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Time-of-flight quantum tomography of an atom in an optical tweezer

Abstract

A single particle trapped in a harmonic potential can exhibit rich motional quantum states within its high-dimensional state space. Quantum characterization of motion is key, for example, in controlling or harnessing motion in trapped ion and atom systems or observing the quantum nature of the vibrational excitations of solid-state objects. Here we show that the direct measurement of position and momentum can be used for quantum tomography of motional states of a single trapped particle. We obtain the momentum of an atom in an optical tweezer via time-of-flight measurements, which, combined with trap harmonic evolution, grants us access to all quadrature distributions. Starting with non-classical motional states of a trapped neutral atom, we demonstrate the Wigner function negativity and coherence of non-stationary states. Our work will enable the characterization of the complex neutral atom motion that is of interest for quantum information and metrology, and for investigations of the quantum behaviour of massive levitated particles.

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Fig. 1: Tomography sequence and notation.
Fig. 2: Single-atom Fock-state preparation and imaging.
Fig. 3: Motional quantum state tomography via time-of-flight imaging and maximum likelihood estimation.

Data availability

The data that support plots and other findings in this paper are available from the authors on reasonable request.

References

  1. Vogel, K. & Risken, H. Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. Phys. Rev. A 40, 2847–2849 (1989).

    Article  ADS  Google Scholar 

  2. Smithey, D. T., Beck, M., Raymer, M. G. & Faridani, A. Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: application to squeezed states and the vacuum. Phys. Rev. Lett. 70, 1244–1247 (1993).

    Article  ADS  Google Scholar 

  3. Lvovsky, A. I. et al. Quantum state reconstruction of the single-photon Fock state. Phys. Rev. Lett. 87, 050402 (2001).

    Article  ADS  Google Scholar 

  4. Gross, C. et al. Atomic homodyne detection of continuous-variable entangled twin-atom states. Nature 480, 219–223 (2011).

    Article  ADS  Google Scholar 

  5. Deleglise, S. et al. Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature 455, 510–514 (2008).

    Article  ADS  Google Scholar 

  6. Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009).

    Article  ADS  Google Scholar 

  7. Leibfried, D. et al. Experimental determination of the motional quantum state of a trapped atom. Phys. Rev. Lett. 77, 4281–4285 (1996).

    Article  ADS  Google Scholar 

  8. Flühmann, C. et al. Encoding a qubit in a trapped-ion mechanical oscillator. Nature 566, 513–517 (2019).

    Article  ADS  Google Scholar 

  9. Dunn, T., Walmsley, I. & Mukamel, S. Experimental determination of the quantum-mechanical state of a molecular vibrational mode using fluorescence tomography. Phys. Rev. Lett. 74, 884–887 (1995).

    Article  ADS  Google Scholar 

  10. O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010).

    Article  ADS  Google Scholar 

  11. Chu, Y. et al. Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator. Nature 563, 666–670 (2018).

    Article  ADS  Google Scholar 

  12. Chang, D. E. et al. Cavity opto-mechanics using an optically levitated nanosphere. Proc. Natl Acad. Sci. USA 107, 1005–1010 (2010).

    Article  ADS  Google Scholar 

  13. Romero-Isart, O., Juan, M. L., Quidant, R. & Cirac, J. I. Toward quantum superposition of living organisms. N. J. Phys. 12, 033015 (2010).

    Article  Google Scholar 

  14. Moore, D. C. & Geraci, A. A. Searching for new physics using optically levitated sensors. Quantum Sci. Technol. 6, 014008 (2021).

    Article  Google Scholar 

  15. Gonzalez-Ballestero, C., Aspelmeyer, M., Novotny, L., Quidant, R. & Romero-Isart, O. Levitodynamics: levitation and control of microscopic objects in vacuum. Science 374, eabg3027 (2021).

    Article  Google Scholar 

  16. Delić, U. et al. Cooling of a levitated nanoparticle to the motional quantum ground state. Science 367, 892–895 (2020).

    Article  ADS  Google Scholar 

  17. Tebbenjohanns, F., Mattana, M. L., Rossi, M., Frimmer, M. & Novotny, L. Quantum control of a nanoparticle optically levitated in cryogenic free space. Nature 595, 378–382 (2021).

    Article  ADS  Google Scholar 

  18. Magrini, L. et al. Real-time optimal quantum control of mechanical motion at room temperature. Nature 595, 373–377 (2021).

    Article  ADS  Google Scholar 

  19. Romero-Isart, O. et al. Optically levitating dielectrics in the quantum regime: theory and protocols. Phys. Rev. A 83, 013803 (2011).

    Article  ADS  Google Scholar 

  20. Weiss, T. & Romero-Isart, O. Quantum motional state tomography with nonquadratic potentials and neural networks. Phys. Rev. Res. 1, 033157 (2019).

    Article  Google Scholar 

  21. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).

    Article  ADS  Google Scholar 

  22. Schellekens, M. et al. Hanbury Brown Twiss effect for ultracold quantum gases. Science 310, 648–651 (2005).

    Article  ADS  Google Scholar 

  23. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

    Article  ADS  Google Scholar 

  24. Bücker, R. et al. Twin-atom beams. Nat. Phys. 7, 608–611 (2011).

    Article  Google Scholar 

  25. Morinaga, M., Bouchoule, I., Karam, J.-C. & Salomon, C. Manipulation of motional quantum states of neutral atoms. Phys. Rev. Lett. 83, 4037–4040 (1999).

