustrates the region of parameter space excluded by these results. For sub-micrometre critical lengths, affected atoms would receive sufficiently large spontaneous momentum kicks to move out of the interferometer output ports. This results in atom loss and in a reduced sensitivity of the interference contrast to the decoherence rate. Therefore, we cut off the curves arising from our interferometry data at 1 μm. We also show exclusion curves from a sodium interferometer from 199240 (solid black), a caesium interferometer from 200137 (solid red), a neutron interferometer from 200241(dashed red), a C70 molecular interferometer from 200242 (dashed black), a caesium interferometer from 200938 (solid blue), a caesium interferometer from 201239 (dashed blue), a C284H190F320N4S12 molecular interferometer from 201343 (solid orange), and a rubidium interferometer from 201325 (solid cyan). For all of the exclusion curves, the change in slope occurs at a critical length scale value equal to the wave packet separation.

Tables

  1. Comparison with other matter-wave interference experiments
    Extended Data Table 1: Comparison with other matter-wave interference experiments

References

  1. Arndt, M. & Hornberger, K. Testing the limits of quantum mechanical superpositions. Nature Phys. 10, 271277 (2014)
  2. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807812 (1935)
  3. Cronin, A. D., Schmiedmayer, J. & Pritchard, D. E. Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 10511129 (2009)
  4. Nimmrichter, S. & Hornberger, K. Macroscopicity of mechanical quantum superposition states. Phys. Rev. Lett. 110, 160403 (2013)
  5. Bassi, A., Lochan, K., Satin, S., Singh, T. & Ulbricht, H. Models of wave-function collapse, underlying theories, and experimental tests. Rev. Mod. Phys. 85, 471527 (2013)
  6. Bordé, C. J. Atomic interferometry with internal state labelling. Phys. Lett. A 140, 1012 (1989)
  7. Kasevich, M. & Chu, S. Atomic interferometry using stimulated Raman transitions. Phys. Rev. Lett. 67, 181184 (1991)
  8. Bonnin, A., Zahzam, N., Bidel, Y. & Bresson, A. Simultaneous dual-species matter-wave accelerometer. Phys. Rev. A 88, 043615 (2013)
  9. Schlippert, D. et al. Quantum test of the universality of free fall. Phys. Rev. Lett. 112, 203002 (2014)
  10. Kuhn, C. C. N. et al. A Bose-condensed, simultaneous dual-species Mach-Zehnder atom interferometer. New J. Phys. 16, 073035 (2014)
  11. Geiger, R. et al. Detecting inertial effects with airborne matter-wave interferometry. Nature Commun. 2, 474 (2011)
  12. Dimopoulos, S., Graham, P., Hogan, J. & Kasevich, M. General relativistic effects in atom interferometry. Phys. Rev. D 78, 042003 (2008)
  13. Hohensee, M. A., Estey, B., Hamilton, P., Zeilinger, A. & Müller, H. Force-free gravitational redshift: proposed gravitational Aharonov-Bohm experiment. Phys. Rev. Lett. 108, 230404 (2012)
  14. Dimopoulos, S., Graham, P., Hogan, J., Kasevich, M. & Rajendran, S. Atomic gravitational wave interferometric sensor. Phys. Rev. D 78, 122002 (2008)
  15. Julsgaard, B., Kozhekin, A. & Polzik, E. S. Experimental long-lived entanglement of two macroscopic objects. Nature 413, 400403 (2001)
  16. Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 18041807 (1982)
  17. Giustina, M. et al. Bell violation using entangled photons without the fair-sampling assumption. Nature 497, 227230 (2013)
  18. Jacques, V. et al. Experimental realization of Wheeler’s delayed-choice gedanken experiment. Science 315, 966968 (2007)
  19. Manning, A. G., Khakimov, R. I., Dall, R. G. & Truscott, A. G. Wheeler’s delayed-choice gedanken experiment with a single atom. Nature Phys. 11, 539542 (2015)
  20. Bordé, C. J. et al. Observation of optical Ramsey fringes in the 10 μm spectral region using a supersonic beam of SF6. J. Phys. (Paris) 42(C8), 1519 (1981)
