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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.

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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.

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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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