    Article  ADS  Google Scholar 

  26. Kurtsiefer, C., Pfau, T. & Mlynek, J. Measurement of the Wigner function of an ensemble of helium atoms. Nature 386, 150–153 (1997).

    Article  ADS  Google Scholar 

  27. Bücker, R. et al. Vibrational state inversion of a Bose-Einstein condensate: optimal control and state tomography. J. Phys. B At. Mol. Opt. Phys. 46, 104012 (2013).

    Article  ADS  Google Scholar 

  28. Fuhrmanek, A. et al. Imaging a single atom in a time-of-flight experiment. N. J. Phys. 12, 053028 (2010).

    Article  Google Scholar 

  29. Bergschneider, A. et al. Experimental characterization of two-particle entanglement through position and momentum correlations. Nat. Phys. 15, 640–644 (2019).

    Article  Google Scholar 

  30. Kaufman, A. M., Lester, B. J. & Regal, C. A. Cooling a single atom in an optical tweezer to its quantum ground state. Phys. Rev. X 2, 041014 (2012).

    Google Scholar 

  31. Kaufman, A. M. et al. Entangling two transportable neutral atoms via local spin exchange. Nature 527, 208–211 (2015).

    Article  ADS  Google Scholar 

  32. Kienzler, D. et al. Quantum harmonic oscillator state synthesis by reservoir engineering. Science 347, 53–56 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Ciampini, M. A. et al. Experimental nonequilibrium memory erasure beyond Landauer’s bound. Preprint at https://arxiv.org/abs/2107.04429 (2021).

  34. Leonhardt, U. Measuring the Quantum State of Light 1st edn (Cambridge Univ. Press, 1997).

  35. Banaszek, K., D’Ariano, G. M., Paris, M. G. A. & Sacchi, M. F. Maximum-likelihood estimation of the density matrix. Phys. Rev. A 61, 010304 (1999).

    Article  ADS  Google Scholar 

  36. Lvovsky, A. I. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. J. Opt. B Quantum Semiclassical Opt. 6, S556 (2004).

    Article  ADS  Google Scholar 

  37. Vanner, M., Hofer, J., Cole, G. & Aspelmeyer, M. Cooling-by-measurement and mechanical state tomography via pulsed optomechanics. Nat. Commun. 4, 2295 (2013).

    Article  ADS  Google Scholar 

  38. McCormick, K. C. et al. Quantum-enhanced sensing of a single-ion mechanical oscillator. Nature 572, 86–90 (2019).

    Article  ADS  Google Scholar 

  39. Parazzoli, L. P., Hankin, A. M. & Biedermann, G. W. Observation of free-space single-atom matter wave interference. Phys. Rev. Lett. 109, 230401 (2012).

    Article  ADS  Google Scholar 

  40. Weiss, D. S. & Saffman, M. Quantum computing with neutral atoms. Phys. Today 70, 44 (2017).

    Article  Google Scholar 

  41. Asteria, L., Zahn, H. P., Kosch, M. N., Sengstock, K. & Weitenberg, C. Quantum gas magnifier for sub-lattice-resolved imaging of 3D quantum systems. Nature 599, 571–575 (2021).

    Article  ADS  Google Scholar 

  42. Holten, M. et al. Observation of Cooper pairs in a mesoscopic two-dimensional Fermi gas. Nature 606, 287–291 (2022).

    Article  ADS  Google Scholar 

  43. Brown, M. O., Thiele, T., Kiehl, C., Hsu, T.-W. & Regal, C. A. Gray-molasses optical-tweezer loading: controlling collisions for scaling atom-array assembly. Phys. Rev. X 9, 011057 (2019).

    Google Scholar 

  44. Hutzler, N. R., Liu, L. R., Yu, Y. & Ni, K.-K. Eliminating light shifts for single atom trapping. N. J. Phys. 19, 023007 (2017).

    Article  Google Scholar 

  45. Lester, B. J. et al. Measurement-based entanglement of noninteracting bosonic atoms. Phys. Rev. Lett. 120, 193602 (2018).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank T. Thiele, S. Pampel and T.-W. Hsu for valuable insights and technical assistance, and K. Lehnert and A. Kaufman for input on the manuscript. We acknowledge funding from NSF grant PHYS 1734006, ONR grants N00014-17-1-2245 and N00014-21-1-2594, NSF QLCI award OMA 2016244, and the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the Baur-SPIE Endowed Professor at JILA. W.J.D. acknowledges support from an NSF Graduate Fellowship.

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M.O.B., A.M.R., O.R.-I. and C.A.R. conceived and designed the experiments. M.O.B. and W.J.D. performed the experiments. M.O.B., S.R.M., W.J.D. and C.A.R. analysed the data. M.O.B., S.R.M., W.J.D., R.J.L.-S., A.M.R., O.R.-I. and C.A.R. contributed materials/analysis tools. M.O.B., S.R.M., W.J.D., R.J.L.-S., A.M.R., O.R.-I. and C.A.R. wrote the paper.

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Correspondence to M. O. Brown or C. A. Regal.

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Brown, M.O., Muleady, S.R., Dworschack, W.J. et al. Time-of-flight quantum tomography of an atom in an optical tweezer. Nat. Phys. (2023). https://doi.org/10.1038/s41567-022-01890-8

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