  21. Keith, D. W., Ekstrom, C. R., Turchette, Q. A. & Pritchard, D. E. An interferometer for atoms. Phys. Rev. Lett. 66, 26932696 (1991)
  22. Müller, H., Chiow, S.-W., Long, Q., Herrmann, S. & Chu, S. Atom interferometry with up to 24-photon-momentum-transfer beam splitters. Phys. Rev. Lett. 100, 180405 (2008)
  23. Chiow, S.-W., Kovachy, T., Chien, H.-C. & Kasevich, M. A. 102h- k large area atom interferometers. Phys. Rev. Lett. 107, 130403 (2011)
  24. Dickerson, S. M., Hogan, J. M., Sugarbaker, A., Johnson, D. M. S. & Kasevich, M. A. Multiaxis inertial sensing with long-time point source atom interferometry. Phys. Rev. Lett. 111, 083001 (2013)
  25. Müntinga, H. et al. Interferometry with Bose-Einstein condensates in microgravity. Phys. Rev. Lett. 110, 093602 (2013)
  26. Gupta, S., Dieckmann, K., Hadzibabic, Z. & Pritchard, D. E. Contrast interferometry using Bose-Einstein condensates to measure h/m and α. Phys. Rev. Lett. 89, 140401 (2002)
  27. Foster, G. T., Fixler, J. B., McGuirk, J. M. & Kasevich, M. A. Method of phase extraction between coupled atom interferometers using ellipse-specific fitting. Opt. Lett. 27, 951953 (2002)
  28. Parazzoli, L. P., Hankin, A. M. & Biedermann, G. W. Observation of free-space single-atom matter wave interference. Phys. Rev. Lett. 109, 230401 (2012)
  29. Sugarbaker, A., Dickerson, S. M., Hogan, J. M., Johnson, D. M. S. & Kasevich, M. A. Enhanced atom interferometer readout through the application of phase shear. Phys. Rev. Lett. 111, 113002 (2013)
  30. Zych, M., Costa, F., Pikovski, I. & Brukner, C. Quantum interferometric visibility as a witness of general relativistic proper time. Nature Commun. 2, 505 (2011)
  31. Kovachy, T. et al. Matter wave lensing to picokelvin temperatures. Phys. Rev. Lett. 114, 143004 (2015)
  32. McGuirk, J. M., Snadden, M. J. & Kasevich, M. A. Large area light-pulse atom interferometry. Phys. Rev. Lett. 85, 44984501 (2000)
  33. Rosi, G., Sorrentino, F., Cacciapuoti, L., Prevedelli, M. & Tino, G. M. Precision measurement of the Newtonian gravitational constant using cold atoms. Nature 510, 518521 (2014)
  34. Chiow, S.-W., Kovachy, T., Hogan, J. M. & Kasevich, M. A. Generation of 43 W of quasi-continuous 780 nm laser light via high-efficiency, single-pass frequency doubling in periodically poled lithium niobate crystals. Opt. Lett. 37, 38613863 (2012)
  35. Szigeti, S. S., Debs, J. E., Hope, J. J., Robins, N. P. & Close, J. D. Why momentum width matters for atom interferometry with Bragg pulses. New J. Phys. 14, 023009 (2012)
  36. Greene, W. H. Econometric Analysis (Pearson, 2012)
  37. Peters, A., Chung, K. Y. & Chu, S. High-precision gravity measurements using atom interferometry. Metrologia 38, 2561 (2001)
  38. Chung, K.-Y., Chiow, S.-w., Herrmann, S., Chu, S. & Müller, H. Atom interferometry tests of local Lorentz invariance in gravity and electrodynamics. Phys. Rev. D 80, 016002 (2009)
  39. Lan, S.-Y., Kuan, P.-C., Estey, B., Haslinger, P. & Müller, H. Influence of the Coriolis force in atom interferometry. Phys. Rev. Lett. 108, 090402 (2012)
  40. Kasevich, M. & Chu, S. Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer. Appl. Phys. B 54, 321332 (1992)
  41. Zawisky, M., Baron, M., Loidl, R. & Rauch, H. Testing the world’s largest monolithic perfect crystal neutron interferometer. Nucl. Instrum. Meth. A 481, 406413 (2002)
  42. Brezger, B. et al. Matter-wave interferometer for large molecules. Phys. Rev. Lett. 88, 100404 (2002)
  43. Eibenberger, S., Gerlich, S., Arndt, M., Mayor, M. & Tüxen, J. Matter-wave interference of particles selected from a molecular library with masses exceeding 10,000 amu. Phys. Chem. Chem. Phys. 15, 1469614700 (2013)
  44. Ma, X.-S. et al. Quantum teleportation over 143 kilometres using active feed-forward. Nature 489, 269273 (2012)

