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Preparation and coherent manipulation of pure quantum states of a single molecular ion

Abstract

Laser cooling and trapping of atoms and atomic ions has led to advances including the observation of exotic phases of matter1,2, the development of precision sensors3 and state-of-the-art atomic clocks4. The same level of control in molecules could also lead to important developments such as controlled chemical reactions and sensitive probes of fundamental theories5, but the vibrational and rotational degrees of freedom in molecules pose a challenge for controlling their quantum mechanical states. Here we use quantum-logic spectroscopy6, which maps quantum information between two ion species, to prepare and non-destructively detect quantum mechanical states in molecular ions7. We develop a general technique for optical pumping and preparation of the molecule into a pure initial state. This enables us to observe high-resolution spectra in a single ion (CaH+) and coherent phenomena such as Rabi flopping and Ramsey fringes. The protocol requires a single, far-off-resonant laser that is not specific to the molecule, so many other molecular ions, including polyatomic species, could be treated using the same methods in the same apparatus by changing the molecular source. Combined with the long interrogation times afforded by ion traps, a broad range of molecular ions could be studied with unprecedented control and precision. Our technique thus represents a critical step towards applications such as precision molecular spectroscopy, stringent tests of fundamental physics, quantum computing and precision control of molecular dynamics8.

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Figure 1: Simplified experimental set-up.
Figure 2: Level diagrams for the rotational levels of 40CaH+ for J {1, 2}.
Figure 3: Raman spectra for Δm = −1 blue-sideband transitions probed with 1-ms pulses.
Figure 4: Coherent spectroscopy and manipulation of pure molecular states.

References

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

    Article  ADS  CAS  Google Scholar 

  2. Mitchell, T. B. et al. Direct observations of structural phase transitions in planar crystallized ion plasmas. Science 282, 1290–1293 (1998)

    Article  ADS  CAS  Google Scholar 

  3. Kitching, J., Knappe, S. & Donley, E. A. Atomic sensors—a review. IEEE Sens. J. 11, 1749–1758 (2011)

    Article  ADS  CAS  Google Scholar 

  4. Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637–701 (2015)

    Article  ADS  CAS  Google Scholar 

  5. Schiller, S. & Korobov, V. Tests of time independence of the electron and nuclear masses with ultracold molecules. Phys. Rev. A 71, 032505 (2005)

    Article  ADS  Google Scholar 

  6. Schmidt, P. O. et al. Spectroscopy using quantum logic. Science 309, 749–752 (2005)

    Article  ADS  CAS  Google Scholar 

  7. Wolf, F. et al. Non-destructive state detection for quantum logic spectroscopy of molecular ions. Nature 530, 457–460 (2016)

    Article  ADS  CAS  Google Scholar 

  8. Carr, L. D., DeMille, D., Krems, R. V. & Ye, J. Cold and ultracold molecules: science, technology and applications. New J. Phys. 11, 055049 (2009)

    Article  ADS  Google Scholar 

  9. Shuman, E. S., Barry, J. F. & Demille, D. Laser cooling of a diatomic molecule. Nature 467, 820–823 (2010)

    Article  ADS  CAS  Google Scholar 

  10. Ospelkaus, S. et al. Controlling the hyperfine state of rovibronic ground-state polar molecules. Phys. Rev. Lett. 104, 030402 (2010)

    Article  ADS  CAS  Google Scholar 

  11. Barrett, M. D. et al. Sympathetic cooling of 9Be+ and 24Mg+ for quantum logic. Phys. Rev. A 68, 042302 (2003)

    Article  ADS  Google Scholar 

  12. Rellergert, W. G. et al. Evidence for sympathetic vibrational cooling of translationally cold molecules. Nature 495, 490–494 (2013)

    Article  ADS  CAS  Google Scholar 

  13. Lien, C.-Y. et al. Broadband optical cooling of molecular rotors from room temperature to the ground state. Nat. Commun. 5, 4783 (2014)

    Article  ADS  CAS  Google Scholar 

  14. Staanum, P. F., Højbjerre, K., Skyt, P. S., Hansen, A. K. & Drewsen, M. Rotational laser cooling of vibrationally and translationally cold molecular ions. Nat. Phys. 6, 271–274 (2010)

    Article  CAS  Google Scholar 

  15. Schneider, T., Roth, B., Duncker, H., Ernsting, I. & Schiller, S. All-optical preparation of molecular ions in the rovibrational ground state. Nat. Phys. 6, 275–278 (2010)

    Article  CAS  Google Scholar 

  16. Hansen, A. K. et al. Efficient rotational cooling of Coulomb-crystallized molecular ions by a helium buffer gas. Nature 508, 76–79 (2014)

    Article  ADS  CAS  Google Scholar 

  17. Tong, X., Winney, A. H. & Willitsch, S. Sympathetic cooling of molecular ions in selected rotational and vibrational states produced by threshold photoionization. Phys. Rev. Lett. 105, 143001 (2010)

    Article  ADS  Google Scholar 

  18. Bressel, U. et al. Manipulation of individual hyperfine states in cold trapped molecular ions and application to HD+ frequency metrology. Phys. Rev. Lett. 108, 183003 (2012)

    Article  ADS  CAS  Google Scholar 

  19. Schmidt, P. O . et al. Spectroscopy of atomic and molecular ions using quantum logic. AIP Conf. Proc. 862, 305–312 (2006)

    Article  ADS  CAS  Google Scholar 

  20. Leibfried, D. Quantum state preparation and control of single molecular ions. New J. Phys. 14, 023029 (2012)

    Article  ADS  Google Scholar 

  21. Ding, S. & Matsukevich, D. N. Quantum logic for the control and manipulation of molecular ions using a frequency comb. New J. Phys. 14, 023028 (2012)

    Article  ADS  Google Scholar 

  22. Vogelius, I. S., Madsen, L. B. & Drewsen, M. Probabilistic state preparation of a single molecular ion by projection measurement. J. Phys. B 39, S1259–S1265 (2006)

    Article  ADS  CAS  Google Scholar 

  23. Kimura, N. et al. Sympathetic crystallization of CaH+ produced by a laser-induced reaction. Phys. Rev. A 83, 033422 (2011)

    Article  ADS  Google Scholar 

  24. Roos, Ch . et al. Quantum state engineering on an optical transition and decoherence in a Paul trap. Phys. Rev. Lett. 83, 4713–4716 (1999)

    Article  ADS  CAS  Google Scholar 

  25. Abe, M., Moriwaki, Y., Hada, M. & Kajita, M. Ab initio study on potential energy curves of electronic ground and excited states of 40CaH+ molecule. Chem. Phys. Lett. 521, 31–35 (2012)

    Article  ADS  CAS  Google Scholar 

  26. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281–324 (2003)

    Article  ADS  CAS  Google Scholar 

  27. Myerson, A. H. et al. High-fidelity readout of trapped-ion qubits. Phys. Rev. Lett. 100, 200502 (2008)

    Article  ADS  CAS  Google Scholar 

  28. Meyer, E. R., Bohn, J. L. & Deskevich, M. P. Candidate molecular ions for an electron electric dipole moment experiment. Phys. Rev. A 73, 062108 (2006)

    Article  ADS  Google Scholar 

  29. Loh, H. et al. Precision spectroscopy of polarized molecules in an ion trap. Science 342, 1220–1222 (2013)

    Article  ADS  CAS  Google Scholar 

  30. Cornell, E. A. & Wieman, C. E. Nobel Lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments. Rev. Mod. Phys. 74, 875–893 (2002)

    Article  ADS  CAS  Google Scholar 

  31. Ketterle, W. Nobel Lecture: When atoms behave as waves: Bose-Einstein condensation and the atom laser. Rev. Mod. Phys. 74, 1131–1151 (2002)