Download references

Author information

Affiliations

  1. Department of Physics, Stanford University, Stanford, California 94305, USA

    • T. Kovachy,
    • P. Asenbaum,
    • C. Overstreet,
    • C. A. Donnelly,
    • S. M. Dickerson,
    • A. Sugarbaker,
    • J. M. Hogan &
    • M. A. Kasevich

Contributions

T.K., P.A., C.O., C.A.D., J.M.H. and M.A.K. carried out the experiment, analysed the data and prepared the manuscript. S.M.D. and A.S. contributed significantly to the early stages of the experiment.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: Dependence of contrast on absolute light shift compensation. (63 KB)

    For 30ħk, the contrast as a fraction of its maximum value is plotted as a function of the asymmetry between the red and blue sidebands for one of the atom optics laser beams. To change the sideband asymmetry, we adjust the temperature of one of the frequency doubling crystals while keeping the sidebands of the second atom optics laser beam symmetric. Where Pred and Pblue are the respective optical powers in the red and blue sidebands, we define an asymmetry parameter 1 − (Pred/Pblue). Since the blue sideband is used to drive the Bragg transitions, we keep Pblue fixed in order to maintain constant Rabi frequency. This prevents us from reaching large negative values of the asymmetry parameter, because there is only enough total optical power available to increase Pred slightly without suppressing Pblue. In order to achieve a more negative effective value of the asymmetry parameter, we suppress the power in the carrier to half its usual amount for the one negative point in the plot. The carrier is blue detuned, so decreasing its power pulls the absolute light shift in the same direction as decreasing Pblue. To account for this, we plot the fractional contrast versus the effective asymmetry parameter that would yield the same light shift as the one that we implement, but at a fixed carrier power. The observed dependence of contrast on the sideband asymmetry indicates the importance of absolute light shift compensation for LMT interferometry. Error bars, 1σ.

  2. Extended Data Figure 2: Examples of data showing interference contrast. (161 KB)

    Plots of P1 versus experimental trial for 2ħk, 30ħk, 60ħk and 90ħk. The red traces have small values of δT and therefore display interference contrast. As discussed in the main text, we do not observe a stable fringe because of the vibration of the retroreflection mirror. For comparison, the grey traces have large values of δT so that contrast is eliminated, and they therefore show the amount of background amplitude noise in P1. Panels from left to right as follows. 2ħk: red trace, δT = 0 μs; grey trace, δT = 2 ms. 30ħk: red trace, δT = −15 μs; grey trace, δT = 100 μs. 60ħk: red trace, δT = 0 μs; grey trace, δT = 100 μs. 90ħk: red trace, δT = 1 μs; grey trace, δT = −50 μs.

  3. Extended Data Figure 3: Bounds on macroscopic extensions of quantum mechanics. (141 KB)

    Exclusion curves for the minimal modification to quantum mechanics proposed in ref. 4. Points in this parameter space below a given curve in the plot have been ruled out by the corresponding experiment. The green curves show the bounds placed by the 2ħk and 90ħk atom interferometry results presented in this work. The grey, shaded area illustrates the region of parameter space excluded by these results. For sub-micrometre critical lengths, affected atoms would receive sufficiently large spontaneous momentum kicks to move out of the interferometer output ports. This results in atom loss and in a reduced sensitivity of the interference contrast to the decoherence rate. Therefore, we cut off the curves arising from our interferometry data at 1 μm. We also show exclusion curves from a sodium interferometer from 199240 (solid black), a caesium interferometer from 200137 (solid red), a neutron interferometer from 200241(dashed red), a C70 molecular interferometer from 200242 (dashed black), a caesium interferometer from 200938 (solid blue), a caesium interferometer from 201239 (dashed blue), a C284H190F320N4S12 molecular interferometer from 201343 (solid orange), and a rubidium interferometer from 201325 (solid cyan). For all of the exclusion curves, the change in slope occurs at a critical length scale value equal to the wave packet separation.

Extended Data Tables

  1. Extended Data Table 1: Comparison with other matter-wave interference experiments (76 KB)

Additional data