    Article  ADS  CAS  Google Scholar 

  32. DeMarco, B. & Jin, D. S. Onset of Fermi degeneracy in a trapped atomic gas. Science 285, 1703–1706 (1999)

    Article  CAS  Google Scholar 

  33. O’Hara, K. M. et al. Ultrastable CO2 laser trapping of lithium fermions. Phys. Rev. Lett. 82, 4204–4207 (1999)

    Article  ADS  Google Scholar 

  34. DeMille, D. Diatomic molecules, a window onto fundamental physics. Phys. Today 68, 34–40 (2015)

    Article  ADS  Google Scholar 

  35. Koelemeij, J. C. J., Roth, B., Wicht, A., Ernsting, I. & Schiller, S. Vibrational spectroscopy of HD+ with 2-ppb accuracy. Phys. Rev. Lett. 98, 173002 (2007)

    Article  ADS  Google Scholar 

  36. Flambaum, V. & Kozlov, M. Enhanced sensitivity to the time variation of the fine-structure constant and m p/m e in diatomic molecules. Phys. Rev. Lett. 99, 150801 (2007)

    Article  ADS  CAS  Google Scholar 

  37. Pupillo, G., Micheli, A., Büchler, H.-P. & Zoller, P. in Cold Molecules: Theory, Experiment, Applications (eds Krems, R. et al..) Ch. 12 (CRC Press, 2009)

  38. DeMille, D. Quantum computation with trapped polar molecules. Phys. Rev. Lett. 88, 067901 (2002)

    Article  ADS  CAS  Google Scholar 

  39. Will, S. A., Park, J. W., Yan, Z. Z., Loh, H. & Zwierlein, M. Coherent microwave control of ultracold Na23K40 molecules. Phys. Rev. Lett. 116, 225306 (2016)

    Article  ADS  Google Scholar 

  40. Hudson, E. R. Method for producing ultracold molecular ions. Phys. Rev. A 79, 032716 (2009)

    Article  ADS  Google Scholar 

  41. Lazarou, C., Keller, M. & Garraway, B. M. Molecular heat pump for rotational states. Phys. Rev. A 81, 013418 (2010)

    Article  ADS  Google Scholar 

  42. Mur-Petit, J. et al. Temperature-independent quantum logic for molecular spectroscopy. Phys. Rev. A 85, 022308 (2012)

    Article  ADS  Google Scholar 

  43. Shi, M., Herskind, P. F., Drewsen, M. & Chuang, I. L. Microwave quantum logic spectroscopy and control of molecular ions. New J. Phys. 15, 113019 (2013)

    Article  ADS  Google Scholar 

  44. Rugango, R. et al. Sympathetic cooling of molecular ion motion to the ground state. New J. Phys. 17, 035009 (2015)

    Article  ADS  Google Scholar 

  45. Ubachs, W., Koelemeij, J. C. J., Eikema, K. S. E. & Salumbides, E. J. Physics beyond the standard model from hydrogen spectroscopy. J. Mol. Spectrosc. 320, 1–12 (2016)

    Article  ADS  CAS  Google Scholar 

  46. Schiller, S., Bakalov, D. & Korobov, V. I. Simplest molecules as candidates for precise optical clocks. Phys. Rev. Lett. 113, 023004 (2014)

    Article  ADS  CAS  Google Scholar 

  47. Karr, J.-Ph. H+2 and HD+: candidates for a molecular clock. J. Mol. Spectrosc. 300, 37–43 (2014)

    Article  ADS  CAS  Google Scholar 

  48. Blythe, P., Roth, B., Fröhlich, U., Wenz, H. & Schiller, S. Production of ultracold trapped molecular hydrogen ions. Phys. Rev. Lett. 95, 183002 (2005)

    Article  ADS  CAS  Google Scholar 

  49. Kajita, M., Gopakumar, G., Abe, M. & Hada, M. Characterizing of variation in the proton-to-electron mass ratio via precise measurements of molecular vibrational transition frequencies. J. Mol. Spectrosc. 300, 99–107 (2014)

    Article  ADS  CAS  Google Scholar 

  50. Beloy, K. et al. Rotational spectrum of the molecular ion NH+ as a probe for α and m e/m p variation. Phys. Rev. A 83, 062514 (2011)

    Article  ADS  Google Scholar 

  51. Kajita, M., Gopakumar, G., Abe, M., Hada, M. & Keller, M. Test of m e/m p changes using vibrational transitions in N+2 . Phys. Rev. A 89, 032509 (2014)

    Article  ADS  Google Scholar 

  52. Hanneke, D., Carollo, R. A. & Lane, D. A. High sensitivity to variation in the proton-toelectron mass ratio in O+2 . Phys. Rev. A 94, 050101 (2016)

    Article  ADS  Google Scholar 

  53. Pašteka, L. F., Borschevsky, A., Flambaum, V. V. & Schwerdtfeger, P. Search for the variation of fundamental constants: strong enhancements in X2Π cations of dihalogens and hydrogen halides. Phys. Rev. A 92, 012103 (2015)

    Article  ADS  Google Scholar 

  54. Stanton, J. F . et al. CFOUR, coupled-cluster techniques for computational chemistry http://www.cfour.de (2017)

  55. Kállay, M. et al. MRCC http://www.mrcc.hu (2017)

  56. Rolik, Z., Szegedy, L., Ladjánszki, I., Ladóczki, B. & Kállay, M. An efficient linear-scaling CCSD(T) method based on local natural orbitals. J. Chem. Phys. 139, 094105 (2013)

    Article  ADS  Google Scholar 

  57. Pople, J. A., Head-Gordon, M. & Raghavachari, K. Quadratic configuration interaction: a general technique for determining electron correlation energies. J. Chem. Phys. 87, 5968–5975 (1987)

    Article  ADS  CAS  Google Scholar 

  58. Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007–1023 (1989)

    Article  ADS  CAS  Google Scholar 

  59. Koput, J. & Peterson, A. A. Ab initio potential energy surface and vibrational-rotational energy levels of X2Σ+ CaOH. J. Phys. Chem. A 106, 9595–9599 (2002)

    Article  CAS  Google Scholar 

  60. Gauss, J., Ruud, K. & Kallay, M. Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level. J. Chem. Phys. 127, 074101 (2007)

    Article  ADS  Google Scholar 

  61. Gauss, J., Ruud, K. & Helgaker, T. Perturbation-dependent atomic orbitals for the calculation of spin-rotation constants and rotational g tensors. J. Chem. Phys. 105, 2804–2812 (1996)

    Article  ADS  CAS  Google Scholar 

  62. Puzzarini, C., Stanton, J. F. & Gauss, J. Quantum-chemical calculation of spectroscopic parameters for rotational spectroscopy. Int. Rev. Phys. Chem. 29, 273–367 (2010)

    Article  CAS  Google Scholar 

  63. Helgaker, T. et al. Recent advances in wave function-based methods of molecular-property calculations. Chem. Rev. 112, 543–631 (2012)

    Article  CAS  Google Scholar 

  64. Gauss, J. & Sundholm, D. Coupled-cluster calculations of spin-rotation constants. Mol. Phys. 91, 449–458 (1997)

    Article  ADS  CAS  Google Scholar 

  65. Jaszun´ski, M. et al. Spin-rotation and NMR shielding constants in HCl. J. Chem. Phys. 139, 234302 (2013)

    Article  ADS  Google Scholar 

  66. Amano, T. The Zeeman effect and hyperfine interactions in J = 1–0 transitions of CH+ and its isotopologues. J. Chem. Phys. 133, 244305 (2010)

    Article  ADS  CAS  Google Scholar 

  67. Sundholm, D., Gauss, J. & Schäfer, A. Rovibrationally averaged nuclear magnetic shielding tensors calculated at the coupled-cluster level. J. Chem. Phys. 105, 11051–11059 (1996)

    Article  ADS  CAS  Google Scholar 

  68. Leibfried, D. et al. Creation of a six-atom Schrödinger cat state. Nature 438, 639–642 (2005)

    Article  ADS  CAS  Google Scholar 

  69. Morigi, G., Eschner, J. & Keitel, C. H. Ground state laser cooling using electromagnetically induced transparency. Phys. Rev. Lett. 85, 4458–4461 (2000)

    Article  ADS  CAS  Google Scholar 

  70. Roos, C. F. et al. Nonlinear coupling of continuous variables at the single quantum level. Phys. Rev. A 77, 040302(R) (2008)

    Article  ADS  Google Scholar 

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Acknowledgements

We thank K. C. Cossel, Y. Wan and D. J. Wineland for comments on the manuscript. This work was supported by the US Army Research Office and the NIST quantum information programme. C.K. acknowledges support from the Alexander von Humboldt foundation. P.N.P. acknowledges support by the state of Baden-Württemberg through bwHPC. This is a contribution of the National Institute of Standards and Technology, not subject to US copyright.

Author information

Authors and Affiliations

Authors

Contributions

C.-w.C. and D.L. conceived and designed the experiments. C.-w.C. and C.K. developed components of the experimental apparatus, and collected and analysed data. C.-w.C. and D.L. wrote the manuscript. D.B.H. and D.R.L. contributed to the development of experimental methods and pulse sequences. P.N.P. computed the molecular constants and level structure. All authors provided suggestions for the experiments, discussed the results and contributed to editing the manuscript.

Corresponding author

Correspondence to Chin-wen Chou.

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Extended data figures and tables

Extended Data Figure 1 Difference in energies ΔE obtained with different methods.

All curves have been shifted to be zero at r = 1.896 Å. The grey dashed line is drawn at 1.25 Å—the lower limit of a substantial probability density at a high vibrational quantum number (v = 10). Basis sets are correlation-consistent basis sets (the ‘cc’ has been omitted for clarity). For r > 3.0 Å, which is outside of the range that is relevant for the electronic and vibrational ground state, CCSD(T) starts to deviate substantially from CCSDT, and deviations lie outside of the energy scale. MVD1, mass–velocity and one-electron Darwin correction; DBOC, diagonal Born–Oppenheimer correction.

Extended Data Figure 2 Spin-rotation factor cIJ, fitted with an eighth-order polynomial.

The squared vibrational wavefunction |Ψvib,0|2 is shown in grey for J = 0.

Extended Data Figure 3 g-factor g fitted with an eighth-order polynomial.

The squared vibrational wavefunction |Ψvib,0|2 is shown in grey for J = 0.

Extended Data Figure 4 Raman transitions.

a, Single-field Raman transition; a photon at frequentcy ω2 is spontaneously emitted. b, Stimulated Raman transition, driven by two fields; a photon at ω2 is stimulated by the second driving field. c, Order of absorption and emission, and detuning of the coherence in the counter-rotating (red) and co-rotating (blue) cases.

Extended Data Figure 5 Flow chart of the purification stages.

Extended Data Table 1 Numerical values of the spin-rotation constant cIJ and g-factor g at r0 = 1.896 Å
Extended Data Table 2 Numerical values of the spin-rotation constant cIJ and g-factor g in the vibrational ground state v = 0 and in the 15 lowest rotational states J
Extended Data Table 3 Comparison between experiment and theory for spectroscopy of the carrier transitions

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Chou, Cw., Kurz, C., Hume, D. et al. Preparation and coherent manipulation of pure quantum states of a single molecular ion. Nature 545, 203–207 (2017). https://doi.org/10.1038/nature22338

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